Maths
Multiplication and division of mixed numbers - Higher
You should have already revised Fraction basics. Now we are going to look at more difficult calculations involving mixed fractions.
Multiplying fractions
Multiplying fractions is easy - we just multiply the numerators (top numbers) and multiply the denominators (bottom numbers). This will probably mean that you can cancel down the answer at the end. Or you can do it before you start.
You can try to find common factors between any of the numerators and any of the denominators. You can cancel down diagonally - they do not have to belong to the same fraction.
- Question
Work out: 2/5 × 7/8
- Answer
We can cancel the top 2 with the bottom 8, so this
becomes this
- Question
Work out:3/8 × 4/5
- Answer
The answer is 3/10
You can cancel the top 4 with the bottom 8.
If you had problems, see if you can fill in the blanks here:
3/8 × 4/5
= 3/? × 1/5
= 3/10
Multiplying with mixed numbers
You will sometimes need to multiply fractions with mixed numbers. You must always remember to turn any mixed numbers into top-heavy fractions before you multiply.
- Question
Work out 21/3 x 13/8
- Answer
The first step is to change both mixed numbers to improper fractions.
21/3 = 7/3
13/8 = 11/8
21/3 x 13/8 = 7/3 x 11/8
Multiply the numerators and multiply the denominators
=
=
Remember to change an improper fraction to a mixed number
=
Dividing fractions
Dividing by fractions is not difficult once you understand the method.
How many quarters are there in a whole pizza? Obviously it is 4.
How many in 6 pizzas? There must be 24.
So 6 ÷ 1/4 = 24
How many people could be fed if we had 6 pizzas and gave each person 3/4 of a pizza?
We need to work out 6 ÷ 3/4
We know that 6 ÷ 1/4 = 24, for each person to have 3 quarters, 24 ÷ 3 = 8, so 6 ÷ 3/4 = 24 ÷ 3 = 8
Some teachers will tell you to turn the last fraction upside down and multiply.
Can you see why this works?
So to work out 2/3 ÷ 3/4 we work out 2/3 × 4/3 = 2 x 4/3 x 3 = 8/9
Remember we only turn the fraction we are dividing by (the second one) upside down.
Here is another question:
- Question
Work out: 3/5 ÷ 6/7
- Answer
3/5 ÷ 6/7
= 3/5 × 7/6
= 1/5 × 7/2 (the top 3 and bottom 6 cancel)
= 1×7/5×2
= 7/10
Try this one:
- Question
Work out: 4/9 ÷ 3/5
- Answer
Did you get 20/27?
If not, check that you only turned the second fraction upside down. See if you can fill in the blanks here:
4/9 ÷ 3/5 = 4/9 × ?/3 = 20/27
Dividing mixed numbers
Again, turn any mixed numbers into top-heavy fractions at the start. Then turn the fraction you are dividing by upside down, and multiply. Here is an example:
3 1/3 ÷ 2 2/3
= 10/3 ÷ 8/3
= 10/3 × 3/8
= 5/4
= 1 1/4
Now try a Test Bite