Division facts (related to multiplication)
Theory
Division facts related to multiplication is a Year 4 maths skill: because multiplication and division are inverse operations, every times-table fact gives you a division fact. This page explains fact families, how to read an array as both multiplication and division, and how to find missing numbers by turning a division into a multiplication. Curriculum: VC2M4A02 / AC9M4A02.
Multiplication and division are inverse operations — they are opposites. Division undoes multiplication. Because \(3 \times 7 = 21\), sharing \(21\) back into equal groups gives \(21 \div 7 = 3\) and \(21 \div 3 = 7\).
A fact family is a group of number sentences that all use the same three numbers. The numbers \(3\), \(7\) and \(21\) make two multiplication facts and two division facts. Knowing one of them helps you work out the others.
To work out a division, ask a multiplication question. \(21 \div 7\) means “7 times what is 21?” Since \(7 \times 3 = 21\), the answer is \(3\). An array of dots in rows and columns shows this at a glance.
The three numbers \(3\), \(7\) and \(21\) make one fact family. The same three numbers give two multiplication facts and two division facts.
How to use multiplication to divide
- Read the division. Look at what is being shared, like \(18 \div 3\). This asks how many groups of \(3\) are in \(18\).
- Ask a times-table question. Change it into “3 times what is 18?” and search your times tables for the matching fact.
- Write the answer and check. Since \(3 \times 6 = 18\), then \(18 \div 3 = 6\). Multiply back to make sure the fact is right.
| \(36 \div 9\) | \(\to\) | \(9 \times \,? = 36\) |
| \(9 \times 4\) | \(=\) | \(36\) |
| \(36 \div 9\) | \(=\) | \(4\) |
The answer is \(4\).
| \(3 \times 5\) | \(=\) | \(15,\quad 5 \times 3 = 15\) |
| \(15 \div 5\) | \(=\) | \(3,\quad 15 \div 3 = 5\) |
The three numbers are \(3\), \(5\) and \(15\).
| \(40 \div \square = 8\) | \(\to\) | \(\square \times 8 = 40\) |
| \(5 \times 8\) | \(=\) | \(40\) |
| \(\square\) | \(=\) | \(5\) |
The missing number is \(5\).
| \(28 \div 4\) | \(\to\) | \(4 \times \,? = 28\) |
| \(4 \times 7\) | \(=\) | \(28\) |
| \(28 \div 4\) | \(=\) | \(7\) |
There are \(7\) pencils in each cup.
Common pitfalls
Frequently asked questions
What is a fact family in maths?
A fact family is a group of number sentences that all use the same three numbers. The numbers \(3\), \(7\) and \(21\) make \(3 \times 7 = 21\), \(7 \times 3 = 21\), \(21 \div 7 = 3\) and \(21 \div 3 = 7\).
How does multiplication help you divide?
Division is the opposite of multiplication, so a times-table fact gives you the answer. To work out \(21 \div 7\), ask “7 times what is 21?” Since \(7 \times 3 = 21\), the answer is \(3\).
What are the division facts for 3, 7 and 21?
The two division facts are \(21 \div 7 = 3\) and \(21 \div 3 = 7\). They come from the multiplication facts \(3 \times 7 = 21\) and \(7 \times 3 = 21\).
How do you find a missing number in a division?
Turn the division into a multiplication. For \(40 \div \square = 8\), think “what times 8 is 40?” Since \(5 \times 8 = 40\), the missing number is \(5\). If the first number is missing, just multiply: \(\square \div 8 = 2\) means \(8 \times 2 = 16\).
Is 21 divided by 7 the same as 7 divided by 21?
No. Order matters in division. \(21 \div 7 = 3\), but \(7 \div 21\) is not \(3\). In these division facts the bigger number goes first.
How do you check a division answer?
Multiply your answer by the number you divided by. If \(35 \div 5\) gives \(7\), check \(5 \times 7 = 35\). If the multiplication is right, the division is right.