1.2 Use the language of algebra  (Page 6/18)

Solution

1. ⓐ The key word is difference , which tells us the operation is subtraction. Look for the words of and and t o find the numbers to subtract.
   
   
   
2. ⓑ The key word is “quotient,” which tells us the operation is division.

This can also be written $10x^2\text{/}7\text{or}\frac{10x^2}{7}.$

Solution

1. ⓐ The key words are more than. They tell us the operation is addition. More than means “added to.”
   
   $\begin{array}{}\\ \hfill \text{Seventeen more than}y\hfill \\ \hfill \text{Seventeen added to}y\hfill \\ \hfill y+17\hfill \end{array}$
2. ⓑ The key words are less than . They tell us to subtract. Less than means “subtracted from.”
   
   $\begin{array}{}\\ \\ \\ \hfill \text{Nine less than}9x^2\hfill \\ \hfill \text{Nine subtracted from}9x^2\hfill \\ \hfill 9x^2-9\hfill \end{array}$

Solution

There are two operation words— times tells us to multiply and sum tells us to add.

1. ⓐ Because we are multiplying 5 times the sum we need parentheses around the sum of m and n , $\left(m+n\right).$ This forces us to determine the sum first. (Remember the order of operations.)
   
   $\begin{array}{}\\ \\ \hfill \text{five times the sum of}m\text{and}n\hfill \\ \hfill 5(m+n)\hfill \end{array}$
2. ⓑ To take a sum, we look for the words “of” and “and” to see what is being added. Here we are taking the sum of five times m and n .
   
   $\begin{array}{c}\hfill \text{the sum}\text{of}\text{five times}m\text{and}n\hfill \\ \hfill 5m+n\hfill \end{array}$