Learn on PengienVision, Mathematics, Grade 5Chapter 8: Apply Understanding of Multiplication to Multiply Fractions

Lesson 6: Area of a Rectangle

In this Grade 5 enVision Mathematics lesson from Chapter 8, students learn how to find the area of a rectangle with fractional side lengths by multiplying fractions using the formula length times width. The lesson uses visual models like unit square grids to show why multiplying numerators and denominators separately gives the correct area, such as finding that a rectangle measuring two-thirds yard by three-fourths yard has an area of ten-twelfths square yard. Students practice applying fraction multiplication to calculate areas of rectangles and squares with various fractional dimensions.

Section 1

Modeling Fraction Multiplication with an Area Model

Property

Multiplying two fractions, ab×cd\frac{a}{b} \times \frac{c}{d}, is equivalent to finding a part of a part, or ab\frac{a}{b} of cd\frac{c}{d}.
An area model visualizes this by partitioning a whole into b×db \times d smaller rectangles.
The product is the fraction of the whole that is represented by the a×ca \times c double-shaded area.

Examples

Book overview

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Chapter 8: Apply Understanding of Multiplication to Multiply Fractions

  1. Lesson 1

    Lesson 1: Multiply a Fraction by a Whole Number

  2. Lesson 2

    Lesson 2: Multiply a Whole Number by a Fraction

  3. Lesson 3

    Lesson 3: Multiply Fractions and Whole Numbers

  4. Lesson 4

    Lesson 4: Use Models to Multiply Two Fractions

  5. Lesson 5

    Lesson 5: Multiply Two Fractions

  6. Lesson 6Current

    Lesson 6: Area of a Rectangle

  7. Lesson 7

    Lesson 7: Multiply Mixed Numbers

  8. Lesson 8

    Lesson 8: Multiplication as Scaling

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Modeling Fraction Multiplication with an Area Model

Property

Multiplying two fractions, ab×cd\frac{a}{b} \times \frac{c}{d}, is equivalent to finding a part of a part, or ab\frac{a}{b} of cd\frac{c}{d}.
An area model visualizes this by partitioning a whole into b×db \times d smaller rectangles.
The product is the fraction of the whole that is represented by the a×ca \times c double-shaded area.

Examples

Book overview

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

Continue this chapter

Chapter 8: Apply Understanding of Multiplication to Multiply Fractions

  1. Lesson 1

    Lesson 1: Multiply a Fraction by a Whole Number

  2. Lesson 2

    Lesson 2: Multiply a Whole Number by a Fraction

  3. Lesson 3

    Lesson 3: Multiply Fractions and Whole Numbers

  4. Lesson 4

    Lesson 4: Use Models to Multiply Two Fractions

  5. Lesson 5

    Lesson 5: Multiply Two Fractions

  6. Lesson 6Current

    Lesson 6: Area of a Rectangle

  7. Lesson 7

    Lesson 7: Multiply Mixed Numbers

  8. Lesson 8

    Lesson 8: Multiplication as Scaling