percentage problem solving year 7

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How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

Related Topics

• How to Find Percent of Increase and Decrease
• How to Find Discount, Tax, and Tip
• How to Do Percentage Calculations
• How to Solve Simple Interest Problems

Step by step guide to solve percent problems

• In each percent problem, we are looking for the base, or part or the percent.
• Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

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Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

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Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

• \(51\) is \(340\%\) of what?
• \(93\%\) of what number is \(97\)?
• \(27\%\) of \(142\) is what number?
• What percent of \(125\) is \(29.3\)?
• \(60\) is what percent of \(126\)?
• \(67\) is \(67\%\) of what?

Download Percent Problems Worksheet

• \(\color{blue}{15}\)
• \(\color{blue}{104.3}\)
• \(\color{blue}{38.34}\)
• \(\color{blue}{23.44\%}\)
• \(\color{blue}{47.6\%}\)
• \(\color{blue}{100}\)

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Free Printable Percent Problems Worksheets for 7th Year

Percent Problems: Discover a collection of free printable math worksheets for Year 7 students, focusing on solving percent problems. Enhance learning and master essential skills with these resources.

Explore Percent Problems Worksheets by Grades

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Explore printable Percent Problems worksheets for 7th Year

Percent Problems worksheets for Year 7 are an essential tool for teachers looking to help their students master the concepts of math, percents, ratios, and rates. These worksheets provide a variety of engaging and challenging problems that are designed to improve students' understanding of the relationships between numbers and their applications in real-world situations. By incorporating these worksheets into their lesson plans, teachers can ensure that their students are developing the necessary skills to solve complex percent problems, while also reinforcing their knowledge of ratios and rates. With a wide range of topics covered, these Year 7 Percent Problems worksheets are an invaluable resource for any math educator looking to enhance their students' learning experience.

In addition to Percent Problems worksheets for Year 7, teachers can also utilize Quizizz, an interactive platform that offers a variety of engaging activities and assessments to support student learning. Quizizz allows educators to create customized quizzes, polls, and other interactive content that can be easily integrated into their lesson plans. This platform not only provides a fun and engaging way for students to practice their math skills, but also offers valuable insights into their progress and understanding of percents, ratios, and rates. By incorporating Quizizz into their teaching strategies, educators can ensure that their Year 7 students are receiving a well-rounded and comprehensive learning experience that will prepare them for success in their future mathematical endeavors.

Percent Worksheets Grade 7

Percent worksheets grade 7 are designed to help students learn and practice finding percentages of numbers. Through these worksheets, students practice questions on finding the percent of the shaded region, finding the percent of whole numbers and decimals, comparing quantities, word problems, and so on.

Benefits of 7th Grade Percent Worksheets

The main benefit of percent worksheets grade 7 is that students practice a variety of questions ranging from word problems to determining percent on a number line to writing a percent through decimal. The structure of the worksheets ensures that a student also has fun while solving problems. These 7th grade math worksheets come with a detailed answer key that provides a step-by-step solution for every problem that, in turn, helps students learn clearly and understand the concept better.

Many websites might provide similar worksheets but Cuemath's percent worksheets for grade 7 come with visual simulation for students to see the problems in action for students to understand the process better.

☛ Practice : Grade 7 Interactive Percent Worksheets

Printable PDFs for Grade 7 Percentage Worksheets

Percent worksheets for 7th grade are simple and easy to work with, students can download the PDF format of these worksheets to practice at their own pace.

• Math 7th Grade Percent Worksheet
• Grade 7 Math Percent Worksheet
• 7th Grade Math Percent Worksheet
• Percent Worksheet for 7th Grade

Interactive Percent Worksheets Grade 7

• Grade 7 Introduction to Percentages Worksheet
• Finding the Percentage of a Number Worksheet for 7th Grade
• 7th Grade Finding the Number Whose Percentage is Given Worksheet
• Percentage Change Worksheet for Grade 7
• Conversion of Fractions, Decimals, and Ratios to Percentages Worksheet for Grade 7

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To write a number as a percentage you have to know how many hundredths it contains:

You should remember these often used percentages:

Percentage Calculations

Below are some of the types of problem that use percentages.

Percentage of a quantity:

To find x percent of a quantity. Calculate: x ⁄ 100  × (the quantity)

One quantity as a percentage of another quantity:

To find a out of b as a percentage. Calculate: a ⁄ b  × 100 ⁄ 1

A man has a total weight of 80 kg.

His muscles weigh 32 kg.

What percentage of his weight is muscle?

A sausage weighs 96 grams and 15% of the sausage is fat.

How many grams of fat are there in the sausage?

Weight of fat = 96 × 0.15 =  14.4 grams

Further Work on Percentages

There are several other types of calculations that use percentages and these are covered in other topics:

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Percentages Worksheets

Welcome to the percentages math worksheet page where we are 100% committed to providing excellent math worksheets. This page includes Percentages worksheets including calculating percentages of a number, percentage rates, and original amounts and percentage increase and decrease worksheets.

As you probably know, percentages are a special kind of decimal. Most calculations involving percentages involve using the percentage in its decimal form. This is achieved by dividing the percentage amount by 100. There are many worksheets on percentages below. In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate.

Most Popular Percentages Worksheets this Week

Percentage Calculations

Calculating the percentage value of a number involves a little bit of multiplication. One should be familiar with decimal multiplication and decimal place value before working with percentage values. The percentage value needs to be converted to a decimal by dividing by 100. 18%, for example is 18 ÷ 100 = 0.18. When a question asks for a percentage value of a number, it is asking you to multiply the two numbers together.

Example question: What is 18% of 2800? Answer: Convert 18% to a decimal and multiply by 2800. 2800 × 0.18 = 504. 504 is 18% of 2800.

• Calculating the Percentage Value (Whole Number Results) Calculating the Percentage Value (Whole Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Number Results) (Select percents) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Decimal Number Results) Calculating the Percentage Value (Decimal Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Number Results) (Select percents) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Whole Dollar Results) Calculating the Percentage Value (Whole Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Dollar Results) (Select percents) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 25%)
• Calculating the Percentage Value (Decimal Dollar Results) Calculating the Percentage Value (Decimal Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Dollar Results) (Select percents) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 25%)

Calculating what percentage one number is of another number is the second common type of percentage calculation. In this case, division is required followed by converting the decimal to a percentage. If the first number is 100% of the value, the second number will also be 100% if the two numbers are equal; however, this isn't usually the case. If the second number is less than the first number, the second number is less than 100%. If the second number is greater than the first number, the second number is greater than 100%. A simple example is: What percentage of 10 is 6? Because 6 is less than 10, it must also be less than 100% of 10. To calculate, divide 6 by 10 to get 0.6; then convert 0.6 to a percentage by multiplying by 100. 0.6 × 100 = 60%. Therefore, 6 is 60% of 10.

Example question: What percentage of 3700 is 2479? First, recognize that 2479 is less than 3700, so the percentage value must also be less than 100%. Divide 2479 by 3700 and multiply by 100. 2479 ÷ 3700 × 100 = 67%.

