+
Addition
- sum
- plus
- added to
- increased by
- more than
- total
- altogether
- combined
- in all
- gain
- older than
- longer than
Learning supports
Math Word-Problem Translation Guide
Connect common English words and phrases to math operations, symbols, and expressions.
Remember:Keywords are clues—not automatic answers. Read the entire sentence and decide what is happening to the quantities.
Download Printable PDFWhy should I care?
Word Problems Are Translation Problems
You are changing everyday language into math language. Once the expression is written correctly, the calculation is usually much easier.
Words→Math expression→Answer
Main reference chart
Words That Suggest Each Operation
Look for these phrases, but always check how they are used in the complete sentence.
−
Subtraction
- difference
- minus
- subtracted from
- decreased by
- less than
- fewer than
- take away
- remaining
- left
- change
- how many more
- how many fewer
×
Multiplication
- product
- times
- multiplied by
- of
- groups of
- double
- twice
- triple
- three times
- factor
- each group has
- area of
÷
Division
- quotient
- divided by
- split equally
- shared equally
- divided into groups
- per
- ratio
- out of
- each person gets
- average
- how many groups
- unit rate
Read from both directions
Words That Can Change the Order
These phrases are common sources of mistakes. Start with the amount that comes after “than” or “from.”
“5 less than x”
5 − x ✕→x − 5 ✓
Start with x. Then subtract 5.“7 subtracted from y”
7 − y ✕→y − 7 ✓
Seven is being taken from y.“The quotient of 12 and n”
n ÷ 12 ✕→12 ÷ n ✓
With “of A and B,” keep A first.“x divided into 20”
x ÷ 20 ✕→20 ÷ x ✓
Twenty is being separated into groups of x.See the translation
From English to Algebra
Identify the main action, keep the order correct, and build complicated phrases one piece at a time.
Nine more than a number
→x + 9Start with the number, then add 9.A number decreased by four
→x − 4Start with the number, then subtract 4.Three times a number
→3xThree is multiplying the unknown number.The quotient of a number and five
→x ÷ 5Divide the number by 5.Seven less than twice a number
→2x − 7Build 2x first, then subtract 7.Half of a number increased by six
→x/2 + 6Half of x is x ÷ 2, then add 6.More than operations
Equality and Inequality Words
Some phrases tell you how two quantities compare.
Equal
is, equals, is the same as, results in
Greater Than
more than, greater than, exceeds
Less Than
less than, fewer than, below
Greater Than or Equal
at least, no less than, minimum of
Less Than or Equal
at most, no more than, maximum of
Watch out
Common Mistakes
- Translating phrases word by word without understanding the situation.
- Writing “5 less than x” as 5 − x.
- Assuming “each” always means multiplication; it can also describe division or a rate.
- Using “factor” as an instruction when it may only name a number being multiplied.
Reliable strategy
Build It in Small Pieces
- Underline the quantities.
- Circle the action or comparison words.
- Identify what happens first.
- Write the expression.
- Read your expression back in words.
Your turn
10-Question Translation Practice
Translate each phrase into a math expression or inequality. Pay close attention to order.
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