A. Translating Words into Math

Translating words into mathematical statements and operations can be challenging.

The following charts summarize common relationships. Keep in mind that there is no way to summarize every possibility. As such, common sense and attention to the context must be applied.

Statement Math Symbols/
Operation
total of, add, sum of, combined, together +
subtraction, subtract, difference between/of, decreased by, minus โˆ’
multiplication, product, of, times ร—
quotient of, ratio of, out of รท
equals, is, will be, gives =
an unknown number/measure/variable, a certain number x, T, r, ฮธ, etc.
5 more than a number x + 5 or d + 5
25 times a number 25x or 25h
Starlight's present age a
Starlight's age 5 years ago a โˆ’ 5
Starlight's age 7 years from now a + 7

If you know a relationship between two or more values in a problem, you may be able to write them all using the same variable.

Statement Math Symbols
Three consecutive numbers x, x + 1, x + 2
Three consecutive even numbers 2x, 2x + 2, 2x + 4
Three consecutive odd numbers 2x + 1, 2x + 3, 2x + 5
The sum of two numbers is 99. x + (99 โˆ’ x) = 99
The two numbers are x and 99 โˆ’ x.
The sum of the squares of two consecutive numbers
A certain number of nickels and their value in dollars n, 0.05n
Four less than triple a number 3w โˆ’ 4
A mother is 5 times as old as her son. 5s
Robert weights 3 kg more than Abdul. 3 + a
A rectangle with a length 3 times the width Length = 3w
Width = w