• Calculating the Percentage a Whole Number is of Another Whole Number Calculating the Percentage a Whole Number is of Another Whole Number (Percents from 1% to 99%) Calculating the Percentage a Whole Number is of Another Whole Number (Select percents) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 25%)
• Calculating the Percentage a Decimal Number is of a Whole Number Calculating the Percentage a Decimal Number is of a Whole Number (Percents from 1% to 99%) Calculating the Percentage a Decimal Number is of a Whole Number (Select percents) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 25%)
• Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Select percents) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 25%)
• Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Select percents) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 25%)

The third type of percentage calculation involves calculating the original amount from the percentage value and the percentage. The process involved here is the reverse of calculating the percentage value of a number. To get 10% of 100, for example, multiply 100 × 0.10 = 10. To reverse this process, divide 10 by 0.10 to get 100. 10 ÷ 0.10 = 100.

Example question: 4066 is 95% of what original amount? To calculate 4066 in the first place, a number was multiplied by 0.95 to get 4066. To reverse this process, divide to get the original number. In this case, 4066 ÷ 0.95 = 4280.

• Calculating the Original Amount from a Whole Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Whole Numbers ) Calculating the Original Amount (Select percents) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Whole Numbers )
• Calculating the Original Amount from a Decimal Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Decimals ) Calculating the Original Amount (Select percents) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Decimals )
• Calculating the Original Amount from a Whole Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
• Calculating the Original Amount from a Decimal Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )
• Mixed Percentage Calculations with Whole Number Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Whole Numbers )
• Mixed Percentage Calculations with Decimal Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Decimals ) Mixed Percentage Calculations (Select percents) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Decimals )
• Mixed Percentage Calculations with Whole Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
• Mixed Percentage Calculations with Decimal Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )

Percentage Increase/Decrease Worksheets

The worksheets in this section have students determine by what percentage something increases or decreases. Each question includes an original amount and a new amount. Students determine the change from the original to the new amount using a formula: ((new - original)/original) × 100 or another method. It should be straight-forward to determine if there is an increase or a decrease. In the case of a decrease, the percentage change (using the formula) will be negative.

• Percentage Increase/Decrease With Whole Number Percentage Values Percentage Increase/Decrease Whole Numbers with 1% Intervals Percentage Increase/Decrease Whole Numbers with 5% Intervals Percentage Increase/Decrease Whole Numbers with 25% Intervals
• Percentage Increase/Decrease With Decimal Number Percentage Values Percentage Increase/Decrease Decimals with 1% Intervals Percentage Increase/Decrease Decimals with 5% Intervals Percentage Increase/Decrease Decimals with 25% Intervals
• Percentage Increase/Decrease With Whole Dollar Percentage Values Percentage Increase/Decrease Whole Dollar Amounts with 1% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 5% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 25% Intervals
• Percentage Increase/Decrease With Decimal Dollar Percentage Values Percentage Increase/Decrease Decimal Dollar Amounts with 1% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 5% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 25% Intervals

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7.3: Solving Basic Percent Problems

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There are three basic types of percent problems:

• Find a given percent of a given number. For example, find 25% of 640.
• Find a percent given two numbers. For example, 15 is what percent of 50?
• Find a number that is a given percent of another number. For example, 10% of what number is 12?

Let’s begin with the first of these types.

Find a Given Percent of a Given Number

Let’s begin with our first example.

What number is 25% of 640?

Let x represent the unknown number. Translate the words into an equation.

\[ \begin{array}{c c c c c} \colorbox{cyan}{What number} & \text{ is } & \colorbox{cyan}{25%} & \text{ of } & \colorbox{cyan}{640} \\ x & = & 25 \% & \cdot & 640 \end{array}\nonumber \]

Now, solve the equation for x.

\[ \begin{aligned} x = 25 \% \cdot 640 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = 0.25 \cdot 640 ~ & \textcolor{red}{ \text{ Change 25% to a decimal: 25% = 0.25.}} \\ x = 160 ~ & \textcolor{red}{ \text{ Multiply: 0.25 \cdot 640 = 160.}} \end{aligned}\nonumber \]

Thus, 25% of 640 is 160.

Alternate Solution

We could also change 25% to a fraction.

\[ \begin{aligned} x = 25 \% \cdot 640 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = \frac{1}{4} \cdot 640 ~ & \textcolor{red}{ \text{ Change 25% to a fraction: 25% = 25/100 = 1/4.}} \\ x = \frac{640}{4} ~ & \textcolor{red}{ \text{ Multiply numerators and denominators.}} \\ x = 160 ~ & \textcolor{red}{ \text{ Divide: 640/4 = 160.}} \end{aligned}\nonumber \]

Same answer.

What number is 36% of 120?

What is number \(8 \frac{1}{3} \%\) of 120?

\[ \begin{array}{c c c c c} \colorbox{cyan}{What number} & \text{ is } & \colorbox{cyan}{8 (1/3)%} & \text{ of } & \colorbox{cyan}{120} \\ x & = & 8 \frac{1}{3} \% & \cdot & 120 \end{array}\nonumber \]

Now, solve the equation for x . Because

\[8 \frac{1}{3} \%= 8.3 \% = 0.08 \overline{3},\nonumber \]

working with decimals requires that we work with a repeating decimal. To do so, we would have to truncate the decimal representation of the percent at some place and satisfy ourselves with an approximate answer. Instead, let’s change the percent to a fraction and seek an exact answer.

\[ \begin{aligned} 8 \frac{1}{3} \% = \frac{8 \frac{1}{3}}{100} ~ & \textcolor{red}{ \text{ Percent: Parts per hundred.}} \\ = \frac{ \frac{25}{3}}{100} ~ & \textcolor{red}{ \text{ Mixed to improper fraction.}} \\ = \frac{25}{3} \cdot \frac{1}{100} ~& \textcolor{red}{ \text{ Invert and multiply.}} \\ = \frac{25}{300} ~ & \textcolor{red}{ \text{ Multiply numerators and denominators.}} \\ = \frac{1}{12} ~ & \textcolor{red}{ \text{ Reduce: Divide numerator and denominator by 25.}} \end{aligned}\nonumber \]

Now we can solve our equation for x .

\[ \begin{aligned} = 8 \frac{1}{3} \% \cdot 120 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = \frac{1}{12} \cdot 120 ~ & \textcolor{red}{8 \frac{1}{3} \% = 1/12.} \\ x = \frac{120}{12} ~ & \textcolor{red}{ \text{ Multiply numerators and denominators.}} \\ x = 10 ~ & \textcolor{red}{ \text{ Divide: 120/12 = 10.}} \end{aligned}\nonumber \]

Thus, \(8 \frac{1}{3} \%\) of 120 is 10.

What number is \(4 \frac{1}{6} \%\) of 1,200?

