Properties of Multiplication Worksheet

Pupils name the property, then finish the equation: press Make a new sheet or pick another sheet type, then Print.

Sheet type

Problems

Answer key

12 problems. Name it, then use it. Sheet 1TJS1J, with its answer key.

Name it, then use it

Name Date Score / 12

The first step of each problem is done. Write the name of the property it uses, then finish the working.

1.4 × 20 × 25 = 4 × 25 × 20Property: _____________= ________ × 20 = ________
2.(3 × 4) × 25 = 3 × (4 × 25)Property: _____________= 3 × ________ = ________
3.2 × 25 = 2 × (20 + 5)Property: _____________= _____ + _____ = ________
4.25 × 11 × 4 = 25 × 4 × 11Property: _____________= ________ × 11 = ________
5.(6 × 2) × 50 = 6 × (2 × 50)Property: _____________= 6 × ________ = ________
6.5 × 24 = 5 × (20 + 4)Property: _____________= ________ + _____ = ________
7.(7 × 2) × 5 = 7 × (2 × 5)Property: _____________= 7 × _____ = ________
8.(9 × 2) × 5 = 9 × (2 × 5)Property: _____________= 9 × _____ = ________
9.3 × 27 = 3 × (20 + 7)Property: _____________= _____ + _____ = ________
10.5 × 25 × 20 = 5 × 20 × 25Property: _____________= ________ × 25 = ________
11.2 × 24 = 2 × (20 + 4)Property: _____________= _____ + _____ = ________
12.2 × 26 × 50 = 2 × 50 × 26Property: _____________= ________ × 26 = ________

Sheet 1TJS1J · Made at homeroomtools.com

Answer key. Name it, then use it

1.4 × 20 × 25 = 4 × 25 × 20Property: commutative= 100 × 20 = 2,000
2.(3 × 4) × 25 = 3 × (4 × 25)Property: associative= 3 × 100 = 300
3.2 × 25 = 2 × (20 + 5)Property: distributive= 40 + 10 = 50
4.25 × 11 × 4 = 25 × 4 × 11Property: commutative= 100 × 11 = 1,100
5.(6 × 2) × 50 = 6 × (2 × 50)Property: associative= 6 × 100 = 600
6.5 × 24 = 5 × (20 + 4)Property: distributive= 100 + 20 = 120
7.(7 × 2) × 5 = 7 × (2 × 5)Property: associative= 7 × 10 = 70
8.(9 × 2) × 5 = 9 × (2 × 5)Property: associative= 9 × 10 = 90
9.3 × 27 = 3 × (20 + 7)Property: distributive= 60 + 21 = 81
10.5 × 25 × 20 = 5 × 20 × 25Property: commutative= 100 × 25 = 2,500
11.2 × 24 = 2 × (20 + 4)Property: distributive= 40 + 8 = 48
12.2 × 26 × 50 = 2 × 50 × 26Property: commutative= 100 × 26 = 2,600

Sheet 1TJS1J · Made at homeroomtools.com

Next step Practice the distributive property alone Make a plain times tables sheet

How it works

A free properties of multiplication worksheet earns its place once pupils know each property and must tell them apart. This page mixes all five: commutative, associative, distributive, identity (× 1) and zero (× 0). Answer key on page 2.

Read the full guide

What the standards call them

Table 3 of the Common Core glossary names the commutative, associative and distributive properties and the multiplicative identity property of 1. It has no row for multiplying by 0, so zero property is a textbook name. Texas names the first three in 3.4(G) and 4.4(D).

Addition beside multiplication

The commutative and associative properties of addition come first, in grade 1 (standard 1.OA.3). As a properties of addition and multiplication worksheet, print Zero or one? Mixed: 62 + 0 = 62 sits beside 62 × 1 = 62 and 62 × 0 = 0, so pupils have to read the sign.

Start with Name the property, 3 choices. Add identity and zero later: × 1 and × 0 lines are quick marks that hide confusion elsewhere.
Have pupils work out both sides of every false equation. Seeing 42 on the left and 32 on the right teaches more than a cross.

Questions and answers

What is the difference between the commutative and associative properties?

Commutative is about order: 7 × 4 = 4 × 7. Associative is about grouping, with the order left alone: (2 × 5) × 3 = 2 × (5 × 3). Subtraction has neither, since 12 − 5 and 5 − 12 differ.

Is a properties of multiplication worksheet grade 3 work?

Partly. Common Core 3.OA.5 asks third graders to use the properties as strategies, and its footnote says they need not use formal terms. Finish the equation, names not needed suits them: 3 × 5 × 2 = 3 × 10 = 30.

