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Q13.

Expert-verified
Found in: Page 73

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Use the distributive property to evaluate the expression.$5 \left(9-3\right)$

$5 \left(9 - 3 \right) = 30$.

See the 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: $8 \text{(12} - \text{4} \text{)} = \text{8} · \text{12} - \text{8} · \text{4} = 96 - 32 = 64$

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

Distributive Property of Multiplication

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

$\begin{array}{l}5\text{\hspace{0.17em}\hspace{0.17em}}\left(9\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}3\right)\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}5\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}9\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}5\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}45\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}15\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}30\\ 5\text{\hspace{0.17em}\hspace{0.17em}}\left(9\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}\right)\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}30\end{array}$