What number is \(105 \frac{1}{4} \%\) of 18.2?

\[ \begin{array}{c c c c c} \colorbox{cyan}{What number} & \text{ is } & \colorbox{cyan}{105 (1/4) %} & \text{ of } & 18.2 \\ x & = & 105 \frac{1}{4} \% & \cdot & 18.2 \end{array}\nonumber \]

In this case, the fraction terminates as 1/4=0.25, so

\[105 \frac{1}{4} \% = 105.25% = 1.0525.\nonumber \]

\[ \begin{aligned} x = 105 \frac{1}{4} \% \cdot 18.2 ~ & \textcolor{red}{ \text{ Original equation.}} \\ x = 1.0525 \cdot 18.2 ~ & \textcolor{red}{5 \frac{1}{4} \% = 1.0525.} \\ x = 19.1555 ~ & \textcolor{red}{ \text{ Multiply.}} \end{aligned}\nonumber \]

Thus, \(105 \frac{1}{4} \%\) of 18.2 is 19.1555.

What number is \(105 \frac{3}{4} \%\) of 222?

Find a Percent Given Two Numbers

Now we’ll address our second item on the list at the beginning of the section.

15 is what percent of 50?

Let x represent the unknown percent. Translate the words into an equation.

\[ \begin{array}{c c c c} \colorbox{cyan}{15} & \text{ is } & \colorbox{cyan}{what percent} & \text{ of } & \colorbox{cyan}{50} \\ 15 & = & x & \cdot & 50 \end{array}\nonumber \]

The commutative property of multiplication allows us to change the order of multiplication on the right-hand side of this equation.

\[15 = 50x.\nonumber \]

\[ \begin{aligned} 15 = 50x ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{15}{50} = \frac{50x}{50} ~ & \textcolor{red}{ \text{ Divide both sides by 50.}} \\ \frac{15}{50} = x ~ & \textcolor{red}{ \text{ Simplify right-hand side.}} \\ x = 0.30 ~ & \textcolor{red}{ \text{ Divide: 15/50 = 0.30.}} \end{aligned}\nonumber \]

But we must express our answer as a percent. To do this, move the decimal two places to the right and append a percent symbol.

Thus, 15 is 30% of 50.

Alternative Conversion

At the third step of the equation solution, we had

\[x = \frac{15}{50}.\nonumber \]

We can convert this to an equivalent fraction with a denominator of 100.

\[x = \frac{15 \cdot 2}{50 \cdot 2} = \frac{30}{100}\nonumber \]

Thus, 15/50 = 30/100 = 30%.

14 is what percent of 25?

10 is what percent of 80?

\[ \begin{array}{c c c c c} \colorbox{cyan}{10} & \text{ is } & \colorbox{cyan}{what percent} & \text{ of } & \colorbox{cyan}{80} \\ 10 & = & x & \cdot & 80 \end{array}\nonumber \]

The commutative property of multiplication allows us to write the right-hand side as

\[10 = 80x.\nonumber \]

\[ \begin{aligned} 10 = 80x ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{10}{80} = \frac{80x}{80} ~ & \textcolor{red}{ \text{ Divide both sides by 80.}} \\ \frac{1}{8} = x ~ & \textcolor{red}{ \text{ Reduce: } 10/80 = 1/8.} \\ 0.125 = x ~ & \textcolor{red}{ \text{ Divide: } 1/8 = 0.125.} \end{aligned}\nonumber \]

Thus, 10 is 12.5% of 80.

\[x = \frac{1}{8} .\nonumber \]

We can convert this to an equivalent fraction with a denominator of 100 by setting up the proportion

\[\frac{1}{8} = \frac{n}{100}\nonumber \]

Cross multiply and solve for n .

\[ \begin{aligned} 8n = 100 ~ & \textcolor{red}{ \text{ Cross multiply.}} \\ \frac{8n}{8} = \frac{100}{8} ~ & \textcolor{red}{ \text{ Divide both sides by 8.}} \\ n = \frac{25}{8} ~ & \textcolor{red}{ \text{ Reduce: Divide numerator and denominator by 4.}} \\ n = 12 \frac{1}{2} ~ & \textcolor{red}{ \text{ Change 25/2 to mixed fraction.}} \end{aligned}\nonumber \]

\[ \frac{1}{8} = \frac{12 \frac{1}{2}}{100} = 12 \frac{1}{2} \%.\nonumber \]

10 is what percent of 200?

Find a Number that is a Given Percent of Another Number

Let’s address the third item on the list at the beginning of the section.

10% of what number is 12?

\[ \begin{array}{c c c c c} \colorbox{cyan}{10%} & \text{ of } & \colorbox{cyan}{what number} & \text{ is } & \colorbox{cyan}{12} \\ 10 \% & \cdot & x & = & 12 \end{array}\nonumber \]

Change 10% to a fraction: 10% = 10/100 = 1/10.

\[ \frac{1}{10} x = 12\nonumber \]

\[ \begin{aligned} 10 \left( \frac{1}{10} x \right) = 10(12) ~ & \textcolor{red}{ \text{ Multiply both sides by 10.}} \\ x = 120 ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]

Thus, 10% of 120 is 12.

Alternative Solution

We can also change 10% to a decimal: 10% = 0.10. Then our equation becomes

\[0.10x = 12\nonumber \]

Now we can divide both sides of the equation by 0.10.

\[ \begin{aligned} \frac{0.10x}{0.10} = \frac{12}{0.10} ~ & \textcolor{red}{ \text{ Divide both sides by 0.10.}} \\ x = 120 ~ & \textcolor{red}{ \text{ Divide: 12/0.10 = 120.}} \end{aligned}\nonumber \]

20% of what number is 45?

\(11 \frac{1}{9} \%\) of what number is 20?

\[ \begin{array}{c c c c c} \colorbox{cyan}{11 (1/9) %} & \text{ of } & \colorbox{cyan}{what number} & \text{ is } \colorbox{cyan}{20} \\ 11 \frac{1}{9} \% & \cdot & x & = & 20 \end{array}\nonumber \]

Change \(11 \frac{1}{9} \%\) to a fraction.

\[ \begin{aligned} 11 \frac{1}{9} \% ~ & \textcolor{red}{ \text{ Percent: Parts per hundred.}} \\ = \frac{ \frac{100}{9}}{100} ~ & \textcolor{red}{ \text{ Mixed to improper: } 11 \frac{1}{9} = 100/9.} \\ = \frac{100}{9} \cdot \frac{1}{100} ~ & \textcolor{red}{ \text{ Invert and multiply.}} \\ = \frac{ \cancel{100}}{9} \cdot \frac{1}{ \cancel{100}} ~ & \textcolor{red}{ \text{ Cancel.}} \\ = \frac{1}{9} ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]

Replace \(11 \frac{1}{9} \%\) with 1/9 in the equation and solve for x .

\[ \begin{aligned} \frac{1}{9} x = 20 ~ & ~ \textcolor{red}{11 \frac{1}{9} \% = 1/9/} \\ 9 \left( \frac{1}{9} x \right) = 9(20) ~ & \textcolor{red}{ \text{ Multiply both sides by 9.}} \\ x = 180 \end{aligned}\nonumber \]

Thus, \(11 \frac{1}{9} \%\) of 180 is 20.

