Same Math › Grade 5 › Unlike denominators with models
How do kids add fractions with unlike denominators?
To add 1/2 + 1/3, the pieces are different sizes, so kids re-cut both into sixths first: 3/6 + 2/6 = 5/6. Models show why you need the same size pieces before adding.
- 1/2 is 3 sixths.
- 1/3 is 2 sixths.
- Same size pieces now: 3/6 + 2/6 = 5/6
Why schools teach it
Kids see why denominators must match
Fifth graders add and subtract fractions with unlike denominators by replacing them with equivalent fractions (5.NF.A.1); the standard's example is 2/3 + 5/4 = 8/12 + 15/12 = 23/12. They also use benchmark fractions to check that answers make sense (5.NF.A.2).
The model stops the most common mistake, 1/2 + 1/3 = 2/5. A child who sees halves and thirds as different-size pieces knows they can't just be counted together.
At the kitchen table
What to say, and what to skip
Say this
Are these pieces the same size?
What size piece could both be cut into?
Sixths work for halves and thirds.How many sixths is 1/2? How many is 1/3?
Does your answer make sense? Is it more than 1/2?
A quick benchmark check.
Skip this
- Adding the tops and the bottoms.1/2 + 1/3 is not 2/5. That answer is smaller than 1/2, which can't be right.
Always multiply the two denominators.
It works, but often gives bigger numbers than needed. 1/4 + 1/8 only needs eighths.- Changing only one fraction when both need it.1/2 + 1/3 needs both turned into sixths.
See it in action
Solving 3/4 − 1/6
Find a size both can be cut into
twelfthsRewrite both fractions
3/4 = 9/12, 1/6 = 2/12Subtract the pieces
9/12 − 2/12 = 7/12
Check: 3/4 is a bit less than 1, and taking away a small piece leaves a bit more than ½. 7/12 fits.
Free practice sheet
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Parents also ask
What's a common denominator?
A size of piece both fractions can be cut into, like sixths for halves and thirds.
Do we have to use the smallest one?
No. Any common denominator works, but the smallest keeps numbers small.
Why not just add tops and bottoms?
Because the pieces are different sizes. Adding them as if they were the same gives wrong answers.
When should answers be simplified?
Many classes ask for it. 4/8 is fine, but 1/2 is the simplest form.