RBSE Class 7 Maths Important Questions Chapter 1 Integers

Rajasthan Board RBSE Class 7 Maths Important Questions Chapter 1 Integers Important Questions and Answers.

RBSE Class 7 Maths Chapter 1 Important Questions Integers

Multiple Choice Questions

Question 1.
The integer whose product with (- 1) is 0, is:
(a) 0
(b) 1
(c) - 1
(d) None of these
Answer:
(a) 0

Question 2.
(- 6) ÷ (- 3) is equal to :
(a) 0
(b) 1
(c) 2
(d) - 2
Answer:
(c) 2

Question 3.
a × (b + c) = a × b + a × c is called :
(a) Commutative property
(b) Associative property
(c) Distributive property
(d) Closure property
Answer:
(c) Distributive property

Question 4.
The additive identity for integers is :
(a) 1
(b) - 1
(c) 0
(d) None of these
Answer:
(c) 0

Question 5.
On a number line, when we add a positive integer, we :
(a) move to the right
(b) move to the left
(c) do not move at all
(d) both (a) and (b)
Answer:
(a) move to the right

Question 6.
a + b = b + a is called :
(a) Commutativity of addition
(b) Commutativity of subtraction
(c) Distributive law
(d) None of these
Answer:
(a) Commutativity of addition

Question 7.
Closure property of addition is :
(a) a (b + c) = ab + ac
(b) a + b = b + a
(c) a + b = an integer
(d) a + b = a natural number
Answer:
(c) a + b = an integer

Question 8.
Multiplication of a positive and a negative integer is :
(a) always positive
(b) always negative
(c) 0
(d) None of these
Answer:
(b) always negative

Fill in the Blanks

Question 1.
The value of (- 1)¹⁰ is __________ .
Answer:
1

Question 2.
360 more than - 360 is __________ .
Answer:
0

Question 3.
The collection of whole numbers and negative numbers is called __________ .
Answer:
integers

Question 4.
__________ is neither positive integer nor negative integer.
Answer:
0

Question 5.
__________ is its own additive inverse.
Answer:
0

State Wheather True or False

Question 1.
The product of a positive and a negative integer is negative.
Answer:
True

Question 2.
The product of three negative integers is a negative integer.
Answer:
True

Question 3.
Of the two integers, if one is negative, then their product must be positive.
Answer:
False

Question 4.
For all non-zero integers a and b, a x b is always greater than either a or b.
Answer:
False

Question 5.
The product of a negative and a positive integer may be zero.
Answer:
False

Very Short Answer Type Questions

Question 1.
Solve the following:
(- 18) × (- 10) × 9
Answer:
(- 18) × (- 10) × 9 = [ (- 18) × (- 10)] × 9 = 180 × 9 = 1620

Question 2.
Using number line find : 3 × (- 5)
Answer:

So, 3 × (- 5) = - 15

Question 3.
Write down a pair of integers whose:
(i) sum is - 5
(ii) difference is - 7 .
Answer:
(i) (- 2) + (- 3) = 5
Hence, the required pair of integers
= (- 2, - 3)

(ii) - 10 - (- 3) = - 10 + 3 = - 7
Hence, the required pair of integers
= (- 10, - 3)

Short Answer Type Questions

Question 1.
Verify the distributive property of integers:
a × (b + c) = (a × b) + (a × c) for a = - 12, 6 = 6 and c = - 2.
Answer:
LHS = a × (b + c)
= - 12 × [6 + (- 2)]
= - 12 × 4 = - 48
RHS = (a × b) + (a × c)
= (- 12 × 6) + (- 12 × - 2)
= - 72 + 24 = - 48
∴ LHS = RHS Hence verified.

Question 2.
Divide the sum of (- 14), (- 21) and 10 by the product of (- 1) and (- 5).
Answer:
Sum of (- 14), (- 21) and 10
= (-14) + (-21)+ 10'
= -35 + 10 = -25
Product of (- 1) and (- 5) = (- 1) × (- 5) = 5
∴ Required quotient = (- 25) + 5 = - 5

Question 3.
Verify that a ÷ (6 + c) ≠ (a ÷ b) + (a ÷ c) for a = - 18, b = 4 and c = 2.
Answer:
LHS = a ÷ (b + c) .
= - 18 ÷ (4 + 2)
= - 18 ÷ 6 = - 3
RHS = (a ÷ b) + (a ÷ c)
= (- 18 ÷ 4) + (-18 ÷ 2)
= \(\frac{-9}{2}\) + (- 9)
= \(\frac{-9-18}{2}=\frac{-27}{2}\)
∴ LHS ≠ RHS Hence verified.