More multiplication & division
Using multiplication and division facts
Multiplication and division facts belong together in fact families. If you know one fact, you can work out three more!
Arrays show multiplication
An array is a set of dots or counters in equal rows. 4 rows of 7 dots is 4 × 7 = 28. Because the rows and columns can be counted either way, 4 × 7 and 7 × 4 both give 28. This is called being commutative.
Fact families
The numbers 4, 7 and 28 make a fact family: 4 × 7 = 28, 7 × 4 = 28, 28 ÷ 4 = 7, 28 ÷ 7 = 4. Multiplication is commutative, but division is not: 28 ÷ 4 is 7 while 28 ÷ 7 is 4.
Multiply in any order
When you multiply three numbers, you can reorder them to make it easier. For 5 × 4 × 3, do 5 × 4 = 20 first, then 20 × 3 = 60.
Remainders
Some divisions do not share out equally. 25 ÷ 2 gives 12 with 1 left over. We write this as 12 remainder 1. The remainder is the part left over.
Sequences
A sequence follows a term-to-term rule. In 18, 27, 36, 45 the rule is add 9. In 135, 126, 117, 108 the rule is subtract 9.
Worked examples
Reading an array
- Count the rows: 4.
- Count how many in each row: 7.
- Multiply: 4 × 7 = 28.
Answer: 4 × 7 = 28
A fact family
- Start with 4 × 7 = 28.
- Swap the order: 7 × 4 = 28.
- Now write the two divisions: 28 ÷ 4 = 7 and 28 ÷ 7 = 4.
Answer: 4 × 7 = 28, 7 × 4 = 28, 28 ÷ 4 = 7, 28 ÷ 7 = 4
Multiplying in any order
- Look at 5 × 4 × 3.
- Multiply 5 × 4 = 20 first.
- Then multiply 20 × 3 = 60.
Answer: 5 × 4 × 3 = 60
A division with a remainder
- Share 25 into groups of 2.
- 2 × 12 = 24, which is close to 25.
- 25 − 24 = 1 is left over.
Answer: 25 ÷ 2 = 12 remainder 1
Continuing a sequence
- Look at 18, 27, 36, 45.
- Each number is 9 more than the last, so the rule is add 9.
- 45 + 9 = 54.
Answer: The next number is 54
Where you see this in real life
- Setting out chairs in equal rows for a class picture.
- Sharing a bag of sweets between friends and seeing how many are left over.
- Counting cans of soup stacked in equal rows on a shelf.
Key words
- Array
- A set of objects arranged in equal rows and columns.
- Commutative
- You can multiply in any order and get the same answer.
- Fact family
- A group of related multiplication and division facts using the same numbers.
- Product
- The answer when you multiply numbers together.
- Quotient
- The answer when you divide one number by another.
- Remainder
- The amount left over when a number does not divide equally.