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

Lesson 2: Add a mixed number and a fraction.

In this Grade 4 Eureka Math lesson from Chapter 26, students learn to add a mixed number and a fraction by applying unit form thinking and number line models. The lesson covers two key strategies: adding like units when the fractional parts sum to less than or equal to 1, and decomposing a fraction to complete a unit of 1 when the fractional parts sum to more than 1. Students build on their understanding of mixed numbers and equivalent fractions to solve problems involving unlike whole and fractional units.

Section 1

Add Like Units and Regroup an Improper Fraction

Property

When adding a mixed number and a fraction with like denominators, add the fractional parts first. If the resulting fraction is improper, regroup it into a whole number and a fraction, then add it to the original whole number.

Abc+dc=A+b+dcA \frac{b}{c} + \frac{d}{c} = A + \frac{b+d}{c}

Examples

Section 2

Making the Next Whole Number

Property

When adding a mixed number and a fraction with like denominators, if the sum of the fractional parts equals one whole, the result is the next whole number. If a+c=ba + c = b, then

Wab+cb=W+a+cb=W+bb=W+1W \frac{a}{b} + \frac{c}{b} = W + \frac{a+c}{b} = W + \frac{b}{b} = W + 1

Examples

Section 3

Add by Making a Whole Using Arrow Way

Property

To add a mixed number and a fraction, decompose the fractional addend to make the next whole number, then add the remaining part. The 'arrow way' notation visually represents this process of adding in parts.

abd+part to make onea+1+remaining partfinal suma \frac{b}{d} \xrightarrow{+\text{part to make one}} a+1 \xrightarrow{+\text{remaining part}} \text{final sum}

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.

  2. Lesson 2Current

    Lesson 2: Add a mixed number and a fraction.

  3. Lesson 3

    Lesson 3: Add mixed numbers.

  4. Lesson 4

    Lesson 4: Subtract a fraction from a mixed number.

  5. Lesson 5

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

  6. Lesson 6

    Lesson 6: Subtract mixed numbers.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Add Like Units and Regroup an Improper Fraction

Property

When adding a mixed number and a fraction with like denominators, add the fractional parts first. If the resulting fraction is improper, regroup it into a whole number and a fraction, then add it to the original whole number.

Abc+dc=A+b+dcA \frac{b}{c} + \frac{d}{c} = A + \frac{b+d}{c}

Examples

Section 2

Making the Next Whole Number

Property

When adding a mixed number and a fraction with like denominators, if the sum of the fractional parts equals one whole, the result is the next whole number. If a+c=ba + c = b, then

Wab+cb=W+a+cb=W+bb=W+1W \frac{a}{b} + \frac{c}{b} = W + \frac{a+c}{b} = W + \frac{b}{b} = W + 1

Examples

Section 3

Add by Making a Whole Using Arrow Way

Property

To add a mixed number and a fraction, decompose the fractional addend to make the next whole number, then add the remaining part. The 'arrow way' notation visually represents this process of adding in parts.

abd+part to make onea+1+remaining partfinal suma \frac{b}{d} \xrightarrow{+\text{part to make one}} a+1 \xrightarrow{+\text{remaining part}} \text{final sum}

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.

  2. Lesson 2Current

    Lesson 2: Add a mixed number and a fraction.

  3. Lesson 3

    Lesson 3: Add mixed numbers.

  4. Lesson 4

    Lesson 4: Subtract a fraction from a mixed number.

  5. Lesson 5

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

  6. Lesson 6

    Lesson 6: Subtract mixed numbers.