\(12 \frac{2}{3} \%\) of what number is 760?

1. What number is 22.4% of 125?

2. What number is 159.2% of 125?

3. 60% of what number is 90?

4. 25% of what number is 40?

5. 200% of what number is 132?

6. 200% of what number is 208?

7. 162.5% of what number is 195?

8. 187.5% of what number is 90?

9. 126.4% of what number is 158?

10. 132.5% of what number is 159?

11. 27 is what percent of 45?

12. 9 is what percent of 50?

13. 37.5% of what number is 57?

14. 162.5% of what number is 286?

15. What number is 85% of 100?

16. What number is 10% of 70?

17. What number is 200% of 15?

18. What number is 50% of 84?

19. 50% of what number is 58?

20. 132% of what number is 198?

21. 5.6 is what percent of 40?

22. 7.7 is what percent of 35?

23. What number is 18.4% of 125?

24. What number is 11.2% of 125?

25. 30.8 is what percent of 40?

26. 6.3 is what percent of 15?

27. 7.2 is what percent of 16?

28. 55.8 is what percent of 60?

29. What number is 89.6% of 125?

30. What number is 86.4% of 125?

31. 60 is what percent of 80?

32. 16 is what percent of 8?

33. What number is 200% of 11?

34. What number is 150% of 66?

35. 27 is what percent of 18?

36. 9 is what percent of 15?

37. \(133 \frac{1}{3} \%\) of what number is 80?

38. \(121 \frac{2}{3} \%\) of what number is 73?

39. What number is \(54 \frac{1}{3} \%\) of 6?

40. What number is \(82 \frac{2}{5} \%\) of 5?

41. What number is \(62 \frac{1}{2} \%\) of 32?

42. What number is \(118 \frac{3}{4} \%\) of 32?

43. \(77 \frac{1}{7} \%\) of what number is 27?

44. \(82 \frac{2}{3} \%\) of what number is 62?

45. What number is \(142 \frac{6}{7} \%\) of 77?

46. What number is \(116 \frac{2}{3} \%\) of 84?

47. \(143 \frac{1}{2} \%\) of what number is 5.74?

48. \(77 \frac{1}{2} \%\) of what number is 6.2?

49. \(141 \frac{2}{3} \%\) of what number is 68?

50. \(108 \frac{1}{3} \%\) of what number is 78?

51. What number is \(66 \frac{2}{3} \%\) of 96?

52. What number is \(79 \frac{1}{6} \%\) of 48?

53. \(59 \frac{1}{2} \%\) of what number is 2.38?

54. \(140 \frac{1}{5} \%\) of what number is 35.05?

55. \(78 \frac{1}{2} \%\) of what number is 7.85?

56. \(73 \frac{1}{2} \%\) of what number is 4.41?

57. What number is \(56 \frac{2}{3} \%\) of 51?

58. What number is \(64 \frac{1}{2} \%\) of 4?

59. What number is \(87 \frac{1}{2} \%\) of 70?

60. What number is \(146 \frac{1}{4} \%\) of 4?

61. It was reported that 80% of the retail price of milk was for packaging and distribution. The remaining 20% was paid to the dairy farmer. If a gallon of milk cost $3.80, how much of the retail price did the farmer receive?

62. At $1.689 per gallon of gas the cost is distributed as follows:

\[ \begin{aligned} \text{Crude oil supplies } & ~ $0.95 \\ \text{Oil Companies } & ~ $0.23 \\ \text{State and City taxes } & ~ $0.23 \\ \text{Federal tax } & ~ $0.19 \\ \text{Service Station } & ~ $0.10 \end{aligned}\nonumber \]

Data is from Money, March 2009 p. 22, based on U. S. averages in December 2008. Answer the following questions rounded to the nearest whole percent.

a) What % of the cost is paid for crude oil supplies?

b) What % of the cost is paid to the service station?

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Percentage Word Problems

Welcome to our Basic Percentage Word Problems. In this area, we have a selection of basic percentage problem worksheets designed for 6th grade students who are just starting to learn about percentages to help them to solve a range of simple percentage problems.

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Percentage Learning

Percentages are another area that children can find quite difficult. There are several key areas within percentages which need to be mastered in order.

Our selection of percentage worksheets will help you to find percentages of numbers and amounts, as well as working out percentage increases and decreases and converting percentages to fractions or decimals.

Key percentage facts:

• 50% = 0.5 = ½
• 25% = 0.25 = ¼
• 75% = 0.75 = ¾
• 10% = 0.1 = 1 ⁄ 10
• 1% = 0.01 = 1 ⁄ 100

How to work out Percentages of a number

This page will help you learn to find the percentage of a given number.

There is also a percentage calculator on the page to support you work through practice questions.

• Percentage Of Calculator

This is the calculator to use if you want to find a percentage of a number.

Simple choose your number and the percentage and the calculator will do the rest.

Basic Percentage Word Problems

Here you will find a selection of worksheets on percentages designed to help your child practise how to apply their knowledge to solve a range of percentage problems..

The sheets are graded so that the easier ones are at the top.

The sheets have been split up into sections as follows:

• spot the percentage problems where the aim is to use the given facts to find the missing percentage;
• solving percentage of number problems, where the aim is to work out the percentage of a number.

Each of the sheets on this page has also been split into 3 different worksheets:

• Sheet A which is set at an easier level;
• Sheet B which is set at a medium level;
• Sheet C which is set at a more advanced level for high attainers.

Spot the Percentages Problems

• Spot the Percentage 1A
• PDF version
• Spot the Percentage 1B
• Spot the Percentage 1C
• Spot the Percentage 2A
• Spot the Percentage 2B
• Spot the Percentage 2C

Percentage of Number Word Problems

• Percentage of Number Problems 1A
• Percentage of Number Problems 1B
• Percentage of Number Problems 1C
• Percentage of Number Problems 2A
• Percentage of Number Problems 2B
• Percentage of Number Problems 2C
• Percentage of Number Problems 3A
• Percentage of Number Problems 3B
• Percentage of Number Problems 3C

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

6th Grade Percentage Word Problems

The sheets in this area are at a harder level than those on this page.

The problems involve finding the percentage of numbers and amounts, as well as finding the amounts when the percentage is given.

• 6th Grade Percent Word Problems
• Percentage Increase and Decrease Worksheets

We have created a range of worksheets based around percentage increases and decreases.

Our worksheets include:

• finding percentage change between two numbers;
• finding a given percentage increase from an amount;
• finding a given percentage decrease from an amount.

Percentage of Money Amounts

Often when we are studying percentages, we look at them in the context of money.

The sheets on this page are all about finding percentages of different amounts of money.

• Money Percentage Worksheets

Percentage of Number Worksheets

If you would like some practice finding the percentage of a range of numbers, then try our Percentage Worksheets page.

