From a part to the whole
You learn to work backwards: when you know how much a part is, find how much the whole is.
How to work it out
- First find what one piece is: divide by the number above the line.
- If there is a 1 on top, you already know one piece.
- Multiply one piece by the number under the line: that is the whole.
A worked example
15 of the marbles is 6 marbles. How many marbles are there altogether?
- The numerator is 1: one piece is 6 marbles.
- The whole is 5 pieces: 5 × 6 = 30.
- There are 30 marbles.
More examples
34 of the children are 12 children. How many children are there altogether?
- Find one piece: divide by 3, because 12 ÷ 3 = 4.
- The whole is 4 pieces: 4 × 4 = 16.
- There are 16 children.
25 of the cards are 14 cards. How many cards are there altogether?
- Find one piece: divide by 2, because 14 ÷ 2 = 7.
- The whole is 5 pieces: 5 × 7 = 35.
- There are 35 cards.
Try it yourself
110 of the are 12 . How many are there altogether?
25 of the cards are 14 cards. How many cards are there altogether?
Watch out
You divide instead of multiplying: 15 is 6, so you work out 6 ÷ 5.
The whole is bigger than a part. Your answer must be bigger than the number you were given.
For 34 is 12, you go straight to 4 × 12 = 48.
12 is 3 pieces, not one. Find one piece first: 12 ÷ 3 = 4, and only then multiply by 4.
Tips
- The whole is always bigger than the part you were given.
- Check by working out the part: 34 of 16 is 12.
Why it works
A fraction divides the whole into equal pieces. If you know how much one piece is, multiply it by the number of pieces. If you are given more than one piece, divide first to find one piece.