7.5 Whole numbers: translating words to mathematical symbols

${\displaystyle \underset{9}{\underbrace{\text{Nine}}}\underset{+}{\underbrace{\text{more than}}}\underset{x}{\underbrace{\text{some number.}}}}$

Translation: ${\displaystyle 9+x}$ .

${\displaystyle \underset{18}{\underbrace{\text{Eighteen}}}\underset{-}{\underbrace{\text{minus}}}\underset{x}{\underbrace{\text{a number.}}}}$

Translation: ${\displaystyle \text{18}-x}$ .

${\displaystyle \underset{\mathrm{y}}{\underbrace{\text{A quantity}}}\underset{-}{\underbrace{\text{less}}}\underset{5}{\underbrace{\text{five.}}}}$

Translation: ${\displaystyle y-5}$ .

${\displaystyle \underset{4}{\underbrace{\text{Four}}}\underset{\cdot }{\underbrace{\text{times}}}\underset{x}{\underbrace{\text{a number}}}\underset{=}{\underbrace{\text{is}}}\underset{\mathrm{16}}{\underbrace{\text{sixteen.}}}}$

Translation: ${\displaystyle 4x=\text{16}}$ .

${\displaystyle \underset{\frac{1}{5}}{\underbrace{\text{One fifth}}}\underset{\cdot }{\underbrace{\text{ of}}}\underset{n}{\underbrace{\text{ a number}}}\underset{=}{\underbrace{\text{ is}}}\underset{\mathrm{30}}{\underbrace{\text{ thirty.}}}}$

Translation: ${\displaystyle \frac{1}{5}n=\text{30}}$ , or ${\displaystyle \frac{n}{5}=\text{30}}$ .

${\displaystyle \underset{5}{\underbrace{\text{ Five}}}\underset{\cdot }{\underbrace{\text{ times}}}\underset{x}{\underbrace{\text{ a number}}}\underset{=}{\underbrace{\text{ is}}}\underset{2}{\underbrace{\text{ two}}}\underset{+}{\underbrace{\text{ more than}}}\underset{2\cdot }{\underbrace{\text{ twice}}}\underset{x}{\underbrace{\text{ the number.}}}}$

Translation: ${\displaystyle 5x=2+2x}$ .

Sometimes the structure of the sentence indicates the use of grouping symbols. We’ll be alert for commas . They set off terms.

${\displaystyle \underset{(x}{\underbrace{\text{A number}}}\underset{÷}{\underbrace{\text{divided by}}}\underset{4)}{\underbrace{\text{four,}}}\underset{-}{\underbrace{\text{minus}}}\underset{6}{\underbrace{\text{six,}}}\underset{=}{\underbrace{\text{is}}}\underset{\mathrm{12}}{\underbrace{\text{twelve}}}}$

Translation: ${\displaystyle \frac{x}{4}-6=\text{12}}$ .

Some phrases and sentences do not translate directly. We must be careful to read them properly. The word from often appears in such phrases and sentences. The word from means “a point of departure for motion.” The following translation will illustrate this use.

Translation: ${\displaystyle x-\text{20}}$ .

The word from indicated the motion (subtraction) is to begin at the point of “some number.”

Ten less than some number. Notice that less than can be replaced by from .

Ten from some number.

Translation: ${\displaystyle x-\text{10}}$ .