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Rational Numbers Class 8 PPT

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Mathematics Presentation for Class 8

Mathematics, chapter 1: rational numbers, chapter 2: linear equations in one variable, chapter 3: understanding quadrilaterals, chapter 4: practical geometry, chapter 5: data handling, chapter 6: squares and square roots, chapter 7: cubes and cube roots, chapter 8: comparing quantities, chapter 9: algebraic expressions and identities, chapter 10: visualizing solid shapes, chapter 11: mensuration, chapter 12: exponents and powers, chapter 13: direct and inverse proportions, chapter 14: factorisation, chapter 15: introduction to graphs, chapter 16: playing with numbers.

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Unit 4: Rational numbers

Classification of numbers.

• Intro to rational & irrational numbers (Opens a modal)
• Classifying numbers (Opens a modal)
• Classify numbers: rational & irrational Get 5 of 7 questions to level up!
• Classify numbers Get 5 of 7 questions to level up!

Rational numbers on the number line

• Decimals & fractions on the number line (Opens a modal)
• Comparing rational numbers (Opens a modal)
• Negative fractions on the number line Get 3 of 4 questions to level up!
• Rational numbers between two rational numbers Get 3 of 4 questions to level up!

Additive and multiplicative inverse

• Inverse property of addition (Opens a modal)
• Inverse property of multiplication (Opens a modal)
• Additive and multiplicative inverse of a rational number Get 3 of 4 questions to level up!

Rational Numbers

Nov 28, 2014

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Rational Numbers. Rational Numbers. The integers which are in the form of p/q where q is not equal to 0 are known as rational numbers. Examples - 5/8; -3/14; 7/-15; -6/-11 Natural numbers – They are counting numbers.

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Presentation Transcript

Rational Numbers • The integers which are in the form of p/q where q is not equal to 0 are known as rational numbers. Examples - 5/8; -3/14; 7/-15; -6/-11 • Natural numbers – They are counting numbers. • Integers - Natural numbers, their negative and 0 form the system of integers. • Fractional numbers – the positive integer which are in the form of p/q where q is not equal to 0 are known as fractional numbers.

Properties Of Rational Numbers Closure Property Rational numbers are closed under addition. That is, for any two rational numbers a and b, a+b s also a rational number. For Example - 8 + 3 = 11 ( a rational number. ) Rational numbers are closed under subtraction. That is, for any two rational numbers a and b, a – b is also a rational number, For Example - 25 – 11 = 14 ( a rational number. ) Rational numbers are closed under multiplication. That is, for any two rational numbers a and b, a * b is also a rational number. For Example - 4 * 2 = 8 (a rational number. ) Rational numbers are not closed under division. That is, for any rational number a, a/0 is not defined. For Example - 6/0 is not defined.

Commutative Property Rational numbers can be added in any order. Therefore, addition is commutative for rational numbers. For Example – Subtraction is not commutative for rational numbers. For Example - Since, -7 is unequal to 7 Hence, L.H.S. Is unequal to R.H.S. Therefore, it is proved that subtraction is not commutative for rational numbers.

Rational numbers can be multiplied in any order. Therefore, it is said that multiplication is commutative for rational numbers. For Example – Since, L.H.S = R.H.S. Therefore, it is proved that rational numbers can be multiplied in any order. Rational numbers can not be divided in any order.Therefore,division is not commutative for rational numbers. For Example – Since, L.H.S. is not equal to R.H.S. Therefore, it is proved that rational numbers can not be divided in any order.

Associative property Addition is associative for rational numbers. That is for any three rational numbers a, b and c, a + (b + c) = (a + b) + c. For Example Since, -9/10 = -9/10 Hence, L.H.S. = R.H.S. Therefore, the property has been proved. Subtraction is not associative for rational numbers. For Example - Since, 19/30 is not equal to 29/30 Hence, L.H.S. is not equal to R.H.S. Therefore, the property has been proved.

Multiplication is associative for rational numbers. That is for any rational numbers a, b and c a* (b*c) = (a*b) * c For Example – Since, -5/21 = -5/21 Hence, L.H.S. = R.H.S Division is not associative for Rational numbers. For Example – Since, Hence, L.H.S. Is Not equal to R.H.S.

