Adding fractions
To add fractions, first make the bottom numbers (denominators) the same, then add the top numbers (numerators).
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Analogy
You cannot add thirds and quarters until you cut both pizzas into twelfths.
Example
1/3 = 4/121/4 = 3/124/12 + 3/12 = 7/12
In practice
Recipes often mix amounts like 1/2 cup and 1/3 cup, and you need a common denominator to total them.
Practice
Flashcards
- What is 1/3 + 1/4?7/12. Both become twelfths: 4/12 + 3/12.
Questions people ask
How do you find a common denominator?
Find a number that both bottom numbers divide into. The easiest choice is often the two numbers multiplied together. For 1/3 and 1/4, 12 works. A smaller shared multiple, called the lowest common multiple, keeps the numbers smaller, but any shared multiple gives the right answer.
Do you add the denominators when adding fractions?
No. The denominator tells you the size of each piece, and that stays the same. Only the numerators are added. So 3/8 + 2/8 = 5/8, not 5/16. You are counting how many eighths you have, and eighths remain eighths.