What does each number tell us?
Draw a strip and divide it into five equal pieces. Colour three pieces.
We write that coloured share as 3/5, said “three fifths”. Each number tells us something:
- 5, on the bottom: the whole strip has five equal pieces.
- 3, on the top: we are counting three of those pieces.
The top number is called the numerator. The bottom number is the denominator. Learn what each number does first; the names can come after.
Try it yourself
Draw three identical strips. Split the first into two equal pieces, the second into three, and the third into five.
Colour one piece in each strip. You have coloured 1/2, 1/3 and 1/5.
The top number is always 1: you chose one piece. But the pieces are not the same size. Splitting the same whole into more pieces makes each piece smaller.
Nothing and everything
Zero fifths, written 0/5, means none of the five parts is selected. Five fifths, written 5/5, means every part is selected, so you have one whole.
A denominator cannot be zero in these fractions. “Divide the whole into zero equal parts” does not give a usable size of piece. One whole can be written as 1/1; splitting it into smaller pieces gives halves, thirds and so on.
Avoid a tempting shortcut
Three fifths does not mean three objects plus five objects. It means three pieces, each one fifth of a whole. Saying the fraction aloud can help you remember that relationship.
Try drawing seven equal boxes in a row and shading two. The fraction is 2/7 even if you separate the shaded boxes. Their positions do not change how many equal parts are selected.