Learn on PengiPengi Math (Grade 5)Chapter 6: Multiplying and Dividing Fractions

Lesson 1: Fractions as Division

In this Grade 5 lesson from Pengi Math Chapter 6, students learn to interpret a fraction a/b as the result of dividing a by b, building a foundational understanding of fractions as division. Using area models, tape diagrams, and number lines, they represent real-world sharing situations and explore the meaning of improper fractions when results are greater than 1. Students also practice determining whether a quotient is less than, equal to, or greater than 1 based on the relationship between the numerator and denominator.

Section 1

Understanding Fractions as Division

Property

A fraction represents division. The fraction ab\frac{a}{b} means "aa divided by bb" or "a÷ba \div b". The numerator (top number) is what we are dividing, and the denominator (bottom number) is what we are dividing by.

Examples

Section 2

Writing Division as a Fraction

Property

A division problem can be written as a fraction, where the dividend is the numerator and the divisor is the denominator.

a÷b=aba \div b = \frac{a}{b}

Examples

Book overview

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Chapter 6: Multiplying and Dividing Fractions

  1. Lesson 1Current

    Lesson 1: Fractions as Division

  2. Lesson 2

    Lesson 2: Multiplying a Fraction by a Whole Number

  3. Lesson 3

    Lesson 3: Multiplying Fractions Using Area Models

  4. Lesson 4

    Lesson 4: The Standard Algorithm for Fraction Multiplication

  5. Lesson 5

    Lesson 5: Multiplying Mixed Numbers

  6. Lesson 6

    Lesson 6: Division of Unit Fractions by Whole Numbers

  7. Lesson 7

    Lesson 7: Division of Whole Numbers by Unit Fractions

  8. Lesson 8

    Lesson 8: Solving Fraction Word Problems with Multiplication and Division

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Understanding Fractions as Division

Property

A fraction represents division. The fraction ab\frac{a}{b} means "aa divided by bb" or "a÷ba \div b". The numerator (top number) is what we are dividing, and the denominator (bottom number) is what we are dividing by.

Examples

Section 2

Writing Division as a Fraction

Property

A division problem can be written as a fraction, where the dividend is the numerator and the divisor is the denominator.

a÷b=aba \div b = \frac{a}{b}

Examples

Book overview

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

Continue this chapter

Chapter 6: Multiplying and Dividing Fractions

  1. Lesson 1Current

    Lesson 1: Fractions as Division

  2. Lesson 2

    Lesson 2: Multiplying a Fraction by a Whole Number

  3. Lesson 3

    Lesson 3: Multiplying Fractions Using Area Models

  4. Lesson 4

    Lesson 4: The Standard Algorithm for Fraction Multiplication

  5. Lesson 5

    Lesson 5: Multiplying Mixed Numbers

  6. Lesson 6

    Lesson 6: Division of Unit Fractions by Whole Numbers

  7. Lesson 7

    Lesson 7: Division of Whole Numbers by Unit Fractions

  8. Lesson 8

    Lesson 8: Solving Fraction Word Problems with Multiplication and Division