Learn on PengiIllustrative Mathematics, Grade 5Chapter 6: Place Value Patterns and Decimal Operations

Lesson 5: Add and Subtract Fractions with Equivalent Expressions

In this Grade 5 Illustrative Mathematics lesson from Chapter 6, students learn to add and subtract fractions with unlike denominators by finding common denominators, including cases where one denominator is a multiple of the other and cases requiring a new common denominator. Students use fraction strips and number lines to represent equivalent fractions and reason through sums and differences such as 5/6 − 1/3 and 3/4 + 1/2. This lesson addresses standard 5.NF.A.1 and builds on prior knowledge of same-denominator fraction operations from earlier grades.

Section 1

Defining a Fraction and Its Whole

Property

A fraction represents a part of a whole that has been divided into equal parts.
The 'whole' can be a single object or a quantity, such as length, area, mass, or volume.
A unit fraction, 1b\frac{1}{b}, represents one of these bb equal parts.

Examples

Section 2

Identifying Equivalent Fractions Using Area Models

Property

Equivalent fractions represent the same portion of a whole.
You can generate an equivalent fraction by multiplying the numerator and the denominator by the same non-zero number, which corresponds to partitioning an area model into smaller equal pieces.

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 3

Adding and Subtracting Like Fractions

Property

Fractions that have the same denominator are called like fractions.

To add (or subtract) two like fractions:

  1. Add (or subtract) the numerators.
  2. Keep the same denominator.

Examples

  • To add 29+59\frac{2}{9} + \frac{5}{9}, we add the numerators: 2+5=72+5=7. The denominator stays the same, so the sum is 79\frac{7}{9}.

Section 4

Adding Unlike Fractions to Get an Improper Fraction

Property

To add fractions with unlike denominators, find a common denominator, convert them to equivalent fractions, and add the numerators.
The sum is an improper fraction if it is greater than 1.

ab+cd=adbd+cbbd=ad+cbbd\frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{cb}{bd} = \frac{ad + cb}{bd}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Defining a Fraction and Its Whole

Property

A fraction represents a part of a whole that has been divided into equal parts.
The 'whole' can be a single object or a quantity, such as length, area, mass, or volume.
A unit fraction, 1b\frac{1}{b}, represents one of these bb equal parts.

Examples

Section 2

Identifying Equivalent Fractions Using Area Models

Property

Equivalent fractions represent the same portion of a whole.
You can generate an equivalent fraction by multiplying the numerator and the denominator by the same non-zero number, which corresponds to partitioning an area model into smaller equal pieces.

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Section 3

Adding and Subtracting Like Fractions

Property

Fractions that have the same denominator are called like fractions.

To add (or subtract) two like fractions:

  1. Add (or subtract) the numerators.
  2. Keep the same denominator.

Examples

  • To add 29+59\frac{2}{9} + \frac{5}{9}, we add the numerators: 2+5=72+5=7. The denominator stays the same, so the sum is 79\frac{7}{9}.

Section 4

Adding Unlike Fractions to Get an Improper Fraction

Property

To add fractions with unlike denominators, find a common denominator, convert them to equivalent fractions, and add the numerators.
The sum is an improper fraction if it is greater than 1.

ab+cd=adbd+cbbd=ad+cbbd\frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{cb}{bd} = \frac{ad + cb}{bd}

Examples