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Fraction rules
Need a fraction rules within reach? Print it for the wall, or make a fact-list version to fill in.
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Reference chart
Fraction rules
Adding and subtracting
- Bottoms already match: add or take away the tops, and leave the bottom exactly as it is.2/5 + 1/5 = 3/5
- Bottoms are different: rewrite both so they match, then add the tops. The bottoms are never added.1/2 + 1/3 = 3/6 + 2/6 = 5/6
Multiplying and dividing
- To multiply, go straight across: tops together, bottoms together. Nothing has to match first.2/3 × 3/4 = 6/12 = 1/2
- To divide, turn the second fraction upside down and multiply instead.1/2 ÷ 1/4 = 1/2 × 4/1 = 2
Tidying the answer
- To simplify, divide the top and the bottom by the same number until nothing else will.6/8 = 3/4, both halved
- To turn a mixed number into a fraction, multiply the whole by the bottom and add the top.2 1/4 = (2 × 4 + 1)/4 = 9/4
What's on this chart
The fraction wall shows a child what a fraction is; this chart tells them what to do with one. They are different problems. A child can understand perfectly well that 1/2 is bigger than 1/3 and still write that 1/2 + 1/3 is 2/5, because the picture and the procedure are stored in different places and only the procedure is being asked for on the page.
Why this chart helps
That very mistake is why the second rule is worded the way it is. Adding the bottoms is the single most common fraction error there is, and it is not carelessness — it is what every other operation the child has met so far would suggest. The chart says plainly that the bottoms are never added, and having that sentence in view is worth more than being corrected on it again.
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