Distributive Property of Multiplication Worksheets, Grades 3 to 5

Under Sheet type, pick a sheet such as Break apart at 5, press Make a new sheet, then press Print.

Sheet type

Problems

Answer key

12 problems. 2-digit × 1-digit with tens and ones. Sheet FABQSN, with its answer key.

2-digit × 1-digit with tens and ones

Name Date Score / 12

Split the 2-digit factor into tens and ones. Write the split, then the two products, then their sum.

1.9 × 15 = 9 × (_____ + _____)= _____ + _____= ________
2.9 × 67 = 9 × (_____ + _____)= ________ + _____= ________
3.4 × 44 = 4 × (_____ + _____)= ________ + _____= ________
4.8 × 14 = 8 × (_____ + _____)= _____ + _____= ________
5.6 × 18 = 6 × (_____ + _____)= _____ + _____= ________
6.3 × 29 = 3 × (_____ + _____)= _____ + _____= ________
7.2 × 48 = 2 × (_____ + _____)= _____ + _____= ________
8.7 × 67 = 7 × (_____ + _____)= ________ + _____= ________
9.9 × 28 = 9 × (_____ + _____)= ________ + _____= ________
10.3 × 96 = 3 × (_____ + _____)= ________ + _____= ________
11.4 × 26 = 4 × (_____ + _____)= _____ + _____= ________
12.4 × 31 = 4 × (_____ + _____)= ________ + _____= ________

Sheet FABQSN · Made at homeroomtools.com

Answer key. 2-digit × 1-digit with tens and ones

1.9 × 15 = 9 × (10 + 5)= 90 + 45= 135
2.9 × 67 = 9 × (60 + 7)= 540 + 63= 603
3.4 × 44 = 4 × (40 + 4)= 160 + 16= 176
4.8 × 14 = 8 × (10 + 4)= 80 + 32= 112
5.6 × 18 = 6 × (10 + 8)= 60 + 48= 108
6.3 × 29 = 3 × (20 + 9)= 60 + 27= 87
7.2 × 48 = 2 × (40 + 8)= 80 + 16= 96
8.7 × 67 = 7 × (60 + 7)= 420 + 49= 469
9.9 × 28 = 9 × (20 + 8)= 180 + 72= 252
10.3 × 96 = 3 × (90 + 6)= 270 + 18= 288
11.4 × 26 = 4 × (20 + 6)= 80 + 24= 104
12.4 × 31 = 4 × (30 + 1)= 120 + 4= 124

Sheet FABQSN · Made at homeroomtools.com

Next step Stack the same products in columns Mix all the properties on one sheet

How it works

These distributive property of multiplication worksheets follow one rule from grade 3 to grade 5: multiply each part, then add. 6 × 14 = 6 × (10 + 4) = 60 + 24 = 84. Answer key on page 2.

Read the full guide

One rule, three grade bands

In grade 3 the property reaches a fact you do not know from two you do. The Common Core's example in 3.OA.5 is 8 × 7 = 8 × (5 + 2) = 40 + 16 = 56. In grades 4 and 5 the same split carries 2-digit and 3-digit numbers. In grade 6 it runs backwards, 36 + 8 = 4 × (9 + 2). The sheets under Run it backwards do that with whole numbers, not letters.

Brackets here, boxes elsewhere

Each distributive property of multiplication worksheet here is written as bracket equations. Drawn as rectangles, the idea is on the area model multiplication worksheets, and stacked in columns it is partial products.

Start with Break apart at 5 before any 2-digit sheet. A pupil who can split 7 into 5 + 2 has the whole method.
Use Subtract from a round number for mental math: 6 × 98 = 600 − 12 = 588 is quicker than 540 + 48.
As an exit check, a pupil who marks 5 × (4 + 3) = 5 × 4 + 3 true multiplied only the first number.

Questions and answers

What is the distributive property of multiplication?

Multiplying a sum gives the same result as multiplying each part and adding: a × (b + c) = a × b + a × c. It is why column multiplication, partial products and the area model all work.

Which grades use distributive property multiplication worksheets?

Grades 3 to 8 in the Common Core. The sheets here cover grades 3 to 5: facts in 3.OA.5 and multi-digit products in 4.NBT.5. Standard 6.NS.4 uses it for the greatest common factor, and 6.EE.3 and 7.EE.1 for variables. No sheet here does those.

Does the distributive property work with subtraction and division?

