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Answers without the blur. Sign up and see all textbooks for free! Q3.

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 # Evaluate the expression using the distributive property and mental math. $3 \left(96\right)$

$3\left(96\right)=288$.

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.

We can write 96 as 90+ 6, to evaluate the expression 3(96), we can use the distributive method of multiplication.

Distributive Property of Multiplication

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

$\begin{array}{l}3\text{\hspace{0.17em}\hspace{0.17em}}\left(\text{\hspace{0.17em}\hspace{0.17em}}96\text{\hspace{0.17em}\hspace{0.17em}}\right)\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}\left(\text{\hspace{0.17em}\hspace{0.17em}}90\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}6\text{\hspace{0.17em}\hspace{0.17em}}\right)\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}90\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}6\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}270\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}18\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}288\text{\hspace{0.17em}}\\ 3\left(96\right)=288\end{array}$ ### Want to see more solutions like these? 