Learn on PengiEureka Math, Grade 4Chapter 25: Extending Fraction Equivalence to Fractions Greater Than 1

Lesson 3: Decompose and compose fractions greater than 1 to express them in various forms.

In this Grade 4 Eureka Math lesson from Chapter 25, students learn to decompose and compose fractions greater than 1, expressing them as improper fractions, mixed numbers, and whole numbers. Through fluency practice and concept development activities, students work with equivalent fractions, number bonds, and number lines to convert between forms such as 7/2 and 3½. This lesson builds the fraction equivalence skills fourth graders need to fluently move between different representations of the same value.

Section 1

Convert Improper Fractions to Mixed Numbers by Decomposing

Property

To convert a fraction greater than 1, $\frac{n}{d}$ , into a mixed number, decompose it into a sum of a fraction that equals a whole number and a remaining fraction.

\frac{n}{d} = \frac{\text{part that makes wholes}}{d} + \frac{\text{remaining part}}{d} = \text{whole number} + \text{remaining fraction}

Examples

Section 2

Convert Improper Fractions to Mixed Numbers Using Multiplication

Property

To convert an improper fraction $\frac{n}{d}$ to a mixed number, you can express the whole number part as a multiplication.
If there are $w$ wholes and a remainder of $r$ , the conversion can be written as:

\frac{n}{d} = \left(w \times \frac{d}{d}\right) + \frac{r}{d} = w \frac{r}{d}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Convert Improper Fractions to Mixed Numbers by Decomposing

Property

To convert a fraction greater than 1, $\frac{n}{d}$ , into a mixed number, decompose it into a sum of a fraction that equals a whole number and a remaining fraction.

\frac{n}{d} = \frac{\text{part that makes wholes}}{d} + \frac{\text{remaining part}}{d} = \text{whole number} + \text{remaining fraction}

Examples

Section 2

Convert Improper Fractions to Mixed Numbers Using Multiplication

Property

\frac{n}{d} = \left(w \times \frac{d}{d}\right) + \frac{r}{d} = w \frac{r}{d}

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Convert Improper Fractions to Mixed Numbers by Decomposing

Property

To convert a fraction greater than 1, $\frac{n}{d}$ , into a mixed number, decompose it into a sum of a fraction that equals a whole number and a remaining fraction.

\frac{n}{d} = \frac{\text{part that makes wholes}}{d} + \frac{\text{remaining part}}{d} = \text{whole number} + \text{remaining fraction}

Examples

Section 2

Convert Improper Fractions to Mixed Numbers Using Multiplication

Property

\frac{n}{d} = \left(w \times \frac{d}{d}\right) + \frac{r}{d} = w \frac{r}{d}