Question

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

Answer 1

Distributive property is $a\times (b+c)=a\times b+a\times c$

Associative property is $a\times b\pm a\times c=a\times (b\pm c)$

using this in given examples.

$\left(i\right)$

$-39\times 99=-39\times [100-1]$

$=-39\times 100-(-39)\times 1\cdots \cdots \left[\text{distributive property}\right]=-3900+39=-3861$

(ii)

$(-85)\times 43+43\times (-15)$

$=43\times (-85)+43\times (-15)\cdots [\because a\times b=b\times a]$

$=43\times [-85-15]\cdots \cdots \left[\text{associative property}\right]$

$=43\times (-100)=-4300$

(iii)

$53\times (-9)-(-109)\times 53$

$53\times (-9)-53\times (-109)\cdots [\because a\times b=b\times a]$

$=53\times \left[\right(-9)-(-109\left)\right]\cdots \cdots \left[\text{associative property}\right]$

$=53\times [-9+109]=53\times 100=5300$

$\left(iv\right)$

$68\times (-17)+(-68)\times 3=68\times (-17)-68\times 3$

$=68\times \left[\right(-17)-3]\cdots \cdots \left[\text{associative property}\right]$

$=68\times (-20)$

$=-1360$