To add fractions, make the denominators (bottom numbers) the same, add the numerators (top numbers), and keep the denominator. If the denominators already match, just add the tops: 2/7 + 3/7 = 5/7. If they don't, rewrite each fraction over a common denominator first — for example 1/4 + 2/3 becomes 3/12 + 8/12 = 11/12.
If the bottom numbers are already the same, skip straight to step 3. You can only add fractions when they are counted in the same-sized pieces.
Find a number both denominators divide into — the least common multiple (LCM) is the smallest choice and keeps the numbers manageable. For 4 and 3 the LCM is 12. Rewrite each fraction: multiply its top and bottom by the same number so the bottom becomes the common denominator. Multiplying top and bottom by the same number doesn't change the fraction's value — you're just cutting the same amount into smaller pieces.
Add the top numbers only and keep the denominator as it is. 3/12 + 8/12 = 11/12 — you're counting 3 twelfths plus 8 twelfths, so the answer is in twelfths. Never add the denominators.
Divide top and bottom by their greatest common factor if they share one. If the answer is improper (top bigger than bottom), you can convert it to a mixed number: 25/6 = 4 1/6.
Same denominators
2/7 + 3/7
Answer: 5/7
Different denominators
1/4 + 2/3
Answer: 11/12
Mixed numbers
1 1/2 + 2 2/3
Answer: 4 1/6
1/4 + 2/3 is not 3/7. The denominator names the size of the pieces — it isn't a quantity you add. Get the pieces the same size first, then count them: 3/12 + 8/12 = 11/12.
When you rewrite 1/4 as twelfths, the top must change too: 1/4 = 3/12, not 1/12. Whatever you multiply the bottom by, multiply the top by the same number.
Students often add 1 1/2 + 2 2/3 by adding the fraction parts and dropping the 1 and the 2. Either convert everything to improper fractions first, or add the wholes and the fractions separately and recombine.
Rewrite both fractions over a common denominator, then add the numerators. For 1/4 + 2/3, the least common multiple of 4 and 3 is 12, so 1/4 = 3/12 and 2/3 = 8/12, giving 3/12 + 8/12 = 11/12.
Because the denominator describes the size of the pieces, not an amount. A quarter and a third are different-sized pieces, so 1 + 2 of them isn't 3 of anything. Once both are written in twelfths, the pieces match and the tops can be counted together.
No — any common denominator works. Multiplying the two denominators together (4 × 3 = 12) always gives one. The least common denominator just keeps the numbers smaller, which means less simplifying at the end.
Either convert each mixed number to an improper fraction and add as usual (1 1/2 + 2 2/3 = 3/2 + 8/3 = 9/6 + 16/6 = 25/6 = 4 1/6), or add the whole numbers and fraction parts separately and combine, carrying if the fraction part goes over one whole.
Write the whole number as a fraction over 1, then use a common denominator. For 2 + 3/5, write 2 = 10/5, so 10/5 + 3/5 = 13/5 = 2 3/5 — which is exactly the mixed number you'd expect.
After adding is when it matters — always check whether the answer can be simplified. Simplifying each fraction before you start is optional but often makes the common denominator smaller and the working easier.
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