Rational Numbers Class 8 Worksheet Maths Chapter 1

Multiple Choice Questions

Q1: Rational numbers include
A) integers
B) decimals
C) fractions
D) integers, decimals and fractions
Ans. D)
Any number that can be written in fraction form is a rational number. This includes integers as well as decimals.

Q2: The word ‘rational’ arises from the term
A) fraction
B) ratio
C) decimal
D) integer
Ans. B)
A ratio 2: 5 can be written as 2/5, i.e., in the form of p/q. And ‘a rational number is defined as a number that can be expressed in the form of p/q’.

Q3: Rational numbers, which have both numerator and denominator as positive integers is called a
A) positive rational number
B) negative rational number
C) Numerator
D) denominator
Ans. A)
Both numerator and denominator of are positive integers; hence it is called a positive rational number.

Q4: Rational numbers which have both numerator and denominator as negative integers is called a
A) positive rational number
B) negative rational number
C) numerator
D) denominator
Ans. A)
When both numerator and denominator are negative integers it is called a positive rational number.

Q5: In a rational number, if the denominator and numerator both are  positive integer and the numerator and the denominator have no common factor other than 1, denominator is greater than numerator then the rational number is said to be in its  
A) irrational form
B) integer form
C) decimal form
D) standard form
Ans. D)
The number 5/7 is in standard form.
∵ 7 = positive integer and 5 & 7 hare no common factor other than 1.

True/False

Q1: Every integer can be expressed as a rational number.

Ans. True

Q2: The sum of two rational numbers is always rational.

Ans. True

Q3: The reciprocal of a negative rational number is always negative.

Ans. True

Q4: Subtracting a rational number is the same as adding its additive inverse.

Ans. True

Q5: The product of two rational numbers with different signs is positive.

Ans. False

Q6: The division of two rational numbers is undefined when the divisor is zero.

Ans. True

Q7: Every fraction is a rational number, but not every rational number is a fraction.

Ans. False (because every rational number can be expressed as a fraction)

Q8: A rational number remains unchanged if both its numerator and denominator are multiplied by the same non-zero integer.

Ans. True

Very Short Answer Questions

Ans. -5/12 + 7/18

=-15+14/36

=-1/36

Q2: Find the value of -15/17 + 12/51
Ans. -15/17 + 12/51
=-45+12/51
=-33/51
= -11/17

Q3: Find the value of -2/7 ÷ 2/9 × 3/7
Ans. -2/7÷2/9×3/7
=-2/7 × 9/2 × 3/7
= -27/49

Q4: Find the value of [2+(3/4-1/5)]÷3
Ans. [2+(3/4 – 1/5)]÷3
=[2+ (15-4/20)]÷3
=[2+11/20]÷3
=(40+11/20)× 1/3
=51/20 × 1/3
=17/20

Q5: Find the value of [12/17 ÷ 18/34 ] ÷ 1/6
Ans. [12/17÷18/34]÷1/6
=12/17×34/18×6
=8

Q6: What should be added to (1/3+1/2) to get 3?
Ans. 3-(1/3+1/2)
=3-(2+3/6)
=3-5/6
=18-5/6
=13/6

Q7: What should be subtracted from 5 to get 13/3?
Ans. 5- 13/3
=(15-13)/3
=2/3

Short Answer Questions

Q1: The sum of two rational number is -43/52. If one of the number is 5/52 then what is the other number?
Ans. -43/52 – 5/52
=-48/52
=-12/13

Q2: If x:2/3 = 2:3 then what is the value of x?
Ans. X:2/3=2:3
=3x/2 =2/3
9x=4
X=4/9

Q3: Rahim has 2000 rs. If he spends ¼ of his money on groceries and 2/5th  of his money on traveling. How much money is left?
Ans. Ram spends on groceries= 2000×1/4 = 500rs
Ram spends on traveling= 2000×2/5=800rs
So, money left: 2000-(500+800)
=700rs

Q4: If 3/5th of a number is 6, then what is that number?
Ans. Let the number is x
So, 3/5th of x =6
3x/5=6
3x=30
X=10

Q5: If 4 shirts can be made from 35 meter of cloth. How much cloth is needed for each shirt?
Ans. 35/4 meters
=8¾ m

Q6: If 3/7th of a bucket is 3 liters. Then what is the capacity of the bucket?
Ans. Let the full bucket is of X liters
So , 3/7th of x =3
3x=21
X=7

Q7: If 3/5 ÷ x = 4/7 , then Find the value of x?
Ans. 3/5÷x=4/7
3/5 × 1/x = 4/7
3/5x = 4/7
20x=21
X= 21/20

Q8: Find the value of 3/4 + 5/6 ÷ 3/5
Ans. 3/4 +5/6 ÷ 3/5
=3/4 + 5/6 ×5/3
=3/4 + 25/18
= (27+50)/36
=77/36