You will find a range of worksheets starting with finding simple percentages such as 1%, 10% and 50% to finding much trickier ones.

• Percentage of Numbers Worksheets

Converting Percentages to Fractions

To convert a fraction to a percentage follows on simply from converting a fraction to a decimal.

Simply divide the numerator by the denominator to give you the decimal form. Then multiply the result by 100 to change the decimal into a percentage.

The printable learning fraction page below contains more support, examples and practice converting fractions to decimals.

• Converting Fractions to Percentages

• Convert Percent to Fraction

Online Percentage Practice Zone

Our online percentage practice zone gives you a chance to practice finding percentages of a range of numbers.

You can choose your level of difficulty and test yourself with immediate feedback!

• Online Percentage Practice
• Ratio Part to Part Worksheets

These sheets are a great way to introduce ratio of one object to another using visual aids.

The sheets in this section are at a more basic level than those on this page.

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Year 7 - Percentage

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Contents: Percentage

Percentage - Percentages for class 7

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Year 7 Mastery - F, D and P: Fractions, Decimals and Percentages - 9 Complete Lessons

Subject: Mathematics

Age range: 11-14

Resource type: Unit of work

Last updated

29 October 2019

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Nine complete lessons on converting between fractions, decimals and percentages. Teaching resources and worksheets following the White Rose Scheme of work. Most powerpoints and worksheets are my own creation using the White Rose exemplar questions as ideas as a guide. Also included a few relevant worksheets that I have picked up from others.

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Great resource. Only one issue some of the worksheets won't unzip as the file names are too long and unable to shorten before unzipping.

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Fantastic resources. Thank you!

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Clear and so useful thanks!

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Praxis Core Math

Course: praxis core math   >   unit 1.

• Rational number operations | Lesson
• Rational number operations | Worked example
• Ratios and proportions | Lesson
• Ratios and proportions | Worked example

Percentages | Lesson

• Percentages | Worked example
• Rates | Lesson
• Rates | Worked example
• Naming and ordering numbers | Lesson
• Naming and ordering numbers | Worked example
• Number concepts | Lesson
• Number concepts | Worked example
• Counterexamples | Lesson
• Counterexamples | Worked example
• Pre-algebra word problems | Lesson
• Pre-algebra word problems | Worked example
• Unit reasoning | Lesson
• Unit reasoning | Worked example

What are percentages?

• p : 100 ‍  
• p 100 ‍  
• 50 : 100 ‍   , which is equivalent to 1 : 2 ‍   .
• 50 100 ‍   , which is equivalent to 1 2 ‍   and 0.5 ‍   .
• Remove the % ‍   symbol: 25 ‍  
• Move the decimal point left 2 ‍   places: 25 . → 0 . 25 ‍  
• Move the decimal point right 2 ‍   places: 0 . 25 → 25 . ‍  
• Add the % ‍   symbol: 25 % ‍  

What skills are tested?

• Using percent relationships to calculate percentages and values
• Solving word problems involving percentages
• Solving word problems involving percent increases and decreases

How do we calculate percentages?

How do we calculate percent changes.

• Find the difference between the initial and final values.
• Divide the difference by the initial value.
• Convert the quotient to a percentage.
• Write an equation that relates the initial and final values using a percentage.
• Plug in the known values.
• Solve for the unknown quantity.
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
• (Choice A)   3 ‍   A 3 ‍  
• (Choice B)   5 ‍   B 5 ‍  
• (Choice C)   8 ‍   C 8 ‍  
• (Choice D)   15 ‍   D 15 ‍  
• (Choice E)   65 ‍   E 65 ‍  
• (Choice A)   3 % ‍   A 3 % ‍  
• (Choice B)   17 % ‍   B 17 % ‍  
• (Choice C)   30 % ‍   C 30 % ‍  
• (Choice D)   43 % ‍   D 43 % ‍  
• (Choice E)   70 % ‍   E 70 % ‍  

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Hamas Took Her, and Still Has Her Husband

The story of one family at the center of the war in gaza..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

I can’t remember the word, but do you know the kind of fungi connection between trees in the forest? How do you call it?

Mycelium. We are just — I just somehow feel that we are connected by this kind of infinite web of mycelium. We are so bound together. And I don’t think we really realized that until all this happened.

[MUSIC PLAYING]

It’s quite hard to explain, to me in a sense, because some people would say, oh, I’m so hoping your father will come, and then everything will be OK. And it’s very hard to explain that really this group of people decided to bring us up together, shared all their resources over 75 years, grow into each other, fight endlessly with each other, love and hate each other but somehow stay together. And their children will then meet and marry and make grandchildren.

And there’s so many levels of connection. And I’m sitting here in the room, and I see their faces, some of them. And we are incredibly — it’s hard to explain how much these people are missing from our kind of forest ground. [CHUCKLES SOFTLY]

From “The New York Times,” I’m Sabrina Tavernise, and this is “The Daily.”

It’s been nearly six months since Hamas attacked Israel on October 7 and took more than 200 people into Gaza. One of the hardest hit places was a village called Nir Oz, near the border with Gaza. One quarter of its residents were either killed or taken hostage.

Yocheved Lifshitz was one of those hostages and so was her husband, Oded Lifshitz. Yocheved was eventually released. Oded was not.

Today, the story of one family at the center of the war.

It’s Friday, March 29.

OK, here we go. OK.

Good morning, Yocheved. Good morning, Sharone.

Good morning.

Yocheved, could you identify yourself for me, please? Tell me your name, your age and where you’re from.

[SPEAKING HEBREW]

OK, I’ll translate. My name is Yocheved Lifshitz. I’m 85 years old. I was born in 1938. When I was 18, I arrived at kibbutz Nir Oz. I came alone with a group of people who decided to come and form and build a community on a very sandy territory, which was close to the Gaza Strip.

And my name is Sharone Lifschitz. I am 52 years old. I was raised in kibbutz Nir Oz by my mom and dad. So I lived there until I was 20. And I live for the last 30-something years in London.

And, Sharone, what do you have next to you?

Next to me I have a poster of my dad in both English and Hebrew. And it says, “Oded Lifshitz, 83.” And below that it says, “Bring him home now.” And it’s a photo where I always feel the love because he is looking at me. And there’s a lot of love in it in his eyes.

And why did you want to bring him here today, Sharone?

Because he should be talking himself. He should be here and able to tell his story. And instead, I’m doing it on his behalf. It should have been a story of my mom and dad sitting here and telling their story.

The story of Oded and Yocheved began before they ever met in Poland in the 1930s. Anti-Semitism was surging in Europe, and their families decided to flee to Palestine — Yocheved’s in 1933, the year Hitler came to power, and Oded’s a year later. Yocheved remembers a time near the end of the war, when her father received news from back home in Poland. He was deeply religious, a cantor in a synagogue. And he gathered his family around him to share what he’d learned.

