Class 8 Maths Notes for Rational Number

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CLASS 8
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RATIONAL NUMBERS
I. Important Concepts/ Result
Any fraction with non-zero denominators is a rational number. Some of the examples of rational
1 1 3
numbers are 2, 5, 5,, and so on. The number ―0‖ is also a rational number, as we can represent it
00 0 1 2 3
in many forms such as 1, , , etc. But, , , , etc. are not rational, since they give us infinite
2 3 0 0 0
values.
II. Some illustrations/Examples (with solution)
Each number below is a rational number.
0 7 2 17 43 4 −4
0= 2, 7=1, , 5 3, = 3 , 0.43=100 ,, – 9, =- 9 ,
1 2 7 3
And also: - 3, , 0.7 or , and -0.3 or - 10 .
5 10
i) MCQs:
Question 1.Which of the following statements is true?
(a) Natural numbers are closed under division.
(b) Whole numbers are not closed under division.
(c) Integers are closed under division.
(d) Rational numbers are closed under division.
Question 2.‗0‘ is not _____
(a) a natural number. (b) a whole number. (c) an integer. (d) a rational number
Question 3.Which of the following is the multiplicative identity for rational numbers?
(a) 1 (b) -1 (c) 0 (d) None of these
Question 4.The additive identity for rational numbers is
(a) 1 (b) -1 (c) 0 (d) None of these
ANSWER MCQs : 1 (c). 2 (a). 3 (a). 4 (c)
ii) Case based study: 1
Three friends Ram, Rahim and David went to ―RADHEY SWEET MART‖ to purchase some sweets,
namkin and cold drinks for New year party. The following chart shows the price and available stock of
sweets and namkin in the shop.

S.NO. SWEETS AND NAMKIN AVAILABLE PRICE
STOCK
1 SWEET LADDU 10 Kg Rs. 400 per Kg
2 JALEBI 8 Kg Rs. 360per Kg
3 BARFI 7 Kg Rs. 300 per Kg
4 MIX-NAMKIN 100 packets Rs. 80 per
packet
5 POTATO CHIPS 80 packets Rs. 30 per
packet
6 COLD DRINKS 50 Bottles Rs. 50per bottle
7 ROASTED DRY FRUITS 12 Kg Rs. 1000 per Kg

Question 1.1: After purchasing 500gm of sweet laddu, jalebi and barfi each, Ram had Rs. 150 left with
him. How much money does Ram had before the purchase?
Question 1.2:Ram wants to purchase one packet of Mix-Namkin and two packets of potato chips with the
remaining Rs. 150. Explain whether he can purchase it or not.
Question 1.3: Rahim had Rs. 200 and wants to purchase one packet of Mix-Namkin, one packet of potato
chips, 250gm Sweet laddu and one bottle of cold drink. But due to insufficient money he had to reduce the
quantity of one of the item. Find out the name of that item along with reason.

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Question 1.4:David had Rs. 250 and wants to purchase those items which were not purchased by his
friends. Choose the correct list of items he will purchase. (i) Jalebi (ii) Roasted Dry fruits (iii) Barfi (iv)
Potato chips
ANSWER Case based study:1.1 𝑅𝑠. 680 1.2𝑅𝑠. 140 , Yes 1.3 Namkin
Packet
1.4 Jalebi, Dry Fruit, Barfi
Short answer type question:
6 −1 1 100
Question 1.Pick up the rational numbers from the following numbers: , , , 0, 0 , 0
7 2
6 −1
Solution:Since rational numbers are in the form of a/b where b ≠ 0.Only 7, 2 , and 0 are the rational
numbers.
3
Question 2.Find the reciprocal of the following rational numbers: (a) − 4 (b) 0
Question 3.Write two such rational numbers whose multiplicative inverse is same as they are.
6 1 4 1
ANSWERS.Short answer type question: 1.7 , − 2 , 0 , 2.(a) − 3 (b) 0 3. 1 𝑎𝑛𝑑 − 1
Long answer type questions: 2
1 1
Question 1. Find 7 rational numbers between 3 𝑎𝑛𝑑 2.
1 2 1
Question 2.If 𝑥 = 2, 𝑦 = − 3and 𝑧 = 4 , verify that 𝑥 × (𝑦 × 𝑧) = (𝑥 × 𝑦) × 𝑧.
21 22 23 24 25 26 27
ANSWER:-Long answer type questions: 1. 60 , 60 , 60 , 60 , 60 , 60 , 60

