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

Lesson 6: Divide Whole Numbers and Unit Fractions

In this Grade 5 lesson from enVision Mathematics Chapter 9, students learn to divide whole numbers by unit fractions and unit fractions by whole numbers using area models and number lines. The lesson covers expressions such as 4 ÷ 1/6 and 1/4 ÷ 6, helping students understand why dividing a whole number by a fraction less than 1 produces a quotient greater than the original number. Students also use multiplication to check division results and apply these skills to real-world problems involving equal sharing and measurement.

Section 1

Model Division of a Unit Fraction with a Tape Diagram

Property

To divide a unit fraction 1b\frac{1}{b} by a whole number cc using a tape diagram, you partition the 1b\frac{1}{b} piece into cc equal parts. Each new, smaller part represents the fraction 1b×c\frac{1}{b \times c} of the whole.

1b÷c=1b×c\frac{1}{b} \div c = \frac{1}{b \times c}

Examples

Section 2

Algorithm for Dividing a Unit Fraction by a Whole Number

Property

To divide a unit fraction by a whole number, multiply the denominator of the fraction by the whole number.

1b÷c=1b×c\frac{1}{b} \div c = \frac{1}{b \times c}

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 2

    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 6Current

    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.

Expand

Section 1

Model Division of a Unit Fraction with a Tape Diagram

Property

To divide a unit fraction 1b\frac{1}{b} by a whole number cc using a tape diagram, you partition the 1b\frac{1}{b} piece into cc equal parts. Each new, smaller part represents the fraction 1b×c\frac{1}{b \times c} of the whole.

1b÷c=1b×c\frac{1}{b} \div c = \frac{1}{b \times c}

Examples

Section 2

Algorithm for Dividing a Unit Fraction by a Whole Number

Property

To divide a unit fraction by a whole number, multiply the denominator of the fraction by the whole number.

1b÷c=1b×c\frac{1}{b} \div c = \frac{1}{b \times c}

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 2

    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 6Current

    Lesson 6: Divide Whole Numbers and Unit Fractions

  7. Lesson 7

    Lesson 7: Solve Problems Using Division