Question

Use the distributive property to evaluate the expression.

$6 ( - 2.3 + 3.8 )$

Short answer

$\text{6} ( - \text{2.3} + \text{3.8} ) = 15$.

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

Example: $\text{6} ( - \text{2} + \text{3} ) = \text{6} · (- \text{2} \text{)} + \text{6} · \text{3} \text{=} - 12 + 18 = 6$

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

Distributive Property of Multiplication

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

$\begin{array}{l}\text{6\hspace{0.17em}\hspace{0.17em}}(-\text{\hspace{0.17em}\hspace{0.17em}2.3\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}3.8\hspace{0.17em}\hspace{0.17em}})=\text{\hspace{0.17em}\hspace{0.17em}6\hspace{0.17em}\hspace{0.17em}}·(-\text{\hspace{0.17em}\hspace{0.17em}2.3\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}6\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}3.8\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}-13.8+28.8=15\\ \text{\hspace{0.17em}6\hspace{0.17em}\hspace{0.17em}}(-\text{\hspace{0.17em}\hspace{0.17em}2.3\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}3.8\hspace{0.17em}\hspace{0.17em}})=15\end{array}$