Question

Find the product, using suitable properties: $15\times (-25)\times (-4)\times (-10)$

Answer 1

Simplify using the associative property of multiplication:

According to the associative property of multiplication,

$a\times \left(b\times c\right)=\left(a\times b\right)\times c$

So, the required product is,

$15\times (-25)\times (-4)\times (-10)=15\times \left[(-25)\times (-4)\right]\times (-10)$

$\Rightarrow 15\times (-25)\times (-4)\times (-10)=15\times \left[25\times 4\right]\times (-10)$ $\left[\because \left(-a\right)\times \left(-b\right)=a\times b\right]$

$\Rightarrow 15\times (-25)\times (-4)\times (-10)=15\times 100\times (-10)$

$\Rightarrow 15\times (-25)\times (-4)\times (-10)=15\times \left[100\times (-10)\right]$

$\Rightarrow 15\times (-25)\times (-4)\times (-10)=15\times \left[-100\times 10\right]$ $\left[\because \left(-a\right)\times \left(+b\right)=-a\times b\right]$

$\Rightarrow 15\times (-25)\times (-4)\times (-10)=15\times \left[-1000\right]$

$\Rightarrow 15\times (-25)\times (-4)\times (-10)=-15000$

Hence, the required product of $15\times (-25)\times (-4)\times (-10)$ is $-15000$.