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

Lesson 3: Use Multiplication to Divide

In this Grade 5 enVision Mathematics lesson from Chapter 9, students learn how to divide a whole number by a unit fraction by connecting division to its inverse operation, multiplication. Using models such as fraction strips and bar diagrams, students discover that dividing by a fraction like one-eighth is equivalent to multiplying by its denominator, and they practice checking quotients with multiplication equations. The lesson builds conceptual understanding of the inverse relationship between multiplication and division as it applies to fraction computation.

Section 1

Whole Number ÷ Unit Fraction

Property

Dividing a whole number, aa, by a unit fraction, 1b\frac{1}{b}, is a way of asking: "How many groups of size 1b\frac{1}{b} are in aa?"
This can be modeled visually to find the total number of fractional parts.

Examples

Section 2

Connecting Division by a Unit Fraction to Multiplication

Property

We noticed in the previous visual models that dividing by a unit fraction (1b\frac{1}{b}) produces the same result as multiplying by the denominator (bb).
To solve a÷1ba \div \frac{1}{b}, you can ask: "aa is 1b\frac{1}{b} of what number?". The shortcut is to multiply the whole number by the denominator:

a÷1b=a×ba \div \frac{1}{b} = a \times b

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 2

    Lesson 2: Fractions and Mixed Numbers as Quotients

  3. Lesson 3Current

    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.

Expand

Section 1

Whole Number ÷ Unit Fraction

Property

Dividing a whole number, aa, by a unit fraction, 1b\frac{1}{b}, is a way of asking: "How many groups of size 1b\frac{1}{b} are in aa?"
This can be modeled visually to find the total number of fractional parts.

Examples

Section 2

Connecting Division by a Unit Fraction to Multiplication

Property

We noticed in the previous visual models that dividing by a unit fraction (1b\frac{1}{b}) produces the same result as multiplying by the denominator (bb).
To solve a÷1ba \div \frac{1}{b}, you can ask: "aa is 1b\frac{1}{b} of what number?". The shortcut is to multiply the whole number by the denominator:

a÷1b=a×ba \div \frac{1}{b} = a \times b

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 2

    Lesson 2: Fractions and Mixed Numbers as Quotients

  3. Lesson 3Current

    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