Fraction addition concepts
Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way
What a learner can do afterwards
- Show that 3/8 = 1/8 + 1/8 + 1/8 and also 3/8 = 1/8 + 2/8
- Write two different decompositions of 5/6
- Use a visual model to justify a decomposition of 2 1/8 into whole-number and fraction parts
- Explain addition and subtraction as joining and separating equal parts of the same-size whole or shared unit, including 7/8 - 3/8 = 4/8, and explain why matching denominators alone do not guarantee equal-size pieces.
1 · Read
A unit fraction has numerator 1. Split a fraction into unit fractions by writing one copy for each counted piece. Keep the denominator and check that the copies add back.
Split a fraction into two groups of pieces and keep its denominator. The two numerators must add to the starting numerator. Both parts must refer to the same-size whole. Fourths of different-size bars are different-size pieces, so adding their counts does not give fourths of either bar.
A fraction can have several valid splits, using two or more groups of pieces. To count equal groups, count how many groups fit: 9/10 = 3/10 + 3/10 + 3/10, so nine tenth-pieces make three groups of three.
Find another two-part split by changing the first numerator and subtracting it from the total. Require both parts to be positive. A numerator of 0 counts no pieces, so that part is not positive. Count each pair once: swapping its parts gives no new pair. List first numerators in order and stop when the next pair reverses one already counted.
Find a missing numerator by subtracting known counts from the total. Add known counts first if there are several. For two equal parts, share the count equally: 6/7 = 3/7 + 3/7. Keep the denominator and add back to check.
A mixed number is its whole-number part plus its fraction part. The fraction numerator counts only pieces beyond the complete units. For a length, the denominator names how many pieces make another unit. Keep complete units separate when asked about the fraction part.
To check a proposed split, add its numerators. A total below the starting numerator is too little; a total above it is too much. Matching denominators alone do not make a split valid.
The next three bars show 2 1/8. Each bar is one whole. The first two are full; the third has one eighth shaded. Together they show 2 + 1/8.
Joining pieces adds their counts. Separating pieces subtracts their counts. For three matching parts, add all three numerators. Keep the denominator. A total numerator equal to the denominator fills exactly one whole.
A fraction can be split into same-denominator pieces in more than one way. Adding joins those pieces; subtracting separates them.
Practice questions and readings written for this learning dataset. Referenced video by Khan Academy.
2 · Watch
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Where it sits
Where this leads
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