Learn on PengiEureka Math, Grade 5Chapter 15: Equivalent Fractions

Lesson 2: Make equivalent fractions with sums of fractions with like denominators.

In this Grade 5 Eureka Math lesson from Chapter 15, students learn to make equivalent fractions by expressing them as sums of fractions with like denominators, using number lines and addition sentences to model relationships such as 1/3 + 1/3 = 2/3. The lesson builds on prior knowledge of equivalent fractions and connects repeated addition to multiplication of unit fractions. Students also practice finding missing numerators and denominators to reinforce fraction equivalence fluency.

Section 1

Rule for Adding Fractions with Like Denominators

Property

To add fractions with like denominators, add the numerators and keep the denominator the same.
This can be represented on a number line as combining lengths from a starting point.

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}

Examples

Section 2

Repeated Addition of Fractions as Multiplication

Property

Any fraction ab\frac{a}{b} can be understood as the repeated addition of the unit fraction 1b\frac{1}{b}.
This sum can be expressed as a multiplication equation where the numerator 'a' is the number of times the unit fraction is added.

ab=a×1b\frac{a}{b} = a \times \frac{1}{b}

Examples

Section 3

Decompose an Improper Fraction as a Sum

Property

An improper fraction can be decomposed into a sum of a whole number and a fraction. To do this, pull out groups of fractions that equal one whole.

74=44+34=1+34 \frac{7}{4} = \frac{4}{4} + \frac{3}{4} = 1 + \frac{3}{4}

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Rule for Adding Fractions with Like Denominators

Property

To add fractions with like denominators, add the numerators and keep the denominator the same.
This can be represented on a number line as combining lengths from a starting point.

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}

Examples

Section 2

Repeated Addition of Fractions as Multiplication

Property

Any fraction ab\frac{a}{b} can be understood as the repeated addition of the unit fraction 1b\frac{1}{b}.
This sum can be expressed as a multiplication equation where the numerator 'a' is the number of times the unit fraction is added.

ab=a×1b\frac{a}{b} = a \times \frac{1}{b}

Examples

Section 3

Decompose an Improper Fraction as a Sum

Property

An improper fraction can be decomposed into a sum of a whole number and a fraction. To do this, pull out groups of fractions that equal one whole.

74=44+34=1+34 \frac{7}{4} = \frac{4}{4} + \frac{3}{4} = 1 + \frac{3}{4}