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Add, subtract, multiply and divide fractions with all the working.
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The Coddy math course teaches the method itself - you work each step on an interactive board and get told exactly where a move went wrong.
Adding and subtracting fractions needs a common denominator, because you can only combine parts of the same size. Multiplying needs no such thing: you multiply the tops and the bottoms and you are done. Dividing is multiplying by the reciprocal. Three different rules for four operations is why fractions feel harder than they are - nothing here is difficult, but the rules do not generalise, so each one has to be known separately.
That is what this page shows. Each step names the rule it is applying, so "do I need a common denominator here?" gets answered in writing rather than by guessing. The route is the one a lesson walks: mixed numbers to improper fractions first, then the operation's own rule, then reduce, then back to a mixed number if the answer is bigger than one.
Everything is exact. One third plus one sixth is one half, not 0.49999999999999994, and a denominator of 999983 does not get rounded away. The answer is offered as a fraction first because that is what the question was about, with the decimal and percentage beside it for when a marking scheme wants those instead.
Type the numerator in the top box and the denominator in the bottom one, for each fraction. A whole number goes in the top box on its own.
Plus, minus, times or divide. The route below changes with it, because each operation has its own rule - which is the thing worth noticing.
The fraction in lowest terms is the headline; underneath it are the mixed number, the decimal and the percentage of the same value.
Each step says what was done and why. The one to read twice is whichever step you would not have thought of yourself.
One row per operation. The middle column is the rule; the right one is what it looks like on real numbers.
| Operation | Rule | Example |
|---|---|---|
| Add | Common denominator, then add the tops | 3/4 + 5/6 = 9/12 + 10/12 = 19/12 |
| Subtract | Common denominator, then subtract the tops | 2/3 - 1/4 = 8/12 - 3/12 = 5/12 |
| Multiply | Tops together, bottoms together | 2/3 × 9/4 = 18/12 = 3/2 |
| Divide | Multiply by the reciprocal | 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 |
| Simplify | Divide top and bottom by their GCF | 18/12 = 3/2 |
| To a mixed number | Divide, keep the remainder on top | 19/12 = 1 7/12 |
| To a decimal | Divide the top by the bottom | 3/8 = 0.375 |
| To a percent | Multiply by 100 | 3/4 = 75% |
The least common denominator of 4 and 6 is 12, so the fractions become 9/12 and 10/12 - and now they are parts of the same size, so the tops add: 19/12. As a mixed number that is 1 7/12. Note that 24 would also have worked as a denominator; you would have got 38/24, which reduces to the same answer with more arithmetic.
No common denominator, no rewriting: multiply across to get 18/12, then reduce by 6 to get 3/2. You could also cancel before multiplying - the 3 into the 9 and the 2 into the 4 - which gives 3/2 straight away and is the same arithmetic done in a smarter order.
Flip the second fraction and multiply: 3/4 × 5/2 = 15/8. The answer is bigger than either starting fraction, which is exactly what dividing by a number smaller than one does. If that feels wrong, ask how many halves fit in three quarters - the answer is more than one.
Multiplying across gives 6/6, which reduces to 1. Two fractions whose product is 1 are reciprocals of each other, and that is the fact the division rule rests on: dividing by 2/3 and multiplying by 3/2 are the same operation.
