Year 6 Maths Multiplication and Division Study Flashcards

[q] Factors, Products and Multiples

Factors are numbers that can be multiplied together to give another number.

[a] Example
3 and 10 are factors of 30 (3 × 10 = 30)
6 and 4 are factors of 24 (6 × 4 = 24)

[q] Common Factors and Common Multiples

Common factors are factors that are common to more than one product.

[a] Common factors are factors that are common to more than one product.

Example

Factors of 12 are: 1, 2, 3, 4, 6, and 12
Factors of 8 are: 1, 2, 4 and 8
So the common factors of 12 and 8 are: 1, 2 and 4.

[q] Prime Numbers
A prime number is a number than can only be divided by 1 and itself (it only has two factors).

[a] A prime number is a number than can only be divided by 1 and itself (it only has two factors).

[q] Prime Factors

[a] A prime factor is a factor that is also a prime number.
3 and 5 are the prime factors of 15 because both 3 and 5 are prime numbers.

Example
To find the prime factors of 36, you first need to look at the factors of 36:
3 and 12 are factors of 36. (3 × 12 = 36)
3 is a prime number but 12 is not, so you need to break 12 down into its factors:
3 and 4 are factors of 12, so now you have: 3, 3 and 4.
4 is not a prime number so again you need to break 4 down into its factors:
2 and 2 are factors of 4. So now you have: 3 × 3 × 2 × 2 = 36
So 3, 3, 2 and 2 are the prime factors of 36.

[q] Square Numbers 

A square number is the answer you get when you multiply any number by itself. The symbol used to show that a number is squared is 2 (so, 42 means 4 squared).

[a] Example
4 × 4 = 4 squared = 4² = 16
5 × 5 = 5 squared = 5² = 25 

[q] Cube Numbers

A cube number is the answer you get when you multiply any number by itself and by itself again. The symbol used to show that a number is cubed is 3 (so, 53 means 5 cubed).

[a] Example
2 × 2 × 2 = 2 cubed = 2³ = 8
3 × 3 × 3 = 3 cubed = 3³ = 27 

[q] Order of Operations 

Calculations should be carried out using this order of operations: Brackets, Indices or Orders, Division, Multiplication, Addition, Subtraction

[a]

[q] Multiplying and Dividing by 10, 100 and 1000

When you multiply or divide by 10, the digits don’t change; they just change position.

[a]

[q] Mental Multiplication

[a] You can decompose numbers to help multiply them.

[q] Multiplying and Dividing by 0 and 1

[a] If you multiply any number by 0, the answer is always 0. If you multiply or divide any number by 1, the answer is always the number itself.

[q] Grid Multiplication

You can use a grid to work out a multiplication sum.

[a] Example: How can you calculate 24 × 37?
1. Partition each number and write it on a grid.
2. Calculate each answer and write it in the correct space on the grid:

3. Add up all the answers to get a total:
600 + 120 + 140 + 28 = 888
So, 24 × 37 = 888

[q] Long Multiplication

Another method for working out multiplication by writing it down is called long multiplication.

[a] Example
How can you calculate 38 × 26?
1. Start by multiplying the units by the units: 6 × 8 = 48. Record the 8 and carry the 4 into the next column.

2. Then, multiply the tens by the units: 6 × 3 = 18 + 4 (that was carried) = 22

[q] Dividing by Single-Digit Numbers

Short division is sometimes called the ‘bus stop’ method. You normally use this when you have a single-digit divisor.

[a] Example
Calculate 78 ÷ 5
1. Divide the most significant digit (in this case the tens digit).
7 divided by 5 = 1r2.
Record the 1 above the line and carry the 2 to the next column.

[q] Long Division

When a division sum has a double-digit divisor, you may need to use long division.

[a] Example
Calculate 477 ÷ 15
1. 477 ÷ 15. There are 30 lots of 15 in 477. Record the 3 in the tens column above the line. 30 × 15 = 450. Subtract this from 477 and put the answer below.

2. 27 ÷ 15. There is 1 lot of 15 in 27. Record the 1 above the line in the units column. 12 is left over. 12 cannot be divided by 15 so there is a remainder of 12.

3. 477 ÷ 15 = 31r12
3 1
15 4 7 7– 4 5 0
2 7– 1 5
r 1 2
15 × 30
15 × 1
To find a decimal answer you need to put a decimal point on the answer line and bring down a zero to the remainder.

477 ÷ 15 = 31.8