Multiplication · Grade 3

Missing Factors and Dividends Worksheets

Look at the blank before choosing an operation. A missing factor and a missing starting total need different related facts.

6 problemsAnswer key includedFree printableA4 & US Letter

Generate & print See the worked example

Find what the blank represents

In 4 × □ = 28, the blank is a factor: four equal groups contain twenty-eight altogether, so each group contains seven. The related division fact 28 ÷ 4 = 7 helps find the missing factor.

4 × 7 = 28
28 ÷ 4 = 7

Check the missing factor by multiplying it by the known factor. The product must match the number after the equal sign.

A blank before division is the starting total

In □ ÷ 6 = 3, the blank is the dividend, or the number being divided. Six equal groups of three make eighteen, so the missing number is 18. Check by substituting: 18 ÷ 6 = 3.

If a child writes 2 for □ ÷ 6 = 3: they may have divided or subtracted the visible numbers without considering the blank's role. Draw six groups with three objects each, count the total, and test that total in the original equation.

Use the whole equation to check

Do not stop after finding a related fact. Put the answer into the blank and read the entire equation aloud. For 5 × □ = 40, substituting eight gives 5 × 8 = 40. Substituting seven would give thirty-five, so it cannot be correct.

Explain with equal groups

For 3 × □ = 18, draw three groups and share eighteen marks equally. For □ ÷ 3 = 6, draw three groups of six and count the starting total. Both pictures contain eighteen objects, but the unknown quantity is different.

Distinguish the division words

In 18 ÷ 3 = 6, eighteen is the dividend, three is the divisor, and six is the quotient. The division questions on this sheet leave the dividend blank. They do not ask for a missing divisor or quotient.

About these six questions

Each sheet contains three missing-factor equations and three missing-dividend equations. Factors are from 2 through 9, and products or dividends range from 4 through 81. Division is exact, with no remainders.

The original equations are preserved, and the answer stays in the original blank position. Use the working space to draw groups or write a related fact. Zero, one, missing divisors, and missing quotients are not included in this focused practice.

Make a practice set

Choose what to print. Selecting both shows the answer key on screen and prints the questions followed by the answers.

Print materials

WorksheetAnswer keyPaper

After the practice

Ask what the blank represents, then substitute the answer to check the complete equation.

Calculation practice
Single Digit Multiplication Worksheets
Use equal groups and arrays to practise multiplication facts with factors from 2 to 9.
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Calculation practice
Division Without Remainders Worksheets
Share equally or make equal groups, then check each quotient with multiplication.
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Word problems
Equal Groups Division Word Problems
Find group count or group size with division facts, or share larger totals to find two-digit amounts.
Share larger amounts equally
4 problems · Answer key included

More about multiplication · Grade 3 worksheets

Grade 3 selected skill connection: 3.OA.A.4. See the Common Core grade guidance. This worksheet does not cover every requirement in the standard.