CBSE Class 7 Mathematics Integers Worksheet Set D

CBSE Class 7 Maths Worksheet - Integers (3)

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INTEGERS (MULTIPLICATION)

Multiplication of Integers

Multiplication is basically repeated addition. Therefore multiplication of integers is the repeated addition as:

Properties of Multiplication of Integers

Distributive Property According to the distributive property of multiplication of integers, if a, b and c are three integers then,
a× (b + c) = (a × b) + (a × c)
Example -

QUESTIONS :-

Q1. SIMPLIFY :-

(i) (−8) × 9 + (−8) × 7
Solution. 
(−8) ×× (9 + 7) [using the distributive law]
= (−8) ×× 16
= −128

(ii) 9 × (−13) + 9 × (−7)
Solution.
9 ×× (−13 + (−7)) [using the distributive law]
= 9 ×× (−20)
= −180

(iii) 20 × (−16) + 20 × 14
Solution.
20 ×× (−16 + 14) [using the distributive law]
= 20 ×× (−2)
= −40

(iv) (−16) × (−15) + (−16) × (−5)
Solution.
(−16) ×X (−15 + (−5)) [using the distributive law]
= (−16) ×X(−20)
= 320

(v) (−11) × (−15) + (−11) × (−25)
Solution.
(−11) ×X(−15 +(−25)) [using the distributive law]
= (−11) ×X (−40)
= 440

(vi) 10 × (−12) + 5 × (−12)
Solution.
(−12) ×× (10 + 5) [using the distributive law]
= (−12) ×× 15
= −180

(vii) (−16) × (−8) + (−4) × (−8)
Solution.
(−16 + (−4)) ×× (−8) [using the distributive law]
= (−20) ×× (−8)
= 160

(viii) (−26) × 72 + (−26) × 28
Solution.
(−26) ×× (72 + 28) [using the distributive law]
= (−26) ××100
= −2600

Q2. Fill in the blanks :-

(i) (−6) × (......) = 6
(ii) (−18) × (......) = (−18)
(iii) (−8) × (−9) = (−9) × (......)
(iv) 7 × (−3) = (−3) × (......)
(v) {(−5)×3} × (−6) = (......) × {3×(−6)}
(vi) (−5) × (......) = 0
Answer.
(i) (−6) × (x) = 6 x = 6−6 = −66= −1x = 6-6 = -66= -1 Thus, x = (−1)
(ii) 1 [∵ Multiplicative identity]
(iii) (−8) [∵ Commutative law]
(iv) 7 [∵ Commutative law]
(v) (−5) [∵ Associative law]
(vi) 0 [∵ Property of zero]

Q3. Prove that :- i). (-3) × {4 × (-5)} = (- 3) × {4 × (-5)}
Solution.
(-3) × {4 × (-5)} = (-3) × (-20) = 3 × 20 = 60
and, {(-3) × 4} × (-5) = (-12) × (-5) = 12 × 5 = 60
Therefore, (- 3) × {4 × (-5)} = {(-3) × 4} × (-5)

(ii) (-2) × {(-3) × (-5)} = (- 2) × {(-3) × (-5)}
Solution.
(-2) × {(-3) × (-5)} = (-2) × 15 = -(2 × 15)= -30
and, {(-2) × (-3)} × (-5) = 6 × (-5) = -(6 × 5) = -30
Therefore, (- 2) × {(-3) × (-5)} = {-2) × (-3)} × (-5)

Q4. Solve that :-7 × (-3) = (-3) × 7
Solution.
7 × (-3) = -(7 × 3) = -21 and (-3) × 7
= -(3 × 7) = -21 Therefore, 7 × (-3)
= (-3) × 7

Q5. Prove that (-5) × (-8) = (-8) × (-5)
Solution.
(-5) × (-8) = 5 × 8 = 40 and (-8) × (-5) = 8 × 5 = 40
Therefore, (-5) × (-8) = (-8) × (-5).

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