topic badge

2.07 Translating expressions and equations


Mathematics is often referred to as a language. That's why we can take practical situations and translate them into algebraic expressions or equations and vice versa.

Translating phrases into expressions

In algebra, the variables that we write represent unknown values. It is these unknown values that we usually try to find.

Any operation can be used in algebraic expressions - in fact, any combination of operations can be used. To be able to turn written expressions into algebra, we can look for certain keywords to indicate addition, subtraction, multiplication, or division.

Addition Subtraction Multiplication Division


the sum of

increased by


more than

added to


the difference of

decreased by

fewer than

less than

subtracted from


the product of

multiplied by



groups/lots of

divided by

the quotient of

separated into equal parts



The letters $x$x and $n$n are popular choices for the unknown amount in a number sentence. However, if a letter is not specified, we can use any letter to represent the unknown number in an expression. 


We can add or multiply in any order. However, for subtraction and division, the order is important.

For example, "$5$5 less than a number" is written as $n-5$n5, not $5-n$5n.

Similarly, "a number divided by $8$8" is written as $n\div8$n÷​8 or $\frac{n}{8}$n8 not $\frac{8}{n}$8n.


Translating sentences into equations

An equation is a type of mathematical sentence that sets two expressions equal. It means that the two expressions have the same value. As with our four operations, we can look for key phrases that indicate equality.




amounts to

Worked example

Question 1

The sum of a number and $24$24 is $35$35. Set-up an equation for this scenario.

Think: We have an unknown, "the number", so let's call "the number" $x$x. We should note some keywords which can help us after we replace "a number" with $x$x. An equation must have an equals sign, unlike an expression which will not.

Do: Using our keywords, we can translate to an equation.



Practice questions

Question 1

What does the algebraic expression $96q$96q represent?

  1. 96 times the number represented by q


    the quotient of the number represented by q and 96


    96 less than the number represented by q


    96 more than the number represented by q


Question 2

Write an equation in simplest form for:

$y$y is $18$18 times $k$k.

Question 3

Roxanne has been out picking flowers, and has $40$40 in total. When she returns, she puts them in $5$5 different vases.

If she puts $p$p flowers in each vase, rewrite the following sentence using algebra:

  1. "There are $5$5 groups of $p$p flowers, which make $40$40 in total."



Write, read, and evaluate expressions in which letters stand for numbers.


Write expressions that record operations with numbers and with letters standing for numbers.


Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.


Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

What is Mathspace

About Mathspace