Learn on PengiIllustrative Mathematics, Grade 5Chapter 2: Fractions as Quotients and Fraction Multiplication

Lesson 10: Multiply More Fractions

In this Grade 5 lesson from Illustrative Mathematics Chapter 2, students multiply whole numbers and mixed numbers by applying properties of operations such as the distributive property to decompose and find products. Students practice expressions like 12 × 9⅔ and 3⅝ × 18, using fraction decomposition to break calculations into manageable parts. The lesson builds fluency with multiplying fractions greater than 1 written as mixed numbers, connecting to real-world contexts involving area.

Section 1

Calculate the area of a rectangle by multiplying its side lengths

Property

The area of a rectangle can be found by multiplying its two side lengths (length and width). The formula is:

Area=length×widthArea = length \times width

Examples

Section 2

Decomposing a Fraction into a Sum of Unit Fractions

Property

A fraction ab\frac{a}{b} can be expressed as the sum of its unit fractions, 1b\frac{1}{b}, added 'a' times.
This can also be written as the product of the numerator 'a' and the unit fraction 1b\frac{1}{b}.

ab=1b+1b+⋯+1b⏟a times=a×1b\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{\text{a times}} = a \times \frac{1}{b}

Examples

Section 3

Calculate Total Area from a Fraction Model

Property

To find the total area from a model representing a whole number WW times a fraction ab\frac{a}{b}, multiply the whole number by the numerator and keep the denominator.

W×ab=W×abW \times \frac{a}{b} = \frac{W \times a}{b}

Examples

Book overview

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

Continue this chapter

Chapter 2: Fractions as Quotients and Fraction Multiplication

  1. Lesson 1

    Lesson 1: Sharing Situations and Division as Fractions

    LearnPractice
  2. Lesson 2

    Lesson 2: Interpret and Solve Division Situations

    LearnPractice
  3. Lesson 3

    Lesson 3: Relate Division and Fractions

    LearnPractice
  4. Lesson 4

    Lesson 4: Relate Division and Multiplication

    LearnPractice
  5. Lesson 5

    Lesson 5: Divide to Multiply Fractions

    LearnPractice
  6. Lesson 6

    Lesson 6: Area with Fractional Side Lengths (< 1)

    LearnPractice
  7. Lesson 7

    Lesson 7: Fractional Side Lengths Greater Than 1

    LearnPractice
  8. Lesson 8

    Lesson 8: Decompose Area and Apply Properties

    LearnPractice
  9. Lesson 9

    Lesson 9: Area Situations

    LearnPractice
  10. Lesson 10Current

    Lesson 10: Multiply More Fractions

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Calculate the area of a rectangle by multiplying its side lengths

Property

The area of a rectangle can be found by multiplying its two side lengths (length and width). The formula is:

Area=length×widthArea = length \times width

Examples

Section 2

Decomposing a Fraction into a Sum of Unit Fractions

Property

A fraction ab\frac{a}{b} can be expressed as the sum of its unit fractions, 1b\frac{1}{b}, added 'a' times.
This can also be written as the product of the numerator 'a' and the unit fraction 1b\frac{1}{b}.

ab=1b+1b+⋯+1b⏟a times=a×1b\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{\text{a times}} = a \times \frac{1}{b}

Examples

Section 3

Calculate Total Area from a Fraction Model

Property

To find the total area from a model representing a whole number WW times a fraction ab\frac{a}{b}, multiply the whole number by the numerator and keep the denominator.

W×ab=W×abW \times \frac{a}{b} = \frac{W \times a}{b}

Examples

Book overview

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

Continue this chapter

Chapter 2: Fractions as Quotients and Fraction Multiplication

  1. Lesson 1

    Lesson 1: Sharing Situations and Division as Fractions

    LearnPractice
  2. Lesson 2

    Lesson 2: Interpret and Solve Division Situations

    LearnPractice
  3. Lesson 3

    Lesson 3: Relate Division and Fractions

    LearnPractice
  4. Lesson 4

    Lesson 4: Relate Division and Multiplication

    LearnPractice
  5. Lesson 5

    Lesson 5: Divide to Multiply Fractions

    LearnPractice
  6. Lesson 6

    Lesson 6: Area with Fractional Side Lengths (< 1)

    LearnPractice
  7. Lesson 7

    Lesson 7: Fractional Side Lengths Greater Than 1

    LearnPractice
  8. Lesson 8

    Lesson 8: Decompose Area and Apply Properties

    LearnPractice
  9. Lesson 9

    Lesson 9: Area Situations

    LearnPractice
  10. Lesson 10Current

    Lesson 10: Multiply More Fractions

    LearnPractice