Question

Solve using Suitable property - : (– 85) × 43 + 43 × ( – 15)​

Answer 1

Step-by-step explanation:

Distributive property is a×(b+c)=a×b+a×c

Associative property is a×b±a×c=a×(b±c)

using this in given examples.

(i)

−39×99

=−39×[100−1]

=−39×100−(−39)×1⋯⋯[distributive property]

=−3900+39=−3861

(ii)

(−85)×43+43×(−15)

=43×(−85)+43×(−15)⋯[∵a×b=b×a]

=43×[−85−15]⋯⋯[associative property]

=43×(−100)=−4300

(iii)

53×(−9)−(−109)×53

53×(−9)−53×(−109)⋯[∵a×b=b×a]

=53×[(−9)−(−109)]⋯⋯[associative property]

=53×[−9+109]=53×100=5300

(iv)

68×(−17)+(−68)×3

=68×(−17)−68×3

=68×[(−17)−3]⋯⋯[associative property]

=68×(−20)

=−1360

Answer 2

(i) -39 × 99 = -39 × [100 -1] = -39 × 100 + (-39) × (-1) = -3900 + 39 = -3861 (ii) (-85) × 43 + 43 × (-15) = 43 × (-85) + 43 × (-15) = 43 × [-85 – 15] = 43 × [-100] = -4300 (iii) 53 × (-9) – (-109) × 53 = 53 × (-9) – 53 × (-109) = 53 × [(-9) – (-109)] = 53 × [-9 + 109] = 53 × 100 = 5300 (iv) 68 × (-17) + (-68) × 3 = 68 × (-17) + 68 × (-3) = 68 × [(-17) + (-3)] = 68 × (-20) = -1360Read more on Sarthaks.com - https://www.sarthaks.com/785126/evaluate-the-following-using-distributive-property-i-39-99-ii-85-43-43-15-iii-53-9-109-53