Is the zero property really a property?

It is a true rule, though the Common Core's table omits it. It follows from the distributive property: a × 0 = a × (0 + 0) = a × 0 + a × 0, which only works if a × 0 is 0.

All 11 sheet types

Name the property 2

Name the property, 3 choices 7 × 4 = 4 × 7 is commutative, (2 × 5) × 3 = 2 × (5 × 3) is associative, and 6 × (10 + 2) = 6 × 10 + 6 × 2 is distributive. Each line prints one true equation with the three names to circle, so nothing has to be computed.
Name the property, all 5 Adds the identity property (38 × 1 = 38) and the zero property (38 × 0 = 0) to the three above. 20 equations, with a word bank of the 5 names printed at the top of the page.

Use the property 5

Fill the blank, mixed properties 8 × 6 = ___ × 8, then (4 × 2) × 5 = 4 × (___ × 5), then 3 × (10 + 4) = 3 × 10 + 3 × ___. The missing number is found without multiplying anything, and the key names the property that gives it.
Finish the equation, names not needed For grade 3. Standard 3.OA.5 asks third graders to use the properties as strategies, and its footnote says they need not use the formal terms. So this sheet has the standard's own kinds of step, such as 3 × 5 × 2 = 3 × 10 = 30, and no naming line.

Show all 11 sheet types (7 more)

Use the property, continued

Name it, then use it Two answer lines per problem. Given 4 × 23 = 4 × (20 + 3), the pupil writes distributive, then finishes: 80 + 12 = 92. Given 25 × 9 × 4 = 25 × 4 × 9, the pupil writes commutative, then 100 × 9 = 900. The page opens on this sheet.
Rewrite with a named property The sheet names the property and the pupil writes the equation. 'Commutative, 12 × 5' gives 12 × 5 = 5 × 12. 'Distributive, 7 × 16' gives 7 × 16 = 7 × 10 + 7 × 6 = 112. Any correct split earns the mark, so the key shows one and says so.
Write your own example Five name lines, each with room for an equation the pupil invents, such as 12 × 1 = 12 for identity. The key cannot list every right answer, so it prints the letter form to mark against.

Multiplying by 1 and by 0 3

Identity property: × 1 4,906 × 1 = 4,906 and 1 × 73 = 73. The numbers are large on purpose: the rule is the same at any size, and a pupil who starts a long multiplication here has not seen it yet. The Common Core glossary calls this the multiplicative identity property of 1.
Zero or one? Mixed 62 × 1 = 62, 62 × 0 = 0, 62 + 0 = 62 and 62 − 0 = 62, shuffled on one page. A pupil who answers 62 × 0 with 62 has read × 0 as + 0. The + 0 and − 0 lines are there to make pupils read the sign.
Zero property: × 0 0 × 517 = 0 and 8 × 0 × 25 = 0. One zero factor makes the whole product zero, however long the chain. The Common Core's table of properties has a row for multiplying by 1 and none for multiplying by 0, so the name on this sheet is the textbook one.

True or false 1

True or false equations 9 × 4 = 4 × 9 is true. 6 × (5 + 2) ≠ 6 × 5 + 2, because the left side is 42 and the right side is 32. Half the equations on each sheet are false, and the key gives both sides' values for every false one.

How this list was compiled: Sheet types, wording and worked examples are own work; every equation was computed twice by script on 2026-09-18. Standards facts were checked on 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 three examples and its footnote 'Students need not use formal terms for these properties', 1.OA.3 for the addition properties, 6.EE.3, and Glossary Table 3 'The properties of operations', which lists the associative and commutative properties of multiplication, the multiplicative identity property of 1 and the distributive property of multiplication over addition, and has no row for multiplying by 0. Texas wording was checked the same day against the Texas Essential Knowledge and Skills for Mathematics, 19 TAC 111.5 and 111.6 (https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111a.pdf): 3.4(G) and 4.4(D) both name the commutative, associative and distributive properties. Definitions, the examples that fail for subtraction and division, and division splitting over a sum on one side only were checked the same day against https://en.wikipedia.org/wiki/Commutative_property , https://en.wikipedia.org/wiki/Associative_property and https://en.wikipedia.org/wiki/Distributive_property . Fix pass 2026-09-20: one sentence that said how common a slip is was reworded; Table 3 of the glossary, 1.OA.3, 3.OA.5 with its footnote and 6.EE.3 were read again in the national copy that day. Licence: own work