R.S Aggarwal Class 8 Chapter 1 Rational numbers Test paper 1 Solution
In this post we have provided Test Paper 1 solution for the RS Aggarwal Mathematics book for class 8. These solutions are made by expert teachers of our website.
Test Paper 1
A) 1) Find the additive inverse of
i) 7/(-10)
Ans: The additive inverse of 7/(-10) is 7/10
ii) 8/5
Ans: The additive inverse of 8/5 is (-8/5)
2) The sum of two rational numbers is -4. If one of them is -11/5, find the other?
Ans: Let the other rational number be m.
∴ m + (-11/5) = -4
Or, m = – 4 + (11/5) = (-20+ 11)/5 = – 9/5
The other number is -9/5.
3) What number should be added to -3/5 to get 2/3?
Ans: The number that should be added to (-3/5) be m
(-3/5) + m = 2/3
Or, m = 2/3 + 3/5
Or, m = 19/15
The number that should be added to (-3/5) to get 2/3 is 19/15.
4) What number should be subtracted from -3/4 to get -1/2?
Ans: Let us assume that we must subtract m from (-3/4) to get (-1/2)
(-3/4) – m = (-1/2)
Or, m = (-3/4) + (1/2) = -1/4
5) Find the multiplicative inverse of:
i) -3/4
Ans: The Multiplicative inverse of -3/4 is -4/3
ii) 11/4
Ans: The multiplicative inverse of 11/4 is 4/11
6) The product of two numbers is -8. If one of them is -12, find the other?
Ans: let the other number be m
So m× (-12) = -8
Or, m = 8/12 = 2/3
7) Evaluate:
i) (-3/5) × (10/7)
Ans:
(-3/5) × (10/7)
= – (3×10) / (5×7)
= – 6/7
ii) (-5/8)-1
Ans:
(-5/8)-1
= 1/ (-5/8)
= -8/5
iii) (-6)-1
Ans:
(-6)-1
= 1/ (-6)
= -1/6
8) Name the property of multiplication shown by each of the following statements:
i) (-12/5) × (3/4) = (3/4) × (-12/5)
Ans: In the above statement the commutative law of multiplication has been shown. This says that two rational numbers can be multiplied in any order.
ii) (-8/15) ×1 = -8/15
Ans: The above statement shows the existence of multiplicative identity for rational numbers. 1 is the multiplicative identity for rational numbers.
iii) [(-2/7) × (7/8)] × (-5/7) = (-2/3) × [(7/8) × (-5/7)]
Ans: The above statement demonstrates associative law of multiplication.
iv) (-2/3) ×0 = 0
Ans: The above statement shows the multiplicative properties of 0.
v) (2/5) × [(-4/5) + (-3/10)] = [(2/5) × (-4/5)] + [(2/5) × (-3/10)]
Ans: The above statement shows the distributive law of multiplication.
9) Find two rational numbers lying between -1/3 and 1/2.
Ans : LCM of 3 and 2 is 6
Now, (-1/3) = (-2/6) and (1/2) = (3/6)
so, two rational numbers lying between (-1/3) and (1/2) are
(-1/6) and (2/6)
B) Mark (✓) against the correct answer in each of the following:
10) What should be added to (-3/5) to get (-1/3)?
a) 4/5
b) 8/5
c) 4/15 (✓)
d) 2/5
Ans: let’s assume that m should be added to (-3/5)
m + (-3/5) = (-1/3)
or, m = (-1/3) + 3/5
or, m = 4/15
11) What should be subtracted from (-2/3) to get (3/4)?
a) (-11/12)
b) (-13/12)
c) (-5/4)
d) (-17/12) (✓)
Ans:
Let’s assume that m should be subtracted from (-2/3) to get 3/4
(-2/3) – m = 3/4
m = -17/12
12) (-5/4)-1 =?
a) 4/5
b) -4/5
c) 5/4
d) 3/5
Ans:
(-5/4)-1
= 1/ (-5/4)
= -4/5
13) The product of two numbers is -1/4. If one of them is -3/10, then the other is
a) 5/6 (✓)
b) -5/6
c) 4/3
d) -8/5
Ans:
Let’s assume that the other number is m
m× (-3/10) = (-1/4)
or, m = 5/6
14) [(-5/6) ÷ (-2/3)] =?
a) -5/4
b) 5/4 (✓)
c) -4/5
d) 4/5
Ans:
[(-5/6) ÷ (-2/3)]
= (-5/6) × (-3/2)
= 5/4
15) (4/3) ÷ ? = (-5/2)
a) (-8/5)
b) 8/5
c) (-8/15) (✓)
d) 8/15
Ans:
(4/3) ÷ ? = (-5/2)
Or, ? = (4/3) ÷ (-5/2)
Or, ? = (4/3) × (-2/5)
Or, ? = -8/15
16) Reciprocal of (-7/9) is
a) 9/7
b) -9/7 (✓)
c) 7/9
d) none of them
Ans : The reciprocal of (-7/9) is 1/ (-7/9) = -9/7
17) A rational number between -2/3 and 1/2 is
a) (-1/6)
b) (-1/12) (✓)
c) (-5/6)
d) 5/6
Ans:
A rational number between -2/3 and 1/2 is
(1/2) × [(-2/3) + (1/2)]
= (1/2) × (-4 + 3)/6
= (1/2) × (-1/6)
= (-1/12)
[C] 18) Fill in the blanks.
i) (25/8) ÷ (……..) = – 10
Ans: Putting m in the blank space
(25/8) ÷ m = – 10
Or, m = (25/8) ÷ (-10)
Or, m = – 5/16
∴ (25/8) ÷ (-5/16) = – 10
ii) (-8/9) × (……..) = (-2/3)
Ans: Putting m in the blank space
(-8/9) × m = (-2/3)
Or, m = (-2/3) ÷ (-8/9)
Or, m = 3/4
∴ (-8/9) × (3/4) = (-2/3)
iii) (-1) + (……..) = (-2/9)
Ans: Putting m in the blank space
(-1) + m = (-2/9)
Or, m = (-2/9) – (-1)
Or, m = 7/9
∴ (-1) + (7/9) = (-2/9)
iv) (2/3) – (……..) = 1/15
Ans: Putting m in the blank space
(2/3) – (m) = 1/15
Or, m = (2/3) – (1/15)
Or, m = 3/5
∴ (2/3) – (3/5) = 1/15
D) 19) Write ‘t’ for true and ‘F’ for false for each of the following:
i) Rational numbers are always closed under subtraction. (T)
ii) Rational numbers are always closed under division. (F)
iii) 1 ÷ 0 = 0 (F)
iv) Subtraction is commutative on rational numbers. (F)
v) – (-7/8) = 7/8 (T)
RS Aggarwal class 8 test paper 1