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

Lesson 2: Add and multiply unit fractions to build fractions greater than 1 using visual models.

In this Grade 4 Eureka Math lesson from Chapter 25, students learn to add and multiply unit fractions to build fractions greater than 1, using visual models such as number lines and number bonds to connect improper fractions and mixed numbers. The lesson develops fluency with equivalent fractions by counting by fractional units like sixths and fifths, and reinforces how whole numbers relate to fractions with the same denominator. Students also practice subtracting fractions from whole numbers, strengthening their understanding of fraction equivalence across values greater than 1.

Section 1

Multiplying a Whole Number by a Unit Fraction

Property

Multiplying a whole number, $n$ , by a unit fraction, $\frac{1}{d}$ , is equivalent to repeated addition.
This relationship is generalized by the rule:

n \times \frac{1}{d} = \underbrace{\frac{1}{d} + \frac{1}{d} + \dots + \frac{1}{d}}_{n \text{ times}} = \frac{n}{d}

Examples

Section 2

Expressing Products as Mixed Numbers

Property

To convert an improper fraction $\frac{n}{d}$ (the product of $n \times \frac{1}{d}$ ) to a mixed number, divide the numerator $n$ by the denominator $d$ . The quotient $q$ is the whole number part, and the remainder $r$ is the new numerator.

\frac{n}{d} = q\frac{r}{d}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Multiplying a Whole Number by a Unit Fraction

Property

Multiplying a whole number, $n$ , by a unit fraction, $\frac{1}{d}$ , is equivalent to repeated addition.
This relationship is generalized by the rule:

n \times \frac{1}{d} = \underbrace{\frac{1}{d} + \frac{1}{d} + \dots + \frac{1}{d}}_{n \text{ times}} = \frac{n}{d}

Examples

Section 2

Expressing Products as Mixed Numbers

Property

\frac{n}{d} = q\frac{r}{d}

Examples

Overview

Lesson overview

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

Overview

Section 1

Multiplying a Whole Number by a Unit Fraction

Property

Multiplying a whole number, $n$ , by a unit fraction, $\frac{1}{d}$ , is equivalent to repeated addition.
This relationship is generalized by the rule:

n \times \frac{1}{d} = \underbrace{\frac{1}{d} + \frac{1}{d} + \dots + \frac{1}{d}}_{n \text{ times}} = \frac{n}{d}

Examples

Section 2

Expressing Products as Mixed Numbers

Property

\frac{n}{d} = q\frac{r}{d}