Distributive Law Distributivity of multiplication over addition and subtraction : For all rational numbers a, b and c, a (b+c) = ab + ac a (b-c) = ab – ac For Example – Since, L.H.S. = R.H.S. Hence, distributive law is proved

The Role Of Zero (0) Zero is called the identity for the addition of rational numbers. It is the additive identity for integers and whole numbers as well. Therefore, for any rational number a, a+0 = 0+a = a For Example - 2+0 = 0+2 = 2 -5+0 = 0+(-5) = -5 The role of one (1) 1 is the multiplicative identity for rational numbers. Therefore, a*1 = 1*a = a for any rational number a. For Example - 2*1 = 2 1*-10 = -10

WORK SHEET Q1)Verify that –(-x) is the same as x for x = 5/6 A1) The additive inverse of x = 5/6 = -x = -5/6 Since, 5/6 + (-5/6) = 0 Hence, -(-x) = x. Q2) Find any four rational numbers between -5/6 and 5/8 A2) Convert the given numbers to rational numbers with same denominators : -5*4-6*4 = -20/24 5*3/8*3 = 15/24 Thus, we have -19/24; -18/24; ........13/24; 14/24 Any four rational numbers can be chosen.

Qn.Find ten rational numbers between and . Ans. And can be represented as respectively. Therefore, ten rational numbers between and are Qn.Represent on the number line. Ans. can be represented on the number line as follows.

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Rational Numbers. Rational Numbers. A whole number or the quotient of any whole numbers, excluding zero as a denominator Examples - 5/8; -3/14; 7/-15; -6/-11 Natural numbers – They are counting numbers. Integers - Natural numbers, their negative and 0 form the system of integers.

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Rational Numbers. Any number that can be expressed as a fraction of two integers. Rational. Irrational. Integers. Whole. Counting numbers. Rational. Fractions. Decimal Repeating & terminating. Irrational. Integers. -1,-2,-3,-4 …. π. 0. Whole. 0. Percents. 1,2,3,4 ….

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Rational Numbers. Some Definitions. Rational Number: Any number that can be converted into a fraction ( Examples: ¼, 3, 4.25, 0). Fraction: A part of a whole ( ¼ , ¾). Mixed Number: A whole number and a fraction (1 ¼ )

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Rational Numbers Explained: Notes, Videos, Mind Maps & More For Class 8 Students

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Learn all about rational numbers in this comprehensive guide for Class 8 students! With detailed notes, videos and mind maps, understand the essential concepts of rational numbers easily and effectively. 

Click here to download class 8 rational Numbers worksheets

Watch video on Rational Numbers Class 8

Whether you're looking for a refresher on rational numbers or in need of a better understanding of the concepts, this comprehensive guide to Class 8 mathematics has got you covered. With notes, videos, and mind maps to help explain the core fundamentals easier and effectively, you'll be well-prepared for any future exams or projects related to rational numbers.

Rational Numbers - Notes, Mind Map, Extra Questions.

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Rational numbers (Class 8th)  - Revision Notes

Rational numbers.

 A number is called Rational if it can be expressed in the form p/q where p and q are integers (q > 0). It includes all natural, whole number and integers.

Example : 1/2, 4/3, 5/7,1 etc. 

Natural Numbers

All the positive integers from 1, 2, 3,……, ∞.

Whole Numbers

All the natural numbers including zero are called Whole Numbers .

All negative and positive numbers including zero are called Integers .

Properties of Rational Numbers

1. closure property.

This shows that the operation of any two same types of numbers is also the same type or not.

a. Whole Numbers

If p and q are two whole numbers then

b. Integers

If p and q are two integers then

c. Rational Numbers

If p and q are two rational numbers then

2. Commutative Property

This shows that the position of numbers does not matter i.e. if you swap the positions of the numbers then also the result will be the same.

If p and q are two whole numbers then 

3. Associative Property

This shows that the grouping of numbers does not matter i.e. we can use operations on any two numbers first and the result will be the same.

If p, q and r are three whole numbers then

If p, q and r are three integers then

If p, q and r are three rational numbers then

The Role of Zero in Numbers (Additive Identity)

Zero is the additive identity for whole numbers, integers and rational numbers.

The Role of one in Numbers (Multiplicative Identity)

One is the multiplicative identity for whole numbers, integers and rational numbers.

Negative of a Number (Additive Inverse)

Reciprocal (multiplicative inverse).

The multiplicative inverse of any rational number

The reciprocal of 4/5 is 5/4.

