Question

Evaluate the expression using the distributive property and mental math.

$- 5 \left(396\right)$

Short answer

$- 5 ( 396 ) = - 1980$.

Step-by-step solution

Step-1 – What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

Step-2 – Distributive Property of Multiplication 

Suppose a, b, and c is three real numbers.

Distributive Property of Multiplication

Property: $-\text{a} \text{(b} - \text{c} \text{)} = (-\text{a} ) · \text{b} - (-\text{a} ) · \text{c}$

Example: $-\text{3} \text{(8} - \text{5} \text{)} = (-\text{3} ) · 8 - (-\text{3} ) · \text{5} = -24+15=- 9$

Step-3:  Use the distributive property to evaluate the expression.

We can write 396 as (400 – 4), to evaluate the expression 7(109), we can use the distributive method of multiplication.

We know that double negative is always positive. $- \text{5} · - \text{4} = + 20$

Distributive Property of Multiplication

Property: $-\text{a} \text{(b} - \text{c} \text{)} = (-\text{a} ) · \text{b} - (-\text{a} ) · \text{c}$

$\begin{array}{l}-5\left(396\right)=-5(400-4)=-5·400+(-5)·(-4)=-2000+20=-1980\\ -5\left(396\right)=-1980\end{array}$