Adding fractions (same denominator)
Add and subtract fractions with the same denominator, including results greater than one whole (e.g. 5/8 + 6/8 = 11/8)
What a learner can do afterwards
- Calculate 3/5 + 4/5 = 7/5 and explain it equals 1 2/5
- Subtract 2/6 from 5/6
- Solve addition problems where the sum exceeds the whole: 7/8 + 3/8
1 · Read
Matching denominators name matching pieces of the same whole or unit. For addition, add the numerators, which count pieces. Keep the denominator, which names their size.
For subtraction with matching denominators, subtract the numerators and keep the denominator. The remainder still uses the original piece size.
To decide whether a sum exceeds one whole, add the numerators and compare their total with the denominator. A larger numerator means more than one whole. An equal numerator means exactly one whole.
A length story needs a unit. Fractions of a meter count equal pieces of one meter, not fractions of whatever ribbon happens to remain. Subtract the cut length from the starting length using that same meter unit.
An addition can pass one whole without changing the denominator. Keep counting the same-size pieces. You may leave the result as a fraction whose numerator is larger than its denominator.
To write 13/5 as a mixed number, group thirteen fifth-pieces into full groups of five. Two full groups use ten pieces. Three remain, so 13/5 = 2 3/5. Each full group makes one whole.
To check an addition, check the piece count and the piece size. The numerator should count all the pieces. The denominator should still name their original size. Adding denominators changes the piece size and does not describe the joined amount.
For a missing amount in a subtraction, compare the starting count with the remaining count. Their difference counts the pieces removed. Check by subtracting that count from the starting numerator.
For three matching fractions, add all three numerators. You can add two first, then add the third. Keep the shared denominator throughout.
Add or subtract only the top numbers, keep the bottom number the same, and rewrite the answer as a mixed number when the top number passes the bottom.
Practice questions and readings written for this learning dataset.
2 · Watch
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Where this leads
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