S.1 Decompose fractions using unit fractions
What does it mean to decompose fractions?
Decomposing fractions means breaking a fraction into a sum of smaller fractions, usually called unit fractions. A unit fraction is a fraction with the number 1 as the numerator, such as 12 or 15.
- 34 = 14 + 14 + 14
- 56 = 16 + 16 + 16 + 16 + 16
Decomposing helps you understand the size of fractions and how they are built from unit fractions.
How do we decompose fractions?
To decompose a fraction, write it as a sum of unit fractions. Each unit fraction has the same denominator as the original fraction.
- Start with the fraction: 45
- Break it into unit fractions with denominator 5
- 45 = 15 + 15 + 15 + 15
The denominator tells how many equal parts make a whole. The numerator tells how many unit fractions you need.
Different ways to decompose fractions
A fraction can often be decomposed in more than one way. You can use only unit fractions or mix larger fractions and unit fractions.
- 23 = 13 + 13
- 23 = 13 + 26
- 34 = 12 + 14
Different decompositions can all be correct as long as the sums are equal to the original fraction.
Using decomposed fractions in math
Decomposing fractions makes it easier to add, subtract, and understand fractions in word problems.
- 38 = 18 + 18 + 18 (easier to add to another fraction with denominator 8)
- 56 = 12 + 13 (helpful when solving problems with halves and thirds)
When working with fractions, breaking them apart helps you see connections and solve problems more flexibly.