Learn on PengiEureka Math, Grade 4Chapter 23: Fraction Comparison

Lesson 2: Reason using benchmarks to compare two fractions on the number line.

In this Grade 4 Eureka Math lesson from Chapter 23: Fraction Comparison, students learn to compare two fractions by reasoning with benchmark values of 0, one-half, and 1 on a number line. Students practice identifying whether fractions like 6/4 or 2/8 fall below, near, or above these benchmarks to determine which fraction is greater. The lesson also extends comparison to fractions between 1 and 2, helping students build flexible thinking about fraction size and placement.

Section 1

Decompose and Locate Improper Fractions on a Number Line

Property

An improper fraction can be decomposed into a whole number and a proper fraction using a number bond.
This helps locate the fraction on a number line between two consecutive whole numbers.

ab=whole number+fractional part\frac{a}{b} = \text{whole number} + \text{fractional part}

Examples

Section 2

Compare Fractions Using Whole Number Benchmarks

Property

To compare fractions using a whole number benchmark (nn, like 1 or 2), first determine if each fraction is less than, equal to, or greater than nn.
If both fractions are on the same side of the benchmark (e.g., both are greater than nn), compare their distances from nn.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Decompose and Locate Improper Fractions on a Number Line

Property

An improper fraction can be decomposed into a whole number and a proper fraction using a number bond.
This helps locate the fraction on a number line between two consecutive whole numbers.

ab=whole number+fractional part\frac{a}{b} = \text{whole number} + \text{fractional part}

Examples

Section 2

Compare Fractions Using Whole Number Benchmarks

Property

To compare fractions using a whole number benchmark (nn, like 1 or 2), first determine if each fraction is less than, equal to, or greater than nn.
If both fractions are on the same side of the benchmark (e.g., both are greater than nn), compare their distances from nn.

Examples