And he said, we don’t have a family anymore. They’ve all been murdered. And he explained to us why there is no God. If there was a God, he would have protected my family. And this means that there is no God.

And suddenly, we stopped going to synagogue. We used to go every Saturday.

So it was a deep crisis for him. The shock and the trauma were very deep.

Abstention.

Abstention. Soviet Union? Yes. Yes. The United Kingdom? Abstained.

Yocheved’s father lived long enough to see a state establish for his children. The UN resolution of 1947 paved the way for a new country for Jews. And the next spring, Israel declared its independence. Yocheved remembers listening to the news on the radio with her parents.

The General Assembly of the United Nations has made its decision on Palestine.

We had a country. So now we’ll have somebody who’s protecting us. It’s a country for the people, to rebuild the people. This was the feeling we had.

In other words, if God could not protect you, this nation maybe could?

Yes. But the next day, it was already sad.

Israel was immediately forced to defend itself when its Arab neighbors attacked. Israel won that war. But its victory came at a great cost to the Palestinian Arabs living there. More than 700,000 either fled or were expelled from their homes. Many became refugees in Gaza in the south.

Suddenly, Yocheved and Oded saw themselves differently from their parents, not as minorities in someone else’s country, but as pioneers in a country of their own, ready to build it and defend it. They moved to the south, near the border line with Gaza. It was there, in a kibbutz, where they met for the first time.

The first time I met him, he was 16, and I was 17. And we didn’t really have this connection happening. But when we arrived at Nir Oz, that’s where some sort of a connection started to happen. And he was younger than I am by a year and a half. So at first I thought, he’s a kid. But for some reason, he insisted. Oded really insisted. And later, turned out he was right.

What was it about him that made you fall in love with him?

He was cute.

He was a cute kid. He was a cute boy.

What’s so funny?

He was a philosopher. He wrote a lot. He worked in agriculture. He was this cute boy. He was only 20, think about it.

And then I married him. And he brought two things with him. He brought a dog and he brought a cactus. And since then we’ve been growing a huge field of cacti for over 64 years.

What did it feel like to be starting a new life together in this new country? What was the feeling of that?

We were euphoric.

And what did you think you were building together?

We thought we were building a kibbutz. We were building a family. We were having babies. That was the vision. And we were thinking that we were building a socialist state, an equal state. And at first, it was a very isolated place. There were only two houses and shacks and a lot of sand. And little by little, we turned that place into a heaven.

Building the new state meant cultivating the land. Oded plowed the fields, planting potatoes and carrots, wheat and cotton. Yocheved was in charge of the turkeys and worked in the kitchen cooking meals for the kibbutz. They believed that the best way to live was communally. So they shared everything — money, food, even child-rearing.

After long days in the fields, Oded would venture outside the kibbutz to the boundary line with Gaza and drink beer with Brazilian peacekeepers from the UN and talk with Palestinians from the villages nearby. They talked about politics and life in Arabic, a language Oded spoke fluently. These were not just idle conversations. Oded knew that for Israel to succeed, it would have to figure out how to live side by side with its Arab neighbors.

He really did not believe in black and white, that somebody is the bad guy and somebody is the good guy, but there is a humanistic values that you can live in.

Sharone, what was your father like?

My father was a tall man and a skinny man. And he was —

he is — first of all, he is — he is a man who had very strong opinion and very well formed opinion. He read extensively. He thought deeply about matters. And he studied the piano. But as he said, was never that great or fast enough for classical. But he always played the piano.

[PIANO MUSIC]

He would play a lot of Israeli songs. He wound play Russian songs. He would play French chansons.

And he had this way of just moving from one song to the next, making it into a kind of pattern. And it was — it’s really the soundtrack of our life, my father playing the piano.

[PLAYING PIANO]:

[CONVERSATION IN HEBREW]:

[PLAYING PIANO]

So one side of him was the piano. Another side was he was a peace activist. He was not somebody who just had ideals about building bridges between nations. He was always on the left side of the political map, and he actioned it.

[NON-ENGLISH CHANTING]:

I remember growing up and going very regularly, almost weekly, to demonstrations. I will go regularly with my father on Saturday night to demonstrations in Tel Aviv. I will sit on his shoulders. He will be talking to all his activist friends. The smoke will rise from the cigarettes, and I will sit up there.

But somehow, we really grew up in that fight for peace.

Yocheved and Oded’s formal fight for peace began after the Arab-Israeli war of 1967. Israel had captured new territory, including the West Bank, the Sinai Peninsula, and the Gaza Strip. That brought more than a million Palestinians under Israeli occupation.

Oded immediately began to speak against it. Israel already had its land inside borders that much of the world had agreed to. In his view, taking more was wrong. It was no longer about Jewish survival. So when Israeli authorities began quietly pushing Bedouin Arabs off their land in the Sinai Peninsula, Oded took up the cause.

He helped file a case in the Israeli courts to try to stop it. And he and Yocheved worked together to draw attention to what was going on. Yocheved was a photographer, so she took pictures showing destroyed buildings and bulldozed land. Oded then put her photographs on cardboard and drove around the country showing them to people everywhere.

They became part of a growing peace movement that was becoming a force helping shape Israeli politics. Israel eventually returned the Sinai Peninsula to Egypt in 1982.

[NON-ENGLISH SPEECH]

Whenever there is a movement towards reconciliation with our neighbors, it’s almost like your ability to live here, your life force, gets stronger. And in a way, you can think of the art of their activism as being a response to that.

And why did he and your mother take up that fight, the cause of the land? Why do you think that was what he fought for?

My father, he had a very developed sense of justice. And he always felt that had we returned those lands at that point, we could have reached long-term agreement at that point. Then we would have been in a very different space now. I know that in 2019, for example, he wrote a column, where he said that when the Palestinians of Gaza have nothing to lose, we lose big time. He believed that the way of living in this part of the world is to share the place, to reach agreement, to work with the other side towards agreements.

He was not somebody who just had ideals about building bridges between nations. Two weeks before he was taken hostage, he still drove Palestinians that are ill to reach hospital in Israel and in East Jerusalem. That was something that meant a lot to him. I think he really believed in shared humanity and in doing what you can.

Do you remember the last conversation you had with your father?

I don’t have a clear memory which one it was. It’s funny. A lot of things I forgot since. A lot of things have gone so blurred.

We actually didn’t have a last conversation. The last thing he said was, Yoche, there is a war. And he was shot in the hand, and he was taken out. And I was taken out. I couldn’t say goodbye to him. And what was done to us was done.

We’ll be right back.

Yocheved, the last thing Oded said was there’s a war. Tell me about what happened that day from the beginning.

That morning, there was very heavy shelling on Nir Oz. We could hear gunfire. And we looked outside, and Oded told me, there are a lot of terrorists outside. We didn’t even have time to get dressed. I was still wearing my nightgown. He was wearing very few clothes. I remember him trying to close the door to the safe room, but it didn’t work. He wasn’t successful in closing it.

