Same Math › Grade 4 › Decomposing fractions
What does decomposing fractions mean?
Decomposing a fraction means breaking it into smaller fractions that add up to it. 5/8 can be 2/8 + 3/8, or 1/8 + 1/8 + 1/8 + 1/8 + 1/8. It's the fraction version of number bonds.
- 2 eighths and
- 3 eighths together make
- 5/8 = 2/8 + 3/8
Why schools teach it
It's how kids learn to add fractions
Fourth graders decompose fractions into sums with the same denominator in more than one way, and the standard's own examples include 3/8 = 1/8 + 1/8 + 1/8 and 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8 (4.NF.B.3b).
Seeing 5/8 as five eighths makes adding fractions obvious: you're counting pieces of the same size. It also explains mixed numbers, which come straight from breaking off whole ones.
At the kitchen table
What to say, and what to skip
Say this
How many eighths is 5/8?
Five pieces, each an eighth.Can you split it into two parts?
Can you find another way?
The standard asks for more than one.How many eighths make one whole?
Eight. That's the key to mixed numbers.
Skip this
- Adding the bottom numbers too.2/8 + 3/8 is 5/8, not 5/16. The pieces are still eighths.
- Mixing denominators.Decomposing keeps the same size pieces.
- Thinking there's one right answer.Any parts that add up correctly are right.
See it in action
Decomposing 2 3/4
Break off the wholes
2 3/4 = 1 + 1 + 3/4Write each whole as fourths
1 = 4/4Put it together
4/4 + 4/4 + 3/4 = 11/4
This is how mixed numbers turn into fractions greater than 1.
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Parents also ask
What is a unit fraction?
A fraction with 1 on top, like 1/8. Every fraction is a sum of unit fractions.
Why only the same denominator?
Pieces have to be the same size to add by counting them. Unlike denominators come in 5th grade.
How is this related to number bonds?
It's the same idea: one whole split into parts. 5 = 2 + 3, so 5/8 = 2/8 + 3/8.
When does this show up again?
In adding and subtracting fractions and mixed numbers, later in 4th grade.