Which rule is used to prove {10 × (5 + 2)} = {(10 × 5) + (10 × 2)} ? Using the same rule find the value of 99 $\times$ 101. [4 MARKS]

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Solution

Rule: 1 Mark
Value: 3 Mark

LHS = {10 × (5 + 2)}
= 10 × (7)
= 70
RHS = {(10 × 5 ) + (10 × 2 )}
= {50 + 20}
= 70

Hence , LHS = RHS

This rule is known as Distributivity of multiplication over addition.

We have to find out the value of
99 $\times$ 101 = 99 $\times$ (100+1) = 9900 + 99 = 9999

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Is {10 × (5 + 2)} = {(10 × 5) + (10 × 2)} ? Which rule is this? [4 MARKS]

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- 10, \frac{- 83}{9}

y = \frac{5 x - 10}{2}; 4 x + 5 = - y

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