And then five terrorists walked in. They shot him through the safe room door. He was bleeding from his arm. He said to me, Yoche, I’m injured. And then he fainted. He was dragged out on the floor. And I didn’t know if he was alive. I thought he was dead. After that, I was taken in my nightgown. I was led outside. I was placed on a small moped, and I was taken to Gaza.

And we were driving over a bumpy terrain that had been plowed. And it didn’t break my ribs, but it was very painful.

And I could see that the gate that surrounds the Gaza Strip was broken, and we were driving right through it.

And as we were heading in, I could see so many people they were yelling, “Yitbach al Yahud,” kill the Jews, slaughter the Jews. And people were hitting me with sticks. And though the drivers on the moped tried to protect me, it didn’t help.

What were you thinking at the time? What was in your mind?

I was thinking, I’m being taken; I’m being kidnapped. I didn’t know where to, but this decision I had in my head was that I’m going to take photographs in my mind and capture everything I’m seeing so that when I — or if and when I am released, I’ll have what to tell.

And when I came to a stop, we were in a village that’s near Nir Oz. It’s called Khirbet Khuza. We came in on the moped, but I was transferred into a private car from there. And I was threatened that my hand would be cut off unless I hand over my watch and my ring. And I didn’t have a choice, so I took my watch off, and I took my ring off, and I handed it to them.

Was it your wedding ring?

Yes, it was my wedding ring.

After that, they led me to a big hangar where the entrance to the tunnel was, and I started walking. And the entrance was at ground level, but as you walk, you’re walking down a slope. And you’re walking and walking about 40 meters deep underground, and the walls are damp, and the soil is damp. And at first, I was alone. I didn’t know that other people had been taken too. But then more hostages came, and we were walking together through the tunnels.

Many of whom were from kibbutz Nir Oz. These were our people. They were abducted but still alive. And we spoke quietly, and we spoke very little. But as we were walking, everybody started telling a story of what had happened to him. And that created a very painful picture.

There were appalling stories about murder. People had left behind a partner.

A friend arrived, who, about an hour or two hours before, had her husband murdered and he died in her hands.

It was a collection of broken up people brought together.

So you were piecing together the story of your community and what had happened from these snapshots of tragedies that you were looking at all around you as you were walking. What’s the photograph you’ll remember most from that day?

It would be a girl, a four-year-old girl. People kept telling her — walk, walk, walk. And we tried to calm her down. And her mom tried to carry her on her arms. It was the most difficult sight to see a child inside those tunnels.

What were you feeling at that moment, Yocheved?

Very difficult.

Where did they lead you — you and your community — from Nir Oz.

They led us to this chamber, a room, that they had prepared in advance. There were mattresses there. And that’s where we were told to sit.

I saw people sitting on the mattresses, bent down, their heads down between their hands. They were broken. But we hardly spoke. Everybody was inside their own world with themselves, closed inside his own personal shock.

Yocheved was without her glasses, her hearing aids, or even her shoes. She said she spent most days lying down on one of the mattresses that had been put out for the hostages. Sometimes her captors would let her and others walk up and down the tunnels to stretch their legs.

She said she was given a cucumber, spreading cheese, and a piece of pita bread every day to eat. They had a little bit of coffee in the morning and water all day long.

One day, a Hamas leader came to the room where she and others were being held. She said she believes it was Yahya Sinwar, the leader of Hamas, who is believed to be the architect of the October 7 attack. Two other hostages who were held with Yocheved also identified the man as Sinwar, and an Israeli military spokesman said he found the accounts reliable.

He came accompanied with a group of other men. He just made rounds between the hostages, I suppose. And he spoke in Hebrew, and he told us not to worry, and soon there’s going to be a deal and we’ll be out. And others told me, don’t speak. And I said, what is there for me to be afraid of? The worst already happened. Worst thing, I’ll be killed.

I want to say something, and I spoke my mind. I told Sinwar, why have you done what you just did to all of the same people who have always helped you? He didn’t answer me. He just turned around and they walked off.

Were you afraid to ask him why Hamas did what it did, to challenge him?

I wasn’t afraid.

I was angry about the whole situation. It was against every thought and thinking we ever had. It was against our desire to reach peace, to be attentive and help our neighbors the way we always wanted to help our neighbors. I was very angry. But he ignored what I said, and he just turned his back and walked away.

In this entire time, you had no answers about Oded?

What was the hardest day for you, the hardest moment in captivity?

It’s when I got sick. I got sick with diarrhea and vomiting for about four days. And I had no idea how this will end. It was a few very rough days. And probably because of that, they decided to free me.

They didn’t tell me they were going to release me. They just told me and another girl, come follow us. They gave us galabiya gowns to wear and scarves to wear over our heads, so maybe they’ll think that we are Arab women. And only as we were walking, and we started going through corridors and ladders and climbing up we were told that we’re going home.

I was very happy to be going out. But my heart ached so hard for those who were staying behind. I was hoping that many others would follow me.

It’s OK. Let’s go. It’s OK. Let’s go.

You go with this one.

Shalom. Shalom.

There was a video that was made of the moment you left your captors. And it seemed to show that you were shaking a hand, saying shalom to them. Do you remember doing that?

I said goodbye to him. It was a friendly man. He was a medic. So when we said goodbye, I shook his hand for peace, shalom, to goodbye.

What did you mean when you said that?

I meant for peace.

Shalom in the sense of peace.

An extraordinary moment as a freed Israeli hostage shakes hands with a Hamas terrorist who held her captive.

I literally saw my mom on CNN on my phone on the way to the airport. And it was the day before I was talking to my aunt, and she said, I just want to go to Gaza and pull them out of the earth. I just want to pull them out of the earth and take them. And it really felt like that, that she came out of the earth. And when she shook the hand of the Hamas person, it just made me smile because it was so her to see the human in that person and to acknowledge him as a human being.

I arrived in the hospital at about 5:30 AM. My mom was asleep in the bed. And she was just — my mom sleeps really peacefully. She has a really quiet way of sleeping. And I just sat there, and it was just like a miracle to have her back with us. It was just incredible because not only was she back, but it was her.

I don’t know how to explain it. But while they were away, we knew so little. We were pretty sure she didn’t survive it. The whole house burned down totally. So other homes we could see if there was blood on the walls or blood on the floor. But in my parents’ home, everything was gone — everything. And we just didn’t know anything. And out of that nothingness, came my mom back.

It was only when she got to the hospital that Yocheved learned the full story of what happened on October 7. Nir Oz had been mostly destroyed. Many of her friends had been murdered. No one knew what had happened to Oded. Yocheved believed he was dead. But there wasn’t time to grieve.

The photograph she had taken in her mind needed to be shared. Yocheved knew who was still alive in the tunnels. So she and her son called as many families as they could — the family of the kibbutz’s history teacher, of one of its nurses, of the person who ran its art gallery — to tell them that they were still alive, captive in Gaza.