Distributivity of Multiplication over Addition and Subtraction for Rational Numbers

This shows that for all rational numbers p, q and r

1. p(q + r) = pq + pr

2. p(q – r) = pq – pr

Check the distributive property of the three rational numbers 4/7,-( 2)/3 and 1/2.

Let’s find the value of

This shows that

Representation of Rational Numbers on the Number Line

On the number line, we can represent the Natural numbers, whole numbers and integers as follows

Rational Numbers can be represented as follows

Rational Numbers between Two Rational Numbers

There could be n number of rational numbers between two rational numbers. There are two methods to find rational numbers between two rational numbers.

We have to find the equivalent fraction of the given rational numbers and write the rational numbers which come in between these numbers. These numbers are the required rational numbers.

Find the rational number between 1/10 and 2/10.

As we can see that there are no visible rational numbers between these two numbers. So we need to write the equivalent fraction.

2/10 = 20/100((multiply the numerator and denominator by 10)

Hence, 2/100, 3/100, 4/100……19/100 are all the rational numbers between 1/10 and 2/10.

We have to find the mean (average) of the two given rational numbers and the mean is the required rational number.

To find mean we have to divide the sum of two rational numbers by 2.

3/20 is the required rational numbers and we can find more by continuing the same process with the old and the new rational number.

Remark : 1. This shows that if p and q are two rational numbers then (p + q)/2 is a rational number between p and q so that

p < (p + q)/2 < q.

2. There are infinite rational numbers between any two rational numbers.

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• Preferences

Rational Numbers Class 8 PowerPoint PPT Presentations

Rational Number Questions

Rational number questions with solutions are provided here for students to practice and prepare for their upcoming examinations. These questions are based on the Class 8 syllabus. They are prepared as per the NCERT (CBSE) guidelines. Solving these questions will help students understand the concept well, and improve their skills.

Also, check:

• Important 2 Marks Questions for Class 8 Maths
• Important 3 Marks Questions for Class 8 Maths
• Important 4 Marks Questions for Class 8 Maths

Rational numbers are the numbers which are represented in the form of p/q, where

(i) p and q are integers

(iii) p and q are co-prime numbers, that is, HCF(p, q) = 1.

Learn more about Rational Numbers .

Rational Number Class 8 Questions with Solution

Let us practice some important rational numbers questions for class 8 to prepare for examinations.

Question 1: Find the additive inverse of the following:

(i) 22/4 (ii) ⅜ (iii) – 24/–5 (iv) 17/(– 6)

The additive inverse of 22/4 is – 22/4 or – 11/2.

The additive inverse of ⅜ is – ⅜.

(iii) – 24/–5

The additive inverse of –24/–5 or 24/5 is – 24/5.

(iv) 17/(– 6)

The additive inverse of 17/(–6) or – 17/6 is 17/6.

Question 2: Find the multiplicative inverse of the following:

(i) 18/7 (ii) 34/6 (iii) 29/3 (iv) –6/7

The multiplicative inverse of 18/7 is 7/18.

The multiplicative inverse of 34/6 is 6/34 or 3/17.

The multiplicative inverse of 29/3 is 3/29.

The multiplicative inverse of –6/7 is –7/6.

Question 3: Evaluate:

\(\begin{array}{l}(i)\: \frac{2}{15}-\frac{17}{9}+\frac{3}{5}-\frac{20}{3}\end{array} \)

\(\begin{array}{l}(ii)\: \frac{254}{105}\times\frac{15}{127}-\frac{150}{169}\times \frac{13}{15}\end{array} \)

\(\begin{array}{l}= \left ( \frac{2}{15}+\frac{3}{5} \right )+\left ( -\frac{17}{9}-\frac{20}{3} \right )\end{array} \)

\(\begin{array}{l}= \left ( \frac{2+9}{15} \right )+\left ( \frac{-17-60}{9} \right )\end{array} \)

\(\begin{array}{l}= \frac{11}{15} – \frac{77}{9} = \frac{33-385}{45}\end{array} \)

\(\begin{array}{l}= -\frac{352}{45} \end{array} \)

\(\begin{array}{l}=\left ( \frac{254}{105}\times\frac{15}{127} \right )-\left ( \frac{150}{169}\times \frac{13}{15} \right )= \frac{2}{7}-\frac{10}{13}\end{array} \)

\(\begin{array}{l}=\frac{26-70}{91}=-\frac{44}{91}\end{array} \)

Question 4: State true or false for the following:

(i) Rational numbers are closed with respect to division.

