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Q14.

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.$\left(4-10\right) 7$

$\left(4 - 10 \right) 7 = - 42$

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: $\text{12} \text{(7} \text{-} \text{4} \text{)} = \text{12} · \text{7} - \text{12} · \text{4} = 84 - 48 = 36$

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

Distributive Property of Multiplication

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

According to the above property, we can evaluate the expression:

$\begin{array}{l}\left(4\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}10\right)\text{\hspace{0.17em}}7=\text{\hspace{0.17em}\hspace{0.17em}}4\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}7\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}10\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}7\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}28\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}70\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}42\\ \text{\hspace{0.17em}}\left(4\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}10\text{\hspace{0.17em}\hspace{0.17em}}\right)\text{\hspace{0.17em}}7\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}42\end{array}$