Keywords for Word Problems: The Complete List (Addition, Subtraction, Multiplication & Division)

This page lists the words that signal each operation in a maths word problem, organised by operation, with worked examples. Common traps are flagged — including the single most-missed word in all of word-problem maths.

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The "Per Trap" — the most missed signal word

"Per" usually signals division (miles per hour = total ÷ hours), but signals multiplication when you're applying a known rate (3 miles per lap × 4 laps = 12 miles). Always check: are you finding a rate (÷) or using one (×)?

➕ Addition

See the full Addition list + more examples →

sum total altogether combined in all both increased by plus added to all together how many in all grand total

Example: Maria has 8 stickers. Her friend gives her 5 more. How many stickers does Maria have in all?

Signal word: "in all"

✓ 8 + 5 = 13 stickers

➖ Subtraction

See the full Subtraction list + more examples →

difference fewer less than remain left how many more decreased by minus take away subtracted from reduced by how much taller/shorter/longer

Example: A parking lot has 24 cars. 9 cars leave. How many cars remain?

Signal word: "remain"

✓ 24 − 9 = 15 cars

✖️ Multiplication

See the full Multiplication list + more examples →

times product each every twice double triple of (fractions/%) groups of multiplied by per (rate contexts) for every as many as

Example: A classroom has 6 tables. Each table has 4 chairs. How many chairs are there in total?

Signal word: "each"

✓ 6 × 4 = 24 chairs

➗ Division

See the full Division list + more examples →

split share equally per (rate/unit) average quotient divided by equal groups how many each cut into distributed evenly out of ratio of

Example: 24 cookies are shared equally among 6 friends. How many cookies does each friend get?

Signal word: "shared equally"

✓ 24 ÷ 6 = 4 cookies each

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This page covers the essentials — the full pack has 129 keywords

Plus the 3-step Word Problem Decoder and 4 mental math shortcuts. Printable PDF, instant download.

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Quick-Reference Table

All ~50 keywords at a glance — built for screenshotting and printing.

➕ Addition	➖ Subtraction	✖️ Multiplication	➗ Division
sum	difference	times	split
total	fewer	product	share equally
altogether	less than	each	per (rate/unit)
combined	remain	every	average
in all	left	twice	quotient
both	how many more	double	divided by
increased by	decreased by	triple	equal groups
plus	minus	of (fractions/%)	how many each
added to	take away	groups of	cut into
all together	subtracted from	multiplied by	distributed evenly
how many in all	reduced by	per (rate contexts)	out of
grand total	how much taller/shorter/longer	for every	ratio of
		as many as

Frequently Asked Questions

What are signal words in math?

Words or phrases in a word problem that indicate which operation to use — e.g., "total" signals addition, "left" signals subtraction, "each" often signals multiplication, and "shared equally" signals division.

How do I know if a word problem is multiplication or division?

Look for whether you're combining equal groups (multiply) or splitting a total into equal groups (divide). "Per," "each," and "groups of" are common cues, but context matters — see the Per Trap below.

What does "per" mean in a word problem?

"Per" almost always signals a rate. When you're finding the rate (miles per hour = total ÷ hours), you divide. When you're applying a known rate (3 miles per lap × 4 laps), you multiply. This is the single most-missed signal word — covered in depth in the full pack.

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