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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 |
---|---|---|
Addition |
a plus
b
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 $a$ |
$a\xb7b,ab,a(b),(a)(b)$
2 a |
Division |
$a$ divided by
b
the quotient of $a$ and b the ratio of $a$ and b b divided into $a$ |
$a\xf7b,a\text{/}b,\frac{a}{b},b\overline{)a}$ |
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 $7.$
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.
ⓐ $14{x}^{2}-13$ ⓑ $12x\xf72$
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 $9{x}^{2}.$
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 .
There are two operation words— times tells us to multiply and sum tells us to add.
Translate the English phrase into an algebraic expression: ⓐ four times the sum of p and q ⓑ the sum of four times p and q .
ⓐ $4\left(p+q\right)$ ⓑ $4p+q$
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