Question

Evaluate the expression using the distributive property and mental math. $2\left(8.95\right)$

Short answer

$2\left(8.95\right)=17.90$

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:$\text{a\hspace{0.17em}\hspace{0.17em}(b\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}b\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}\hspace{0.17em}}$

Example: $\text{12\hspace{0.17em}\hspace{0.17em}(3\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}12\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}3\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}12\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em}}=36+48=84$

.:  Evaluate the expression using the distributive property and mental math.       

We can write 8.95 as 8.90 + 0.05, to evaluate the expression 2(8.95), we can use the distributive method of multiplication.

Distributive Property of Multiplication

Property:$\text{a\hspace{0.17em}\hspace{0.17em}(b\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}b\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}\hspace{0.17em}}$

$\begin{array}{l}2\left(8.95\right)=2(8.90+0.05)=2·8.90+2·0.05=17.80+0.1=17.90\\ 2\left(8.95\right)=17.90\end{array}$