Questions for Practice:
MCQs:
7
1. Write additive inverse of − :
13
7
(a)13 (b) 13 (c) -13 (d) 0
2. Find the multiplicative inverse of -17
𝟏
(a) − 𝟏𝟕 (b) 289 (c) -289 (d) -17
𝟕 7
3. Multiply 𝟏𝟑by the reciprocal of − 16
𝟏𝟔 𝟏𝟔 𝟑 𝟏𝟑
(a)− 𝟏𝟑 (b) 𝟏𝟑 (c) 𝟏𝟔 (d) − 𝟏𝟔
4.Fill in the blanks:______ has no reciprocal.
(a) One (b) Zero (c) Two (d) Three
13
5. is the reciprocal of ____________.
6
𝟔 𝟏𝟑 𝟔
(a) 𝟏𝟑 (b )− 𝟔 (c) − 𝟏𝟑 (d) 0
𝟐 𝟏
6. Find the rational number between 𝟑 𝒂𝒏𝒅 𝟐.
𝟕 𝟕 𝟓 𝟔
(a) − 𝟏𝟐 (b) 𝟏𝟐 (c) 𝟑 (d) 𝟑
7. Choose rational number greater than -3
(a) -3 (b) -4 (c) -5 (d) -1/2
8. Write the additive inverse of
𝟔 𝟏𝟑 𝟏𝟑 𝟔
(a) (b) (c) − (d)
𝟏𝟑 𝟏𝟔 𝟔 𝟓
9. Which of the following is the multiplicative identity for rational numbers?
(a) 1 (b) -1 (c) 0 (d) None of these
10.The additive identity for rational numbers is
(a) 1 (b) -1 (c) 0 (d) None of these

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ii) Short answer type question:
8 4
1. What is the sum of the rational numbers − 19 and − 57.
3 1
2. What number should be added to 8to get − 24 ?
4 5 7 11
3. Which of the rational numbers , , and is the smallest?
9 6 12  24
4 5 7 2
4. Which of the rational numbers , , , is the greatest?
9  12  18  3
2 4 7  11
5. Simplify: + + +
3 5 15 20
3 5
6. What number should be subtracted from so as to get ?
4 6
 15
7. The sum of two rational numbers is -7. If one of the numbers is , find the other number.
19
 20
8. The product of two numbers is . If one of the numbers is 4, find the other.
9
5  35
9. Fill in the blanks: ÷ (_____) =
12 18
 16  4
10. Find the value of ( ÷ ).
21 3

iii) long answer type questions:
1. Fill in the blanks:
(i) The product of a positive number and its reciprocal is _________.
(ii) The rational number _________ has no reciprocal.
(iii) The reciprocal of the reciprocal of a number is _________.
(iv) The rational number _________ is neither positive nor negative.
(v) _________ is the only rational number which is equal its additive inverse.

2. Write:
(i) A rational number which has no reciprocal.
(ii) A rational number whose product with a given rational number is equal to the given rational
number.
iii) Case based study:
1
1. A dog buried 3 bones in the backyard. The first bone is buried -2 2 feet, the second bone is
2 30
buried - 2 6 feet and third bone is- 4 feet.
1 2 30
(a) Simplify. (-2 2 ) × (- 2 6 ) (- 4 )
(b) How much deeper is third bone buried from the first bone?
1 3
2. Raju earns Rs16000/month. He spends of his income on food; of the remainder on house
4 10
5
rent and 21 of the remainder on education of children.
(a) How much money is still left with him?
(b) On which segment Raju spent maximum money?
ANSWER :- MCQs : 1. (a) 2. (a) 3. (a) 4. (b) 5. (a) 6. (b) 7. (d) 8. (a) 9. (a) 10. (c)

4

28 5 5 7  13
Short answer type question: 1. 2. 3. 4. 5.
57 12 6 18 60
 19  118 5  14 4
6. 7. 8. 9. 10.
12 19 9 3 70

long answer type questions::- Fill in the blanks 1. (i) One (ii) Zero (iii) One (iv) Zero (ii) One
2. (i) Zero (ii) One
7
Case based study: 01 (a)  96 (b) -5 Case based study: 02 (a) Rs. 6400 (b) Food
8
Chapter Test (One 20 mark)
SECTION A (2 MARKS FOR EACH QUESTION)
8 4
1. What is the sum of the rational numbers and .
19 57
3 1
2. What number should be added to to get ?
8 24
4 5 7 11
3. Which of the rational numbers , , and is the smallest?
9 6 12  24
4 5 7 2
4. Which of the rational numbers , , , is the greatest?
9  12  18  3
2 4 7  11
5. Simplify: + + +
3 5 15 20
3 5
6. What number should be subtracted from so as to get ?
4 6
SECTION A ( 4 MARKS FOR EACH QUESTION)
 15
7. The sum of two rational numbers is -7. If one of the numbers is , find the other number.
19
 20
8. The product of two numbers is . If one of the numbers is 4, find the other.
9
Chapter Test (One 30 mark)
SECTION A ( 2 MARKS FOR EACH QUESTION)
7
1. Write additive inverse of 13
2. Find the multiplicative inverse of -17
7 7
3. Multiply 13 by the reciprocal of 16
2 1
4. Find the rational number between 3 and 2 .
8 4
5. What is the sum of the rational numbers 19 and 57 .
5  35
6. Fill in the blanks: ÷ (_____) =
12 18
SECTION B ( 3 MARKS FOR EACH QUESTION)
3 1
7. What number should be added to to get ?
8 24
 16 4
8. Find the value of ( ÷ ).
21 3
5

SECTION C ( 4 MARKS FOR EACH QUESTION)

1 1
9. Find 7 rational numbers between and .
3 2
10. Question 2.
1
1 2
If x = , y = and z = 4 , verify that x × (y × z) = (x × y) × z.
2 3
11. Fill in the blanks:
(i) The product of a number and its product is _________.
(ii) The rational number _________ has no reciprocal.
(iii) The reciprocal of the reciprocal of a number is _________.
(iv) The rational number _________ is neither positive nor negative.

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