Evaluate the following, using distributive property
i. -39 × 99
ii. (-85) × 43 + 43 × (-15)
iii. 53 × (-9) - (-109) × 53
iv. 68 × (-17) + (-68) × 3

Solution:

To answer the given question let us examine the problem deeply using the properties of integers and the distributive property which says for any three numbers A (B + C) the equation is resolved as A × (B + C) = AB + AC or A (B - C) = AB - AC.

Let us apply the same individually to solve the given problems.

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)

= -1360

✦ Try This: Evaluate 78 × (-16) + (-78) × 3

Now to evaluate the given expression we can apply integer rules, distributive property rule and the rule of multiplication

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 1

NCERT Exemplar Class 7 Maths Chapter 1 Exercise Problem 124

Evaluate the following, using distributive property: i. -39 × 99 ii. (-85) × 43 + 43 × (-15) iii. 53 × (-9) - (-109) × 53 iv. 68 × (-17) + (-68) × 3

Summary:

After applying the integer rules and using the distributive property rule we examined that i. -39 × 99 = -3861 ii. (-85) × 43 + 43 × (-15) = -4300iii. 53 × (-9) - (-109) × 53 = 5300 iv. 68 × (-17) + (-68) × 3 = -1360

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