Question

Evaluate the expression. Justify each of your steps.

$15\left(-7\right)\left(4\right)$

Short answer

Value of given expression is $-420$.

Step-by-step solution

Step-1- Concept of commutative property and associative property of multiplication

The commutative property is a math rule says thatthe order in which we multiply numbers does not change the final product.

$A\times B=B\times A$

The associative property of multiplication statesthat the product of three or more numbers remains the same regardless of how the numbers are grouped,

$A\times \left(B\times C\right)=\left(A\times B\right)\times C$.

Step-2-Evaluating given expression

$15\left(-7\right)\left(4\right)$

On simplifying, we get,

$15\left(-7\right)\left(4\right)=\left[15\left(-7\right)\right]\left(4\right)$.

Using Commutative property,

$15\left(-7\right)\left(4\right)=\left[\left(-7\right)15\right]\left(4\right)$.

Using associative property,

$\begin{array}{c}15\left(-7\right)\left(4\right)=\left(-7\right)\left[15\left(4\right)\right]\\ 15\left(-7\right)\left(4\right)=\left(-7\right)\left[60\right]\\ 15\left(-7\right)\left(4\right)=-420\end{array}$

Step-3-Conclusion

Therefore, the value of given expression is $-420$.