• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

Suggested languages for you:

Americas

Europe

Q41.

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.$5 \left( 7 + 2 + 4 \right)$

$5 \left(7 + 2 + 4 \right) = 65$.

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

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

Distributive Property of Multiplication

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

$\begin{array}{l}5\text{\hspace{0.17em}\hspace{0.17em}}\left(7\text{\hspace{0.17em}}+\text{\hspace{0.17em}}2\text{\hspace{0.17em}}+\text{\hspace{0.17em}}4\text{\hspace{0.17em}}\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}5\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}7\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}5\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}2\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}5\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}4\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}35\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}10\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}20\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}65\\ \\ 5\text{\hspace{0.17em}\hspace{0.17em}}\left(7\text{\hspace{0.17em}}+\text{\hspace{0.17em}}2\text{\hspace{0.17em}}+\text{\hspace{0.17em}}4\text{\hspace{0.17em}}\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}65\end{array}$