Adding fractions (unlike denominators)
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator
What a learner can do afterwards
- Compute 2/3 + 5/4 by converting to twelfths: 8/12 + 15/12 = 23/12
- Subtract 1 3/5 from 3 1/4 using a common denominator
- Explain the strategy of finding a common denominator and verify using a visual model
1 · Read
Fractions with different denominators count different-size pieces. Find a positive common multiple of the denominators. Rewrite each fraction with that denominator before adding or subtracting its numerator.
To rewrite a fraction, divide the new denominator by the old denominator. Multiply the old numerator by that whole-number multiplier too. Applying the same multiplier to both numbers preserves the value.
Adding numerators and denominators separately does not match piece sizes. Check a proposed shortcut by rewriting with a common denominator and computing the actual result. Keep the common denominator during addition.
Once denominators match, add the numerators even if the total exceeds one whole. A question asking for the numerator needs that piece count. To rename an improper result, group its pieces into complete wholes and a remainder.
A visual conversion keeps the same whole and shaded amount. Split every original piece into the same number of smaller pieces. The total and shaded piece counts both grow by that multiplier.
The least common denominator is the smallest positive common multiple of the denominators. List positive multiples of each denominator until the lists first share a number. Larger common multiples work too, but are not the least.
Each whole in a mixed number contributes as many pieces as the denominator. For 2 2/7, two wholes give fourteen sevenths; add two more to get 16/7. To use a requested denominator that is a multiple of the old one, divide the new denominator by the old one. Multiply the improper fraction's numerator and denominator by that multiplier. This counts the same amount in smaller pieces.
An improper fraction already counts all its pieces, so you can scale it directly. Changing it to a mixed number first is optional. To repair an error from adding both denominators, scale each original fraction to a shared denominator.
Subtract 1 1/2 from 2 1/3. Convert the mixed numbers: 2 1/3 = 7/3 and 1 1/2 = 3/2. In sixths they are 14/6 and 9/6. Subtract 14 - 9 = 5, giving 5/6.
To check visually, use equal pieces of one fixed unit. Draw enough same-size bars for the starting amount, or use one block for each included piece. Split bars into the common denominator's pieces. For subtraction, cross out the removed count and count what remains. For addition, join the included counts.
The blocks check the example above. Each is one sixth. Nine of fourteen are crossed out, leaving five.
A numerator counts pieces of the size named by the denominator. When a question asks for that count, keep the stated denominator while calculating and report the numerator. Simplify only when asked, by dividing both numbers by a common factor greater than 1.
Give every fraction the same size pieces first, then add or subtract the numerators.
Practice questions and readings written for this learning dataset. Includes retained and revised fraction flashcards, with video references from Khan Academy.
2 · Watch
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