Subtraction, yes: 9 × 7 = 70 − 7. With division, only when the sum is divided: (60 + 24) ÷ 6 = 10 + 4. Splitting the divisor fails: 84 ÷ 14 is 6, but 84 ÷ 10 plus 84 ÷ 4 is 29.4.

All 13 sheet types

Break apart a fact 4

Break apart at 5 8 × 7 = 8 × (5 + 2) = 40 + 16 = 56. Splitting a 6, 7, 8 or 9 into 5 and a bit turns one hard fact into two easy ones. It is the example the Common Core gives for the property in grade 3.
Break apart the 11s and 12s 7 × 12 = 7 × (10 + 2) = 70 + 14 = 84. The two tables past 10 need no memorizing once a pupil can split off the ten.
Choose your own split 7 × 8 can be 7 × (5 + 3) = 35 + 21 = 56 or 7 × (4 + 4) = 28 + 28 = 56. Any two numbers that add up to the factor will do, so the key shows one split and the product every split must reach.
Nines as ten minus one 9 × 7 = (10 − 1) × 7 = 70 − 7 = 63. The property holds over subtraction as well as addition, so every nines fact is a tens fact with one group taken away.

Show all 13 sheet types (9 more)

Brackets and blanks 3

Brackets first or multiply out 4 × (6 + 3) worked brackets first is 4 × 9 = 36. Multiplied out, it is 24 + 12 = 36. Both routes on one line is a proof a pupil can check alone.
Fill the missing number in the brackets 6 × (10 + ___) = 60 + 24, so the blank is 4. One number is missing from every line, sometimes inside the brackets and sometimes among the products.
True or false with brackets 5 × (4 + 3) = 5 × 4 + 5 × 3 is true: both sides are 35. 5 × (4 + 3) = 5 × 4 + 3 is false, because the right side is 23. Half the false lines leave the second number unmultiplied, the slip this sheet is built to catch.

2-digit and 3-digit numbers 4

2-digit × 1-digit with tens and ones 6 × 14 = 6 × (10 + 4) = 60 + 24 = 84. The page opens on this sheet. Each problem has a line for the split, a line for the two products and a line for the sum.
3-digit × 1-digit in expanded form 7 × 318 = 7 × (300 + 10 + 8) = 2,100 + 70 + 56 = 2,226. Three products this time, and the same three numbers turn up as the partial products of the column method.
Subtract from a round number 6 × 98 = 6 × (100 − 2) = 600 − 12 = 588. For a factor that ends in 8 or 9, going up to the round number and taking the extra away is quicker than splitting into tens and ones.
Two brackets, four products (30 + 4) × (10 + 3) = 300 + 90 + 40 + 12 = 442, which is 34 × 13. Each number in the first bracket multiplies each number in the second: the same four products an area model puts in boxes.

Run it backwards 2

Collect a common factor 7 × 6 + 3 × 6 = (7 + 3) × 6 = 10 × 6 = 60. Read from right to left, the property joins two products that share a factor. The sheet picks pairs whose other factors add up to 10, 20 or 100.
Common factor with subtraction 8 × 47 − 8 × 37 = 8 × (47 − 37) = 8 × 10 = 80. Working the two products first means 376 − 296. Spotting the shared 8 means one easy fact.

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, that it also holds over subtraction, the mental arithmetic use (6 × 16 = 6 × 10 + 6 × 6 = 96) and the remark that written multiplication rests on it were checked 2026-09-18 against https://en.wikipedia.org/wiki/Distributive_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 8 × 7 = 8 × (5 + 2) and the footnote that students need not use formal terms, 3.MD.7c, 4.NBT.5, 5.OA.1, 5.OA.2 (add 8 and 7, then multiply by 2), 5.NBT.7, 6.NS.4 (36 + 8 as 4 (9 + 2)), 6.EE.3 (3 (2 + x) and 24x + 18y), 7.EE.1 and 8.EE.7b. 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), which name the distributive property as a strategy, and 5.4(E) and 5.4(F) on parentheses and brackets. That file stops at grade 5, so grade 6 and later items carry Common Core numbers only. Fix pass 2026-09-20: the worked example of 3-digit × 1-digit in expanded form was changed from 4 × 236 to 7 × 318 = 2,226, computed by script that day, because 236 × 4 is the worked example of the 3-digit by 1-digit page; 3.OA.5, 6.NS.4, 6.EE.3, 7.EE.1 and 8.EE.7 were read again in the national copy the same day. Licence: own work