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

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## Translate an english phrase to an algebraic expression

In the last section, we listed many operation symbols that are used in algebra, then we translated expressions and equations into English phrases and sentences. Now we’ll reverse the process. We’ll translate English phrases into algebraic expressions. The symbols and variables we’ve talked about will help us do that. [link] summarizes them.

Operation Phrase Expression
the sum of $a$ and b
$a$ increased by b
b more than $a$
the total of $a$ and b
b added to $a$
$a+b$
Subtraction $a$ minus b
the difference of $a$ and b
$a$ decreased by b
b less than $a$
b subtracted from $a$
$a-b$
Multiplication $a$ times b
the product of $a$ and b
twice $a$
$a·b,ab,a\left(b\right),\left(a\right)\left(b\right)$

2 a
Division $a$ divided by b
the quotient of $a$ and b
the ratio of $a$ and b
b divided into $a$
$a÷b,a\text{/}b,\frac{a}{b},b\overline{)a}$

Look closely at these phrases using the four operations:

Each phrase tells us to operate on two numbers. Look for the words of and and to find the numbers.

Translate each English phrase into an algebraic expression: the difference of $17x$ and $5$ the quotient of $10{x}^{2}$ and $7.$

## 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 $10{x}^{2}\text{/}7\phantom{\rule{0.2em}{0ex}}\text{or}\phantom{\rule{0.2em}{0ex}}\frac{10{x}^{2}}{7}.$

Translate the English phrase into an algebraic expression: the difference of $14{x}^{2}$ and 13 the quotient of 12 x and 2.

$14{x}^{2}-13$ $12x÷2$

Translate the English phrase into an algebraic expression: the sum of $17{y}^{2}$ and $19$ the product of $7$ and $y.$

$17{y}^{2}+19$ 7 y

How old will you be in eight years? What age is eight more years than your age now? Did you add 8 to your present age? Eight “more than” means 8 added to your present age. How old were you seven years ago? This is 7 years less than your age now. You subtract 7 from your present age. Seven “less than” means 7 subtracted from your present age.

Translate the English phrase into an algebraic expression: Seventeen more than y Nine less than $9{x}^{2}.$

## Solution

1. The key words are more than. They tell us the operation is addition. More than means “added to.”
$\begin{array}{}\\ \hfill \text{Seventeen more than}\phantom{\rule{0.2em}{0ex}}y\hfill \\ \hfill \text{Seventeen added to}\phantom{\rule{0.2em}{0ex}}y\hfill \\ \hfill y+17\hfill \end{array}$
2. The key words are less than . They tell us to subtract. Less than means “subtracted from.”
$\begin{array}{}\\ \\ \\ \hfill \phantom{\rule{5em}{0ex}}\text{Nine less than}\phantom{\rule{0.2em}{0ex}}9{x}^{2}\hfill \\ \hfill \phantom{\rule{5em}{0ex}}\text{Nine subtracted from}\phantom{\rule{0.2em}{0ex}}9{x}^{2}\hfill \\ \hfill \phantom{\rule{5em}{0ex}}9{x}^{2}-9\hfill \end{array}$

Translate the English phrase into an algebraic expression: Eleven more than $x$ Fourteen less than $11a.$

$x+11$ $11a-14$

Translate the English phrase into an algebraic expression: 13 more than z 18 less than 8 x .

$z+13$ $8x-18$

Translate the English phrase into an algebraic expression: five times the sum of m and n the sum of five times m and n .

## 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.)
$\begin{array}{}\\ \\ \hfill \text{five times the sum of}\phantom{\rule{0.2em}{0ex}}m\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}n\hfill \\ \hfill 5\phantom{\rule{0.2em}{0ex}}\left(m+n\right)\hfill \end{array}$
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 .
$\begin{array}{c}\hfill \text{the sum}\phantom{\rule{0.2em}{0ex}}\text{of}\phantom{\rule{0.2em}{0ex}}\text{five times}\phantom{\rule{0.2em}{0ex}}m\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}n\hfill \\ \hfill 5m+n\hfill \end{array}$

Translate the English phrase into an algebraic expression: four times the sum of p and q the sum of four times p and q .

$4\left(p+q\right)$ $4p+q$

what is the answer for this 3×9+28÷4-8
315
lashonna
how do you do xsquard+7x+10=0
What
(x + 2)(x + 5), then set each factor to zero and solve for x. so, x = -2 and x = -5.
bruce
I skipped it
What
In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the percent decrease.
how do i set this up
Jenise
25%
Melissa
25 percent
Muzamil
950,000 - 712,500 = 237,500. 237,500 / 950,000 = .25 = 25%
Melissa
I've tried several times it won't let me post the breakdown of how you get 25%.
Melissa
Subtract one from the other to get the difference. Then take that difference and divided by 950000 and you will get .25 aka 25%
Melissa
Finally 👍
Melissa
one way is to set as ratio: 100%/950000 = x% / 712500, which yields that 712500 is 75% of the initial 950000. therefore, the decrease is 25%.
bruce
twenty five percent...
Jeorge
thanks melissa
Jeorge
950000-713500 *100 and then divide by 950000 = 25
Muzamil
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
6t+3
Melissa
6t +3
Bollywood
Tricia got a 6% raise on her weekly salary. The raise was $30 per week. What was her original salary? Iris Reply let us suppose her original salary is 'm'. so, according to the given condition, m*(6/100)=30 m= (30*100)/6 m= 500 hence, her original salary is$500.
Simply
28.50
Toi
thanks
Jeorge
How many pounds of nuts selling for $6 per pound and raisins selling for$3 per pound should Kurt combine to obtain 120 pounds of trail mix that cost him $5 per pound? Valeria Reply Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost$8 per square foot and decorator tiles that code $20 per square foot. How many square feet of each tile should she use so that the overal cost of he backsplash will be$10 per square foot?
I need help with maths can someone help me plz.. is there a wats app group?
WY need
Fernando
How did you get $750? Laura Reply if y= 2x+sinx what is dy÷dx formon25 Reply does it teach you how to do algebra if you don't know how Kate Reply Liam borrowed a total of$35,000 to pay for college. He pays his parents 3% interest on the $8,000 he borrowed from them and pays the bank 6.8% on the rest. What average interest rate does he pay on the total$35,000? (Round your answer to the nearest tenth of a percent.)
exact definition of length by bilbao
the definition of length
literal meaning of length
francemichael
exact meaning of length
francemichael
exact meaning of length
francemichael
how many typos can we find...?
5
Joseph
In the LCM Prime Factors exercises, the LCM of 28 and 40 is 280. Not 420!