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

Lesson 2: Multiply a Whole Number by a Fraction

In this Grade 5 lesson from enVision Mathematics, students learn how to multiply a whole number by a fraction by finding a fractional part of a whole, using visual models such as diagrams and number lines to understand the process. Students apply the associative property of multiplication to rewrite expressions like three-fourths times 8 as 3 times one-fourth times 8, breaking the problem into manageable steps. The lesson builds toward fluency with fraction multiplication through guided practice and real-world word problems involving measurement and reasoning.

Section 1

Multiplying a Fraction by a Whole Number

Property

To find a fraction of a whole number, multiply the numerator by the whole number and place the product over the original denominator.
The word "of" in mathematics usually means to multiply.

ab of c=ab×c=a×cb\frac{a}{b} \text{ of } c = \frac{a}{b} \times c = \frac{a \times c}{b}

Section 2

Commutative Property of Multiplication

Property

Due to the commutative property, multiplying a fraction by a whole number can be interpreted in two equivalent ways: finding a fraction of a set, or as repeated addition of the fraction.

ab×c ("a/b of c")=c×ab ("c groups of a/b")\frac{a}{b} \times c \text{ ("a/b of c")} = c \times \frac{a}{b} \text{ ("c groups of a/b")}

Examples

Section 3

Multiplying Using Unit Fractions

Property

To multiply a fraction by a whole number, you can decompose the fraction and multiply by the unit fraction first.

ab×n=a×(1b×n)\frac{a}{b} \times n = a \times \left(\frac{1}{b} \times n\right)

Examples

  • 34×8=3×(14×8)=3×2=6\frac{3}{4} \times 8 = 3 \times \left(\frac{1}{4} \times 8\right) = 3 \times 2 = 6
  • 25×15=2×(15×15)=2×3=6\frac{2}{5} \times 15 = 2 \times \left(\frac{1}{5} \times 15\right) = 2 \times 3 = 6
  • 56×12=5×(16×12)=5×2=10\frac{5}{6} \times 12 = 5 \times \left(\frac{1}{6} \times 12\right) = 5 \times 2 = 10

Explanation

This method breaks down the multiplication into two simpler steps. First, find the unit fraction part of the whole number, which is like dividing the whole number by the denominator. Then, multiply that result by the numerator. This strategy is very useful because it often allows you to work with smaller, more manageable numbers.

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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

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  2. Lesson 2Current

    Lesson 2: Multiply a Whole Number by a Fraction

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  3. Lesson 3

    Lesson 3: Multiply Fractions and Whole Numbers

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  4. Lesson 4

    Lesson 4: Use Models to Multiply Two Fractions

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  5. Lesson 5

    Lesson 5: Multiply Two Fractions

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  6. Lesson 6

    Lesson 6: Area of a Rectangle

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  7. Lesson 7

    Lesson 7: Multiply Mixed Numbers

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  8. Lesson 8

    Lesson 8: Multiplication as Scaling

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Lesson overview

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Section 1

Multiplying a Fraction by a Whole Number

Property

To find a fraction of a whole number, multiply the numerator by the whole number and place the product over the original denominator.
The word "of" in mathematics usually means to multiply.

ab of c=ab×c=a×cb\frac{a}{b} \text{ of } c = \frac{a}{b} \times c = \frac{a \times c}{b}

Section 2

Commutative Property of Multiplication

Property

Due to the commutative property, multiplying a fraction by a whole number can be interpreted in two equivalent ways: finding a fraction of a set, or as repeated addition of the fraction.

ab×c ("a/b of c")=c×ab ("c groups of a/b")\frac{a}{b} \times c \text{ ("a/b of c")} = c \times \frac{a}{b} \text{ ("c groups of a/b")}

Examples

Section 3

Multiplying Using Unit Fractions

Property

To multiply a fraction by a whole number, you can decompose the fraction and multiply by the unit fraction first.

ab×n=a×(1b×n)\frac{a}{b} \times n = a \times \left(\frac{1}{b} \times n\right)

Examples

  • 34×8=3×(14×8)=3×2=6\frac{3}{4} \times 8 = 3 \times \left(\frac{1}{4} \times 8\right) = 3 \times 2 = 6
  • 25×15=2×(15×15)=2×3=6\frac{2}{5} \times 15 = 2 \times \left(\frac{1}{5} \times 15\right) = 2 \times 3 = 6
  • 56×12=5×(16×12)=5×2=10\frac{5}{6} \times 12 = 5 \times \left(\frac{1}{6} \times 12\right) = 5 \times 2 = 10

Explanation

This method breaks down the multiplication into two simpler steps. First, find the unit fraction part of the whole number, which is like dividing the whole number by the denominator. Then, multiply that result by the numerator. This strategy is very useful because it often allows you to work with smaller, more manageable numbers.

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

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  2. Lesson 2Current

    Lesson 2: Multiply a Whole Number by a Fraction

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  3. Lesson 3

    Lesson 3: Multiply Fractions and Whole Numbers

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  4. Lesson 4

    Lesson 4: Use Models to Multiply Two Fractions

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  5. Lesson 5

    Lesson 5: Multiply Two Fractions

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  6. Lesson 6

    Lesson 6: Area of a Rectangle

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  7. Lesson 7

    Lesson 7: Multiply Mixed Numbers

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  8. Lesson 8

    Lesson 8: Multiplication as Scaling

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