And then in November came a hostage release. More than 100 people came out. The family was certain that Oded was gone. But Sharone decided to make some calls anyway. She spoke to one former neighbor then another. And finally, almost by chance, she found someone who’d seen her father. They shared a room together in Gaza before he’d gotten ill and was taken away. Sharone and her brothers went to where Yocheved was staying to tell her the news.

She just couldn’t believe it, actually. It was as if, in this great telenovela of our life, at one season, he was left unconscious on the floor. And the second season open, and he is in a little room in Gaza with another woman that we know. She couldn’t believe it.

She was very, very, very excited, also really worried. My father was a very active and strong man. And if it happened 10 years ago, I would say of course he would survive it. He would talk to them in Arabic. He will manage the situation. He would have agency. But we know he was injured. And it makes us very, very worried about the condition in which he was — he’s surviving there. And I think that the fear of how much suffering the hostages are going through really makes you unable to function at moment.

Yocheved, the government has been doing a military operation since October in Gaza. You have been fighting very hard since October to free the hostages, including Oded. I wonder how you see the government’s military operation. Is it something that harms your cause or potentially helps it?

The only thing that will bring them back are agreements. And what is happening is that there are many soldiers who have been killed, and there is an ongoing war, and the hostages are still in captivity. So it’s only by reaching an agreement that all of the hostages will be released.

Do you believe that Israel is close to reaching an agreement?

I don’t know.

You told us that after the Holocaust, your father gathered your family together to tell you that God did not save you. It was a crisis for him. I’m wondering if this experience, October 7, your captivity, challenged your faith in a similar way.

No, I don’t think it changed me. I’m still the same person with the same beliefs and opinions. But how should I say it? What the Hamas did was to ruin a certain belief in human beings. I didn’t think that one could reach that level that isn’t that much higher than a beast. But my opinion and my view of there still being peace and reaching an arrangement stayed the same.

You still believe in peace?

Why do you believe that?

Because I’m hoping that a new generation of leaders will rise, people who act in transparency, who speak the truth, people who are honest, the way Israel used to be and that we’ll return to be like we once were.

I go to many rallies and demonstrations, and I meet many people in many places. And a large part of those people still believe in reaching an arrangement in peace and for there to be no war. And I still hope that this is what we’re going to be able to have here.

Bring them home now! Bring them home now! Bring them home now! Bring them home now! Bring them home! Now! Bring them home! Now! Bring them home! Now! Bring them home!

Yocheved is now living in a retirement home in the suburbs of Tel Aviv. Five other people around her age from Nir Oz live there too. One is also a released hostage. She hasn’t been able to bring herself to go back to the kibbutz. The life she built there with Oded is gone — her photographs, his records, the piano. And the kibbutz has become something else now, a symbol instead of a home. It is now buzzing with journalists and politicians. For now, Yocheved doesn’t know if she’ll ever go back. And when Sharone asked her, she said, let’s wait for Dad.

So I’m today sitting in this assisted living, surrounded by the same company, just expecting Oded, waiting for Oded to come back. And then each and every one of us will be rebuilding his own life together and renewing it.

What are you doing to make it a home for Oded?

We have a piano. We were given a piano, a very old one with a beautiful sound. And it’s good. Oded is very sensitive to the sound. He has absolute hearing. And I’m just hoping for him to come home and start playing the piano.

Do you believe that Oded will come home?

I’d like to believe. But there’s a difference between believing and wanting. I want to believe that he’ll be back and playing music. I don’t think his opinions are going to change. He’s going to be disappointed by what happened. But I hope he’s going to hold on to the same beliefs. His music is missing from our home.

[SPEAKING HEBEW]:

[SPEAKING HEBREW] [PLAYING PIANO]

I know that my father always felt that we haven’t given peace a chance. That was his opinion. And I think it’s very hard to speak for my father because maybe he has changed. Like my mom said, she said, I hope he hasn’t changed. I haven’t changed. But the truth is we don’t know. And we don’t the story. We don’t know how the story — my father is ending or just beginning.

But I think you have to hold on to humanistic values at this point. You have to know what you don’t want. I don’t want more of this. This is hell. This is hell for everybody. So this is no, you know? And then I believe that peace is also gray, and it’s not glorious, and it’s not simple. It’s kind of a lot of hard work. You have to reconcile and give up a lot. And it’s only worth doing that for peace.

[PIANO PLAYING CONTINUES]

After weeks of negotiations, talks over another hostage release and ceasefire have reached an impasse. The sticking points include the length of the ceasefire and the identity and number of Palestinian prisoners to be exchanged for the hostages.

[BACKGROUND CONVERSATION IN HEBREW]:

Here’s what else you should know today. Sam Bankman-Fried was sentenced to 25 years in prison on Thursday, capping an extraordinary saga that upended the multi-trillion-dollar crypto industry. Bankman-Fried, the founder of the cryptocurrency exchange, FTX, was convicted of wire fraud, conspiracy, and money laundering last November.

Prosecutors accused him of stealing more than $10 billion from customers to finance political contributions, venture capital investments, and other extravagant purchases. At the sentencing, the judge pointed to testimony from Bankman-Fried’s trial, saying that his appetite for extreme risk and failure to take responsibility for his crimes amount to a quote, “risk that this man will be in a position to do something very bad in the future.”

Today’s episode was produced by Lynsea Garrison and Mooj Zaidie with help from Rikki Novetsky and Shannon Lin. It was edited by Michael Benoist, fact checked by Susan Lee, contains original music by Marion Lozano, Dan Powell, Diane Wong, Elisheba Ittoop, and Oded Lifshitz. It was engineered by Alyssa Moxley. The translation was by Gabby Sobelman. Special thanks to Menachem Rosenberg, Gershom Gorenberg, Gabby Sobelman, Yotam Shabtie, and Patrick Kingsley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Sabrina Tavernise. See you on Monday.

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Hosted by Sabrina Tavernise

Produced by Lynsea Garrison and Mooj Zadie

With Rikki Novetsky and Shannon Lin

Edited by Michael Benoist

Original music by Marion Lozano ,  Dan Powell ,  Diane Wong and Elisheba Ittoop

Engineered by Alyssa Moxley

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music

Warning: this episode contains descriptions of violence.

It’s been nearly six months since the Hamas-led attacks on Israel, when militants took more than 200 hostages into Gaza.

In a village called Nir Oz, near the border, one quarter of residents were either killed or taken hostage. Yocheved Lifshitz and her husband, Oded Lifshitz, were among those taken.

Today, Yocheved and her daughter Sharone tell their story.

On today’s episode

Yocheved Lifshitz, a former hostage.

Sharone Lifschitz, daughter of Yocheved and Oded Lifshitz.

Background reading

Yocheved Lifshitz was beaten and held in tunnels built by Hamas for 17 days.

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We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

Fact-checking by Susan Lee .

Additional music by Oded Lifshitz.

Translations by Gabby Sobelman .

Special thanks to Menachem Rosenberg, Gershom Gorenberg , Gabby Sobelman , Yotam Shabtie, and Patrick Kingsley .

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

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