Fractions and Decimals
Understanding fractions
Place fractions on a number line, find equivalent fractions, compare them, and switch between mixed numbers and improper fractions.
A fraction is a number in its own right, with a place on the number line like any other. The bottom number says how many equal parts one whole has been cut into, and the top number says how many of those parts you have. So 3/4 is three of the four parts that make one whole, and it sits three quarters of the way from 0 to 1.
Have a play
Move along the line and watch the quarters go past. See which fractions land on a whole number and which land between two of them.
Tap anywhere on the line.
The one move that makes fractions easy
Multiplying the top and the bottom by the same number does not change what a fraction is worth — it only cuts the same amount into more, smaller pieces. So 2/3, 4/6 and 8/12 are three names for one number. Dividing top and bottom by the same number does the reverse, and that is how a fraction is written in its simplest form.
Worked example
Which is larger, 3/5 or 5/8?
You cannot compare fifths with eighths directly, so find a bottom number both can be written with: 40.
40 is the lowest common multiple of 5 and 8, so both fractions can be rewritten without changing what they are worth.
Try it together
Now let us decide which is larger, 5/6 or 7/9.
Same method: give them a common bottom number first, then compare the tops.
1.What is the LCM of 6 and 9?
Have a go
Have a go on your own. Fill in the missing number: 3/8 = ?/24
Hint: The bottom has been multiplied by 3.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.