Learn on PengiEureka Math, Grade 5Chapter 16: Making Like Units Pictorially

Lesson 2: Add fractions with sums between 1 and 2.

In this Grade 5 Eureka Math lesson from Chapter 16, students practice adding fractions with unlike denominators that produce sums between 1 and 2, such as 1/2 + 3/4. Students use pictorial models and equivalent fractions to find common units before adding, building on their understanding of part-whole relationships. The lesson develops estimation strategies alongside procedural skills, helping students predict whether a sum will be greater or less than 1 whole before solving.

Section 1

Estimating Fraction Sums Using Benchmarks

Property

To estimate if the sum of two fractions is greater than 1, compare each fraction to the benchmark of 12\frac{1}{2}.
If both fractions are greater than 12\frac{1}{2}, their sum will be greater than 1.
If ab>12\frac{a}{b} > \frac{1}{2} and cd>12\frac{c}{d} > \frac{1}{2}, then ab+cd>1\frac{a}{b} + \frac{c}{d} > 1.

Examples

Section 2

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

Section 3

Decompose an Improper Fraction into a Mixed Number

Property

To convert an improper fraction ab\frac{a}{b} (where a>ba > b) to a mixed number, decompose it into a sum of a whole number and a proper fraction.
This is done by pulling out a fraction equivalent to 1.

ab=bb+a−bb=1+a−bb=1a−bb\frac{a}{b} = \frac{b}{b} + \frac{a-b}{b} = 1 + \frac{a-b}{b} = 1\frac{a-b}{b}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Estimating Fraction Sums Using Benchmarks

Property

To estimate if the sum of two fractions is greater than 1, compare each fraction to the benchmark of 12\frac{1}{2}.
If both fractions are greater than 12\frac{1}{2}, their sum will be greater than 1.
If ab>12\frac{a}{b} > \frac{1}{2} and cd>12\frac{c}{d} > \frac{1}{2}, then ab+cd>1\frac{a}{b} + \frac{c}{d} > 1.

Examples

Section 2

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

Section 3

Decompose an Improper Fraction into a Mixed Number

Property

To convert an improper fraction ab\frac{a}{b} (where a>ba > b) to a mixed number, decompose it into a sum of a whole number and a proper fraction.
This is done by pulling out a fraction equivalent to 1.

ab=bb+a−bb=1+a−bb=1a−bb\frac{a}{b} = \frac{b}{b} + \frac{a-b}{b} = 1 + \frac{a-b}{b} = 1\frac{a-b}{b}

Examples