Learn on PengiEureka Math, Grade 4Chapter 26: Addition and Subtraction of Fractions by Decomposition

Lesson 4: Subtract a fraction from a mixed number.

In this Grade 4 Eureka Math lesson from Chapter 26, students learn how to subtract a fraction from a mixed number using multiple strategies, including counting back, decomposing the mixed number, and converting to a fraction greater than one. Students practice breaking apart the whole number portion to regroup and subtract like units, building on their understanding of equivalent fractions and mixed numbers. This lesson strengthens foundational fraction skills as part of the broader unit on addition and subtraction of fractions by decomposition.

Section 1

Subtract by Decomposing the Subtrahend to Reach a Whole

Property

To subtract a fraction from a mixed number when regrouping is needed (e.g., Abc−dcA \frac{b}{c} - \frac{d}{c} where b<db < d), break the subtrahend (dc\frac{d}{c}) into two parts. First, subtract the part that gets you to the whole number (Abc−bc=AA \frac{b}{c} - \frac{b}{c} = A). Then, subtract the remaining part of the fraction from that whole number to find the difference.

Examples

Section 2

Subtracting by Regrouping from the Mixed Number

Property

When subtracting Abc−dcA \frac{b}{c} - \frac{d}{c} where the fraction part is too small (b<db < d), regroup by converting 1 whole into a fraction. This changes the mixed number into a form that allows for subtraction.

Abc=(A−1)+1+bc=(A−1)+cc+bc=(A−1)b+ccA \frac{b}{c} = (A-1) + 1 + \frac{b}{c} = (A-1) + \frac{c}{c} + \frac{b}{c} = (A-1) \frac{b+c}{c}

Examples

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Chapter 26: Addition and Subtraction of Fractions by Decomposition

  1. Lesson 1

    Lesson 1: Estimate sums and differences using benchmark numbers.

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  2. Lesson 2

    Lesson 2: Add a mixed number and a fraction.

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  3. Lesson 3

    Lesson 3: Add mixed numbers.

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  4. Lesson 4Current

    Lesson 4: Subtract a fraction from a mixed number.

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  5. Lesson 5

    Lesson 5: Subtract a mixed number from a mixed number.

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  6. Lesson 6

    Lesson 6: Subtract mixed numbers.

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Lesson overview

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Section 1

Subtract by Decomposing the Subtrahend to Reach a Whole

Property

To subtract a fraction from a mixed number when regrouping is needed (e.g., Abc−dcA \frac{b}{c} - \frac{d}{c} where b<db < d), break the subtrahend (dc\frac{d}{c}) into two parts. First, subtract the part that gets you to the whole number (Abc−bc=AA \frac{b}{c} - \frac{b}{c} = A). Then, subtract the remaining part of the fraction from that whole number to find the difference.

Examples

Section 2

Subtracting by Regrouping from the Mixed Number

Property

When subtracting Abc−dcA \frac{b}{c} - \frac{d}{c} where the fraction part is too small (b<db < d), regroup by converting 1 whole into a fraction. This changes the mixed number into a form that allows for subtraction.

Abc=(A−1)+1+bc=(A−1)+cc+bc=(A−1)b+ccA \frac{b}{c} = (A-1) + 1 + \frac{b}{c} = (A-1) + \frac{c}{c} + \frac{b}{c} = (A-1) \frac{b+c}{c}

Examples

Book overview

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

Continue this chapter

Chapter 26: Addition and Subtraction of Fractions by Decomposition

  1. Lesson 1

    Lesson 1: Estimate sums and differences using benchmark numbers.

    LearnPractice
  2. Lesson 2

    Lesson 2: Add a mixed number and a fraction.

    LearnPractice
  3. Lesson 3

    Lesson 3: Add mixed numbers.

    LearnPractice
  4. Lesson 4Current

    Lesson 4: Subtract a fraction from a mixed number.

    LearnPractice
  5. Lesson 5

    Lesson 5: Subtract a mixed number from a mixed number.

    LearnPractice
  6. Lesson 6

    Lesson 6: Subtract mixed numbers.

    LearnPractice