Free associative property of multiplication worksheets show that moving the brackets never changes a product: (2 × 5) × 7 = 2 × (5 × 7). Sheets show the rule, then put it to work, each with an answer key.
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Grouping, not order
When three numbers are multiplied, it does not matter which pair you multiply first. The numbers stay in the same order and only the brackets move. Common Core 3.OA.5 gives the example 3 × 5 × 2, worked as 15 × 2 or as 3 × 10.
Choosing the easy pair
An associative property of multiplication worksheet is mental math practice. In 7 × 25 × 4, left to right means 175 × 4, but grouping 25 × 4 first gives 7 × 100 = 700. The same move explains 6 × 40 = (6 × 4) × 10 = 240 and halving and doubling: 16 × 25 = 8 × 50 = 400.
Print Work it both ways first. Until a pupil has seen both routes reach 70, the shortcut sheets look like a trick.
On Find the pair that makes 100, have pupils circle the pair before they multiply: 25 × 4, 50 × 2 or 20 × 5.
Questions and answers
What is the difference between the associative and commutative properties?
Commutative is about order: 3 × 8 = 8 × 3. Associative is about grouping: (3 × 8) × 2 = 3 × (8 × 2). Many shortcuts use both, and Reorder and regroup asks pupils to name the property behind each step.
Which grade learns the associative property of multiplication?
Grade 3 in the Common Core, under 3.OA.5, as a strategy. It returns in grade 5 for volume (5.MD.5a) and in grade 6 for expressions with letters (6.EE.3). Texas names the associative property as a strategy in 3.4(G) and 4.4(D).
Does the associative property work for subtraction or division?
No. (5 − 3) − 2 = 0 but 5 − (3 − 2) = 4, and (4 ÷ 2) ÷ 2 = 1 but 4 ÷ (2 ÷ 2) = 4. Addition and multiplication are the two school operations where brackets move freely.
All 14 sheet types
See that it holds 4
Fill the missing factor(2 × 5) × 7 = 2 × (___ × 7), so the blank is 5. The three numbers keep their order on both sides, which is the clue pupils learn to use.
Move the bracketsGiven (4 × 3) × 2, the pupil writes 4 × (3 × 2), then checks that both come to 24. Writing the second grouping is harder than recognizing it, so this sheet follows the fill-in one.
True or false: regrouped factors(3 × 2) × 4 = 3 × (2 × 4) is true: both sides are 24. (3 × 2) × 4 = 3 × (2 + 4) is false, since the right side is 18. Other false lines change one of the three numbers.
Work it both ways(2 × 5) × 7 = 10 × 7 = 70 and 2 × (5 × 7) = 2 × 35 = 70. The page opens on this sheet: each problem is worked with the brackets in both places, and the two answers must match.
Show all 14 sheet types (10 more)
Group to make it easier 8
Find the pair that makes 103 × 5 × 2 = 3 × (5 × 2) = 3 × 10 = 30. Left to right it is 15 × 2, which is fine, but pupils who look for the 5 and the 2 first never need to work it out. This is the Common Core's own grade 3 example.
Find the pair that makes 1007 × 25 × 4 = 7 × (25 × 4) = 7 × 100 = 700. Left to right means 175 × 4. The pairs to spot are 25 × 4, 50 × 2 and 20 × 5.
Four factors in a row2 × 5 × 4 × 25 = (2 × 5) × (4 × 25) = 10 × 100 = 1,000. No number changes place. Two pairs of brackets do all the work.
Halve one and double the other16 × 25 = (8 × 2) × 25 = 8 × (2 × 25) = 8 × 50 = 400. Halving 16 and doubling 25 keeps the product the same, because the 2 has only moved from one bracket to the other.
Multiply by a multiple of 106 × 40 = 6 × (4 × 10) = (6 × 4) × 10 = 24 × 10 = 240. The shortcut of doing the fact and writing a zero is this regrouping, written out once so pupils see why it works.
Reorder and regroup5 × 7 × 2 = 7 × 5 × 2 = 7 × (5 × 2) = 7 × 10 = 70. The friendly pair is not side by side here, so the first step is a swap (commutative) and the second is a regrouping (associative). Pupils label each step.
Split a factor then regroup15 × 6 = 15 × (2 × 3) = (15 × 2) × 3 = 30 × 3 = 90. Breaking 6 into 2 × 3 lets the 15 meet the 2 first and turns the problem into a round number times 3.
Use the 4s to get the 8s8 × 6 = (2 × 4) × 6 = 2 × (4 × 6) = 2 × 24 = 48. Doubling a fact you know works from the 2s to the 4s, the 4s to the 8s and the 3s to the 6s.
Where it does not work 2
Associative or commutative?3 × 8 = 8 × 3 changes the order, so it is commutative. (3 × 8) × 2 = 3 × (8 × 2) keeps the order and moves the brackets, so it is associative. Pupils write A or C beside each equation.
Same or different: all four operations(5 − 3) − 2 = 0 but 5 − (3 − 2) = 4, and (4 ÷ 2) ÷ 2 = 1 but 4 ÷ (2 ÷ 2) = 4. Pupils work both groupings and circle Same or Different. Addition and multiplication always come out the same. On this sheet subtraction and division never do.
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 (rearranging the parentheses does not change the result), its difference from commutativity, and subtraction and division as operations that are not associative were checked 2026-09-18 against https://en.wikipedia.org/wiki/Associative_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.5 with its example 3 × 5 × 2 (found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30) and the footnote that students need not use formal terms, 3.NBT.3 (one-digit numbers times multiples of 10 such as 9 × 80), 4.NBT.5, 5.MD.5a (threefold whole-number products as volumes, to represent the associative property), 5.NBT.7 and 6.EE.3. 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(G) and 4.4(D) name the associative property as a strategy. That file stops at grade 5, so the grade 6 item carries a Common Core number only. Fix pass 2026-09-20: 3.OA.5 with its example, 5.MD.5a and 6.EE.3 were read again in the national copy, and Texas 3.4(G) and 4.4(D) in the current chapter 111 text, that day. Licence: own work