Composing Fractions with Unit Fractions
This Grade 4 Eureka Math skill teaches students that any fraction a/b can be composed by adding a unit fractions of size 1/b. For example, 3/4 = 1/4 + 1/4 + 1/4, and 5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6. This applies to improper fractions too: 4/3 = 1/3 + 1/3 + 1/3 + 1/3. Students learn to see any fraction as a count of equal-sized unit parts, building a concrete understanding of fractions from Chapter 21 of Eureka Math Grade 4 that supports fraction arithmetic and comparison.
Key Concepts
Any fraction $\frac{a}{b}$ is the sum of 'a' unit fractions of size $\frac{1}{b}$.
$$\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}} {a \text{ times}}$$.
Common Questions
What is a unit fraction?
A unit fraction has a numerator of 1. Examples include 1/2, 1/3, 1/4, and 1/5. Unit fractions represent one equal part of a whole divided into that many pieces.
How do you compose 3/4 from unit fractions?
3/4 = 1/4 + 1/4 + 1/4. You add three copies of the unit fraction 1/4.
How do you compose 5/6 from unit fractions?
5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6. You add five copies of the unit fraction 1/6.
Does this work for improper fractions?
Yes. 4/3 = 1/3 + 1/3 + 1/3 + 1/3. The numerator tells you how many unit fractions to add, regardless of whether the fraction is proper or improper.
Why is understanding unit fractions important?
Unit fractions are the building blocks of all fractions. Recognizing any fraction as a count of unit parts supports addition, subtraction, and comparison of fractions.