Multiplication & division
Exploring multiplication and division
When you have more than one group all the same size, you can multiply to find how many there are altogether. Division shares them back into equal groups. Multiplication and division are connected.
Multiplication as groups and arrays
Multiplication is a quick way to add equal groups. An array shows the groups in neat rows and columns. An array with 3 rows of 4 shows 3 × 4 = 12. Because you can turn an array around, 3 × 4 gives the same answer as 4 × 3. This is called commutative.
Division as sharing
Division shares a number into equal groups. If 20 sweets are shared equally between 5 children, each child gets 20 ÷ 5 = 4 sweets. Multiplication and division undo each other: 5 × 4 = 20 and 20 ÷ 5 = 4.
Fact families
A fact family uses the same three numbers to make four facts. For 3 × 4 = 12 the family is: • 3 × 4 = 12 • 4 × 3 = 12 • 12 ÷ 3 = 4 • 12 ÷ 4 = 3
Multiples and multiplying by 10
Multiples of 2 are even numbers. Multiples of 5 end in 5 or 0. Multiples of 10 end in 0. To multiply by 10, each digit moves up one place, so the answer ends in 0. For example, 7 × 10 = 70 and 23 × 10 = 230.
Worked examples
Reading an array (multiplication)
- The array has 3 rows with 4 dots in each row.
- Count the rows (3) and the dots in a row (4).
- Multiply: 3 × 4.
Answer: The array shows 3 × 4 = 12 dots.
Sharing equally (division)
- There are 12 apples to share into 3 baskets.
- Share them equally: 12 ÷ 3.
- Each basket gets the same number.
Answer: Each basket has 12 ÷ 3 = 4 apples.
Writing a fact family
- Use the numbers 2, 5 and 10.
- Write both multiplications: 2 × 5 = 10 and 5 × 2 = 10.
- Write both divisions: 10 ÷ 2 = 5 and 10 ÷ 5 = 2.
Answer: The fact family is 2 × 5 = 10, 5 × 2 = 10, 10 ÷ 2 = 5, 10 ÷ 5 = 2.
Multiplying by 10
- A school has 23 boxes of 10 pencils.
- Multiply the number of boxes by 10: 23 × 10.
- Multiplying by 10 gives an answer ending in 0.
Answer: The school has 23 × 10 = 230 pencils.
Where you see this in real life
- Working out how many players are in 8 teams of 6.
- Sharing sweets equally between friends.
- Counting boxes of 10 pencils to find the total.
Key words
- Array
- Objects arranged in equal rows and columns.
- Multiple
- A number you reach by counting in equal steps, such as multiples of 5: 5, 10, 15.
- Commutative
- You can multiply in either order and get the same answer, like 3 × 4 = 4 × 3.
- Fact family
- Four multiplication and division facts made from the same three numbers.
- Product
- The answer when you multiply numbers together.