Question

Use the distributive property and mental math to simplify the expression. $$ \begin{aligned} 9(1.95) &=9(?-2) \\ &=? \end{aligned}$$

Short answer

The simplified expression is 17.55.

Step-by-step solution

Break Down the Problem

This problem requires use of the distributive property, which states that for all real numbers a, b, and c, \(a(b + c) = ab + ac\) and \(a(b - c) = ab - ac\). Here, represent 1.95 as a difference from 2, so instead of 1.95 use 2-0.05.

Apply the Distributive Property

Apply the distributive property to the modified expression. Instead of calculating \(9 \times 1.95\), calculate \(9 \times (2 - 0.05)\). This becomes \(9 \times 2 - 9 \times 0.05\)

Perform Arithmetic

Arithmetic operation can be performed without pen and paper or a calculator. Calculate \(9 \times 2\) to get 18, and \(9 \times 0.05\) to get 0.45.

Subtract to Find Final Answer

Subtract the second result from the first to find the final answer. Hence, \(18 - 0.45 = 17.55\).