Fractions: the denominator says in how many pieces
You learn to read and use fractions: below the line is how many pieces there are, above the line is how many you have.
How to work it out
- Look below the line: that is how many equal pieces the whole is divided into.
- Look above the line: that is how many pieces you have or take.
- Read a fraction from a strip or a number line by counting the pieces.
- To find a fraction of a number, divide by the denominator and multiply by the numerator.
A worked example
Which fraction goes with the arrow?
- Look at the piece from 0 to 1: it is divided into 8 pieces, so 8 below the line.
- Count from 0 to the arrow: 3 pieces, so 3 above the line.
- It is 38.
More examples
Which part is shaded?
- Count the pieces: there are 4, so put 4 below the line.
- Count the shaded pieces: there are 3, so put 3 above the line.
- It is 34.
14 of 24
- The denominator is 4: divide 24 into 4 equal pieces.
- Work it out: 24 ÷ 4 = 6.
- It is 6.
34 of 24
- Divide 24 into 4 pieces: 24 ÷ 4 = 6.
- The numerator is 3: take 3 pieces.
- Work it out: 3 × 6 = 18.
- It is 18.
Try it yourself
13 of 30
110 of 250
Watch out
You count the lines instead of the pieces: with 4 pieces you count 5 lines.
Count the spaces between the lines, not the lines themselves. The line at 0 does not count.
You divide by the number above the line: 14 of 20 becomes 20 ÷ 1 = 20.
Always divide by the number below the line. For 34 of 24 you then multiply by 3.
Tips
- With a strip, count all the pieces for below the line, shaded and white.
- On the number line one whole is always the piece from 0 to 1.
Exceptions
- When the numerator is bigger than the denominator, like 54, it is more than one whole.
Why it works
The number below the line is called the denominator: it names how big the pieces are. The number above the line is called the numerator: it counts how many pieces you have. The pieces must be equal or the fraction does not work. Fair sharing is dividing, so to find part of a number you divide by the denominator.