Commutative Property of Multiplication Worksheets

All 6 sheet types

Turnaround facts 3

Fill the blank turnaround fact 3 × 8 = ___ × 3, so the blank is 8. The blank moves from line to line: sometimes a factor on the right, sometimes one on the left, sometimes the product.
True or false: swapped factors 6 × 4 = 4 × 6 is true. 6 × 4 = 6 + 4 is false (24 against 10), and so is 6 × 4 = 4 × 5 (24 against 20). Half the lines are false, in those two ways.
Write the turnaround fact Given 7 × 9 = 63, the pupil writes 9 × 7 = 63. Squares such as 6 × 6 = 36 are left out, because their turnaround is the same fact.

Learn fewer facts 1

Harder table from an easier one If 2 × 7 = 14 is known, then 7 × 2 = 14 is known too. The first half of the 7 times table is already in the 2s, 3s, 4s, 5s and 6s. Each line gives the easy fact and asks for its partner in the harder table.

Where order does matter 1

Does the order matter? Four operations 3 + 4 = 4 + 3 and 2 × 5 = 5 × 2, but 5 − 3 is 2 while 3 − 5 is not, and 8 ÷ 2 is 4 while 2 ÷ 8 is not. Pupils work out both orders where they can and circle Same or Different.

Three factors 1

Reorder three factors 4 × 9 × 25 = 4 × 25 × 9 = 100 × 9 = 900. Swapping the 9 and the 25 brings the friendly pair together. Only the order changes on this sheet.

How it works

These commutative property of multiplication worksheets all make one point. Swap the two factors and the product stays the same, so 3 × 8 = 8 × 3 = 24. The sheets drill turnaround facts and test where order does matter.

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Why the order does not matter

Turn a 3 by 8 array a quarter turn and it becomes 8 by 3, with the same 24 dots. At grade 3 that picture is the proof. The sheets here practice the rule in equations and do not draw the array. Common Core 3.OA.5 says pupils need not use the formal name, so this page says turnaround facts too.

Half the chart for free

A 10 by 10 printable multiplication chart has 100 boxes but only 55 facts to learn: 10 squares on the diagonal and 45 turnaround pairs. A commutative property of multiplication worksheet can show that saving line by line. Harder table from an easier one, under Learn fewer facts, gives 2 × 7 = 14 and asks for 7 × 2.

Turn a 3 by 8 array on the board first. A pupil who has watched it turn has the reason, not only the rule.
In long multiplication, put the smaller number underneath: 243 × 6 is one row of working, 6 × 243 is three.

Questions and answers

What is the commutative property of multiplication?

Changing the order of the factors does not change the product: a × b = b × a. Common Core 3.OA.5 gives the example that if 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.

Is 3 × 8 the same as 8 × 3?

The product is the same, 24. The picture is not. The Common Core reads 5 × 7 as 5 groups of 7 (3.OA.1), so 3 × 8 is 3 groups of 8. In a word problem the order still says which picture to draw.

Does the commutative property work for subtraction and division?

No. 5 − 3 is 2 but 3 − 5 is not, and 8 ÷ 2 is 4 but 2 ÷ 8 is not. Only addition and multiplication commute. The sheet Does the order matter? Four operations puts all four on one page.

Notes

Sheets, puzzles and cards made here are practice material. They are not an assessment, they follow no single curriculum, and they do not replace a specialist's advice about a child's handwriting or learning.

More notes about this page

Facts on this page were checked against standard reference sources. If you spot a mistake, please tell us through the contact page.

How this list was compiled: Sheet types, wording and worked examples are own work; every worked example was computed twice by script on 2026-09-18. The statement of the property (the result stays the same when the operands swap order), subtraction and division as operations that are not commutative, the first recorded use of the term by François Servois in 1814, its origin in the French commutatif and commuter (to exchange or switch), and Euclid assuming the property for multiplication in the Elements were checked 2026-09-18 against https://en.wikipedia.org/wiki/Commutative_property. Standards wording checked 2026-09-18 against the full text of the Common Core State Standards for Mathematics (national copy, https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf, read again 2026-09-20): 3.OA.1 (5 × 7 as 5 groups of 7), 3.OA.3, 3.OA.5 with its example (if 6 × 4 = 24 is known, then 4 × 6 = 24 is also known) and the footnote that students need not use formal terms, 3.OA.7, 3.OA.9 (patterns in the multiplication table), 4.NBT.5, 6.RP.3c (a percent as a rate per 100) and 6.EE.2a. Texas Essential Knowledge and Skills, 19 TAC Chapter 111 Subchapter A, adopted 2012 (https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111a.pdf): 3.4(E) (repeated addition, equal-sized groups, arrays, equal jumps on a number line, skip counting) and 3.4(G) and 4.4(D), which name the commutative property as a strategy. That file stops at grade 5, so grade 6 items carry Common Core numbers only. The chart counts are arithmetic: an n by n chart has n squares on the diagonal and n × (n − 1) ÷ 2 turnaround pairs, which gives 55 facts for 10 by 10 and 78 for 12 by 12. Fix pass 2026-09-20: the question on where the word commutative comes from was cut from the page, so the Servois and Euclid facts above are no longer published; one sentence that said how often one order is easier was reworded; 3.OA.1 and 3.OA.5 with its footnote were read again in the national copy that day. Licence: own work