find the square of each of the following by distributive method 51
Answers
Answer:
Question 1:
Fill in the blanks to make each of the following a true statement:
(i) 785 × 0=....
(ii) 4567 × 1=...
(iii) 475 × 129=129 × ....
(iv) .... × 8975=8975 × 1243
(v) 10 × 100 × ...=10000
(vi) 27 × 18=27 × 9+27 × ...+27 × 5
(vii) 12 × 45=12 × 50 − 12 × ...
(viii) 78 × 89=78 × 100 − 78...+78 × 5
(ix) 66 × 85=66 × 90 − 66 × ... − 66
(x) 49 × 66+49 × 34=49 × (...+...)
ANSWER:
(i) 785 × 0 = 0
(ii) 4567 × 1 = 4567 (Multiplicative identity)
(iii) 475 × 129 = 129 × 475 (Commutativity)
(iv) 1243 × 8975 = 8975 × 1243 (Commutativity)
(v) 10 × 100 × 10 = 10000
(vi) 27 × 18 = 27 × 9 + 27 × 4 + 27 × 5
(vii) 12 × 45 = 12 × 50 − 12 × 5
(viii) 78 × 89 = 78 × 100 − 78 × 16 + 78 × 5
(ix) 66 × 85 = 66 × 90 − 66 × 4 − 66
(x) 49 × 66 + 49 × 34 = 49 × (66 + 34)
Page No 4.14:
Question 2:
Determine each of the following products by suitable rearrangements:
(i) 2 × 1497 × 50
(ii) 4 × 358 × 25
(iii) 495 × 625 × 16
(iv) 625 × 20 × 8 × 50
ANSWER:
(i) 2 × 1497 × 50
= (2 × 50) × 1497 = 100 × 1497 = 149700
(ii) 4 × 358 × 25
= (4 × 25) × 358 = 100 × 358 = 35800
(iii) 495 × 625 × 16
= (625 × 16) × 495 = 10000 × 495 = 4950000
(iv) 625 × 20 × 8 × 50
= (625 × 8) × (20 × 50) = 5000 × 1000 = 5000000
Page No 4.14:
Question 3:
Using distributivity of multiplication over addition of whole numbers, find each of the following products:
(i) 736 × 103
(ii) 258 × 1008
(iii) 258 × 1008
ANSWER:
(i) 736 × 103
= 736 × (100 + 3)
{Using distributivity of multiplication over addition of whole numbers}
= (736 × 100) + (736 × 3)
= 73600 + 2208 = 75808
(ii) 258 × 1008
= 258 × (1000 + 8)
{Using distributivity of multiplication over addition of whole numbers}
= (258 × 1000) + (258 × 8)
= 258000 + 2064 = 260064
(iii) 258 × 1008
= 258 × (1000 + 8)
{Using distributivity of multiplication over addition of whole numbers}
= (258 × 1000) + (258 × 8)
= 258000 + 2064 = 260064