Learn on PengiEureka Math, Grade 4Chapter 25: Extending Fraction Equivalence to Fractions Greater Than 1

Lesson 3: Decompose and compose fractions greater than 1 to express them in various forms.

In this Grade 4 Eureka Math lesson from Chapter 25, students learn to decompose and compose fractions greater than 1, expressing them as improper fractions, mixed numbers, and whole numbers. Through fluency practice and concept development activities, students work with equivalent fractions, number bonds, and number lines to convert between forms such as 7/2 and 3½. This lesson builds the fraction equivalence skills fourth graders need to fluently move between different representations of the same value.

Section 1

Convert Improper Fractions to Mixed Numbers by Decomposing

Property

To convert a fraction greater than 1, nd\frac{n}{d}, into a mixed number, decompose it into a sum of a fraction that equals a whole number and a remaining fraction.

nd=part that makes wholesd+remaining partd=whole number+remaining fraction\frac{n}{d} = \frac{\text{part that makes wholes}}{d} + \frac{\text{remaining part}}{d} = \text{whole number} + \text{remaining fraction}

Examples

Section 2

Convert Improper Fractions to Mixed Numbers Using Multiplication

Property

To convert an improper fraction nd\frac{n}{d} to a mixed number, you can express the whole number part as a multiplication.
If there are ww wholes and a remainder of rr, the conversion can be written as:

nd=(w×dd)+rd=wrd\frac{n}{d} = \left(w \times \frac{d}{d}\right) + \frac{r}{d} = w \frac{r}{d}

Examples

Book overview

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Chapter 25: Extending Fraction Equivalence to Fractions Greater Than 1

  1. Lesson 1

    Lesson 1: Add a fraction less than 1 to, or subtract a fraction less than 1 from, a whole number using decomposition and visual models.

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  2. Lesson 2

    Lesson 2: Add and multiply unit fractions to build fractions greater than 1 using visual models.

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Decompose and compose fractions greater than 1 to express them in various forms.

    LearnPractice
  4. Lesson 4

    Lesson 4: Decompose and compose fractions greater than 1 to express them in various forms.

    LearnPractice
  5. Lesson 5

    Lesson 5: Compare fractions greater than 1 by reasoning using benchmark fractions.

    LearnPractice
  6. Lesson 6

    Lesson 6: Compare fractions greater than 1 by creating common numerators or denominators.

    LearnPractice
  7. Lesson 7

    Lesson 7: Solve word problems with line plots.

    LearnPractice

Lesson overview

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Expand

Section 1

Convert Improper Fractions to Mixed Numbers by Decomposing

Property

To convert a fraction greater than 1, nd\frac{n}{d}, into a mixed number, decompose it into a sum of a fraction that equals a whole number and a remaining fraction.

nd=part that makes wholesd+remaining partd=whole number+remaining fraction\frac{n}{d} = \frac{\text{part that makes wholes}}{d} + \frac{\text{remaining part}}{d} = \text{whole number} + \text{remaining fraction}

Examples

Section 2

Convert Improper Fractions to Mixed Numbers Using Multiplication

Property

To convert an improper fraction nd\frac{n}{d} to a mixed number, you can express the whole number part as a multiplication.
If there are ww wholes and a remainder of rr, the conversion can be written as:

nd=(w×dd)+rd=wrd\frac{n}{d} = \left(w \times \frac{d}{d}\right) + \frac{r}{d} = w \frac{r}{d}

Examples

Book overview

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

Continue this chapter

Chapter 25: Extending Fraction Equivalence to Fractions Greater Than 1

  1. Lesson 1

    Lesson 1: Add a fraction less than 1 to, or subtract a fraction less than 1 from, a whole number using decomposition and visual models.

    LearnPractice
  2. Lesson 2

    Lesson 2: Add and multiply unit fractions to build fractions greater than 1 using visual models.

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Decompose and compose fractions greater than 1 to express them in various forms.

    LearnPractice
  4. Lesson 4

    Lesson 4: Decompose and compose fractions greater than 1 to express them in various forms.

    LearnPractice
  5. Lesson 5

    Lesson 5: Compare fractions greater than 1 by reasoning using benchmark fractions.

    LearnPractice
  6. Lesson 6

    Lesson 6: Compare fractions greater than 1 by creating common numerators or denominators.

    LearnPractice
  7. Lesson 7

    Lesson 7: Solve word problems with line plots.

    LearnPractice