Learn on PengienVision, Mathematics, Grade 5Chapter 9: Apply Understanding of Division to Divide Fractions

Lesson 2: Fractions and Mixed Numbers as Quotients

In this Grade 5 lesson from enVision Mathematics Chapter 9, students learn how to express division quotients as fractions and mixed numbers, such as writing 4 ÷ 3 as 4/3 or 1⅓. The lesson uses real-world sharing problems to show how a whole number divided by another whole number can result in a fraction or mixed number rather than a whole number quotient. Students practice converting between division expressions, improper fractions, and mixed numbers across a range of problems.

Section 1

Expressing a Remainder as a Fraction

Property

When a division problem a÷ba \div b results in a whole number quotient qq and a remainder rr, the exact answer can be expressed as a mixed number:

a÷b=qrba \div b = q \frac{r}{b}

Examples

Section 2

Application: Solving Division Word Problems with Fractions

Property

To find the amount for a single share in an equal sharing situation, divide the total amount by the number of shares. The result can be expressed as a fraction or a mixed number.

Size of one share=Total amountNumber of shares \text{Size of one share} = \frac{\text{Total amount}}{\text{Number of shares}}

Examples

Book overview

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Chapter 9: Apply Understanding of Division to Divide Fractions

  1. Lesson 1

    Lesson 1: Fractions and Division

  2. Lesson 2Current

    Lesson 2: Fractions and Mixed Numbers as Quotients

  3. Lesson 3

    Lesson 3: Use Multiplication to Divide

  4. Lesson 4

    Lesson 4: Divide Whole Numbers by Unit Fractions

  5. Lesson 5

    Lesson 5: Divide Unit Fractions by Non-Zero Whole Numbers

  6. Lesson 6

    Lesson 6: Divide Whole Numbers and Unit Fractions

  7. Lesson 7

    Lesson 7: Solve Problems Using Division

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Expressing a Remainder as a Fraction

Property

When a division problem a÷ba \div b results in a whole number quotient qq and a remainder rr, the exact answer can be expressed as a mixed number:

a÷b=qrba \div b = q \frac{r}{b}

Examples

Section 2

Application: Solving Division Word Problems with Fractions

Property

To find the amount for a single share in an equal sharing situation, divide the total amount by the number of shares. The result can be expressed as a fraction or a mixed number.

Size of one share=Total amountNumber of shares \text{Size of one share} = \frac{\text{Total amount}}{\text{Number of shares}}

Examples

Book overview

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

Continue this chapter

Chapter 9: Apply Understanding of Division to Divide Fractions

  1. Lesson 1

    Lesson 1: Fractions and Division

  2. Lesson 2Current

    Lesson 2: Fractions and Mixed Numbers as Quotients

  3. Lesson 3

    Lesson 3: Use Multiplication to Divide

  4. Lesson 4

    Lesson 4: Divide Whole Numbers by Unit Fractions

  5. Lesson 5

    Lesson 5: Divide Unit Fractions by Non-Zero Whole Numbers

  6. Lesson 6

    Lesson 6: Divide Whole Numbers and Unit Fractions

  7. Lesson 7

    Lesson 7: Solve Problems Using Division