Calculating
Multiplication and division
In this unit you multiply and divide with the 2, 5 and 10 tables. Multiplication is putting equal groups together, and division is sharing into equal groups. They are opposites, so one helps you find the other.
Multiplication is equal groups
Multiplication is a quick way to add equal groups. 5 + 5 + 5 + 5 is four groups of 5, which is 5 x 4 = 20. An array shows this neatly: 5 rows of 4 dots is 5 x 4 = 20. You can multiply in any order, so 5 x 4 = 4 x 5.
Multiplying by 2 is doubling
Multiplying a number by 2 is the same as doubling it: 5 x 2 = 5 + 5 = 10. You can use a 5 times fact to find a 10 times fact by doubling. 5 x 3 = 15, so double it: 10 x 3 = 30.
Equal facts
Different multiplications can have the same answer, so they are equal in value. 5 x 4 = 20 and 10 x 2 = 20, so 5 x 4 = 10 x 2. Number facts on both sides of the = sign have the same value.
Division is sharing
Division shares a number into equal groups. 20 shared into 4 groups is 20 / 4 = 5. Division is the inverse of multiplication: 5 x 4 = 20 so 20 / 4 = 5. Halving is dividing by 2, and finding a quarter is dividing by 4.
Worked examples
Multiplication as an array
- The array has 5 rows with 4 dots in each row.
- This is 5 groups of 4, written 5 x 4.
- Count them: 5 + 5 + 5 + 5 = 20.
Answer: 5 x 4 = 20
Multiply by 2 by doubling
- Start with the 5 times fact: 5 x 3 = 15.
- Multiplying by 2 is doubling, so double the answer.
- Double 15 to get 30, which is 10 x 3.
Answer: 5 x 3 = 15, so 10 x 3 = 30
Two facts that are equal
- Work out 5 x 4 = 20.
- Work out 10 x 2 = 20.
- Both equal 20, so they are equal in value.
Answer: 5 x 4 = 10 x 2
Division as sharing (the inverse)
- Share 20 into 4 equal groups.
- Each group gets 5, so 20 / 4 = 5.
- This is the inverse of 5 x 4 = 20.
Answer: 20 / 4 = 5
Where you see this in real life
- Sharing sweets equally between friends.
- Setting out chairs in equal rows for an event.
- Doubling a recipe to make twice as much.
- Counting money or objects in 2s, 5s and 10s.
Key words
- Multiply
- To put equal groups together, a quick way of adding the same number again and again.
- Array
- Rows and columns of dots or objects that show a multiplication.
- Double
- To make twice as much. Doubling is the same as multiplying by 2.
- Divide
- To share a number into equal groups.
- Half
- One of two equal parts. Finding a half is dividing by 2.
- Quarter
- One of four equal parts. Finding a quarter is dividing by 4.
- Inverse
- The opposite operation. Division is the inverse of multiplication.