Question

Evaluate the expression using the distributive property and mental math.

$7 ( 109 )$

Short answer

$7 (109 ) = 763$.

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

Example: $\text{12} \text{(3} \text{+} \text{4} \text{)} = \text{12} · \text{3} + \text{12} · \text{4} = 36 + 48 = 84$

Step-3:  Evaluate the expression using the distributive property and mental math.        

We can write 109 as (100 + 9), to evaluate the expression 7(109), we can use the distributive method of multiplication.

Distributive Property of Multiplication

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

$\begin{array}{l}7\left(109\right)=4(100+9)=7·100+7·9=700+63=763\\ 7\left(109\right)=763\end{array}$