Number
Multiplying and dividing fractions and decimals
Multiply and divide fractions and decimals, and know when the answer will be smaller than what you started with.
Multiplying fractions is the easiest of the four operations, and it surprises people: you multiply the top numbers together and the bottom numbers together, and that is the whole method. No common denominator is needed, because you are not adding anything.
'Of' means multiply
Half of 12 is 1/2 × 12 = 6. Two thirds of 9 is 2/3 × 9 = 6. Whenever a question says 'of', it is asking you to multiply — which is why multiplying by a fraction smaller than 1 makes things smaller, not bigger.
Worked example
What is 0.6 × 0.4?
Ignore the decimal points and multiply: 6 × 4 = 24.
0.6 is 6 tenths and 0.4 is 4 tenths, so the digits behave exactly like whole numbers.
Try it together
Now let us work out 4/5 ÷ 2/3 together.
Dividing by a fraction looks strange until you notice what it is really asking: how many two-thirds fit into four-fifths? The trick that answers it is to turn the second fraction upside down and multiply.
1.Turn the second fraction upside down. What is 2/3 the other way up?
Have a go
Have a go on your own: 2/3 × 6 = ?
Hint: A third of 6 is 2.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.