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

Book overview

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Chapter 23: Fraction Comparison

  1. Lesson 1

    Lesson 1: Reason using benchmarks to compare two fractions on the number line.

  2. Lesson 2Current

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

  3. Lesson 3

    Lesson 3: Find common units or number of units to compare two fractions.

  4. Lesson 4

    Lesson 4: Find common units or number of units to compare two fractions.

Lesson overview

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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

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 23: Fraction Comparison

  1. Lesson 1

    Lesson 1: Reason using benchmarks to compare two fractions on the number line.

  2. Lesson 2Current

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

  3. Lesson 3

    Lesson 3: Find common units or number of units to compare two fractions.

  4. Lesson 4

    Lesson 4: Find common units or number of units to compare two fractions.