(ii) Every whole number is a rational number.

(iii) Every integer is a rational number.

(iv) There are infinitely many rational numbers between any two rational numbers.

(v) 1 and –1 are the only rational numbers which are equal to their reciprocal.

(i) Rational numbers are closed with respect to division. (False)

(ii) Every whole number is a rational number. (True)

(iii) Every integer is a rational number. (False)

(iv) There are infinitely many rational numbers between any two rational numbers. (True)

(v) 1 and –1 are the only rational numbers which are equal to their reciprocal. (True)

Question 5: Find five rational numbers between ⅔ and ⅘ .

We have the equivalent fractions,

⅔ = (2 × 5)/(3 × 5) = 10/15 and ⅘ = (4 × 3)/(5 × 3) = 12/15

To find five rational numbers lets multiply both numerator and denominator of the equivalent fractions by 5, we get

(10 × 5)/(15 × 5) = 50/75 and (12 × 5)/(15 × 5) = 60/75

Therefore, five rational numbers between ⅔ = 50/75 and ⅘ = 60/75 are

51/75, 52/75, 53/75, 54/75, 55/75.

• Exponents and Powers
• Algebraic expressions
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• Ratio and Proportion

Question 6: State which property is in the following:

(i) ⅖ + ( –⅚ + ½) = {⅖ + ( –⅚)} + ½

(ii) 3 – 45/7 + 3/2 = (3 + 3/2) – 45/7

(iii) 300 × 45 = (300 × 40) + (300 × 5)

(iv) 2/19 × 19/2 = 1

(v) 3/7 + (–3/7) = 0

Question 7: Find ten rational numbers between 2 and 3.

Multiply and divide both the numbers by 11, we get

(2 × 11)/11 = 22/11 and (3 × 11)/11 = 33/11

Rational numbers between 2 = 22/11 and 3 = 33/11 are:

23/11, 24/11, 25/11, 26/11, 27/11, 28/11, 29/11, 30/11, 31/11, 32/11.

Question 8: From a 50 m cloth, 7/3 m cloth cut out to make a shirt and 14/5 is cut out to make a curtain. Find the remaining length of the cloth?

Total length of the cloth = 50 m

Cloth used for making shirt = 7/3 m

Cloth used for making curtain = 14/5 m

Remaining cloth = 50 – 7/3 – 14/5 = 50 – {7/3 + 14/5}

= 50 – {77/15} = (750 – 77)/15 = 673/15 m

Question 9: A train covers 256 km in an hour. How much distance it would cover in 35/8 hours?

Distance covered by the train in one hour = 256 km

Distance covered in 35/8 hours = 256 × 35/8 = 1120 km

Question 10: The monthly salary of a man is ₹ 65000, one-fifth of his salary is spend paying the rent, 5/26th of his remaining salary is spent in buying groceries, and half of the rest salary is spent miscellaneous expenses. How much his monthly saving?

Total salary = ₹ 65000

Amount spend in paying the rent = ⅕ × 65000 = ₹ 13000

Remaining amount = 65000 – 13000 = ₹ 52000

Amount spend in groceries = 5/26 × 52000 = ₹ 10000

Remaining amount = 52000 – 10000 ₹ 42000

Miscellaneous expenses = ½ × 42000 = ₹ 21000

∴ his monthly savings = ₹ 21000.

Video Lesson on Rational Numbers Class 8

Practice Questions on Rational Numbers Class 8

1. State true or false for the following:

(i) All integers are rational number.

(ii) Multiplicative inverse does not exist for rational numbers.

(iii) 1 is the additive identity for rational numbers.

(iv) ⅔ lies in between the rational numbers ⅛ and 7/9.

2. Find rational numbers between ⅖ and 9/5.

3. Represent the following rational numbers on the number line

(i) ⅔ (ii) ⅗ (iii) –9/4

4. A rational number x is equal to ⅖ times the sum of 34/7 and 1/14. Find the rational number.

5. Reena could run 21/5 m in an hour. How much she can run in 34/7 hours?

Keep visiting BYJU’S to get more such Maths lessons in a simple, concise and easy to understand way. Also, register at BYJU’S – The Learning App to get complete assistance for Maths preparation with video lessons, notes, tips and other study materials.

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Rational Numbers and Operations - Mathematics - 7th Grade

Rational numbers and operations - mathematics - 7th grade presentation, free google slides theme and powerpoint template.

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