Learn on PengienVision, Mathematics, Grade 4Chapter 10: Extend Multiplication Concepts to Fractions

Lesson 3: Multiply a Fraction by a Whole Number: Use Symbols

Property.

Section 1

Justifying the Rule with the Associative Property

Property

To multiply a whole number nn by a fraction ab\frac{a}{b}, you can decompose the fraction, apply the associative property, and then multiply the whole number by the numerator.
This demonstrates the rule n×ab=n×abn \times \frac{a}{b} = \frac{n \times a}{b}.

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

Examples

Section 2

Multiplying a Whole Number by a Fraction

Property

To multiply a whole number (nn) by a fraction (ab\frac{a}{b}), multiply the whole number by the numerator (aa) and keep the denominator (bb) the same.

n×ab=n×abn \times \frac{a}{b} = \frac{n \times a}{b}

Examples

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Chapter 10: Extend Multiplication Concepts to Fractions

  1. Lesson 1

    Lesson 1: Fractions as Multiples of Unit Fractions

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  2. Lesson 2

    Lesson 2: Multiply a Fraction by a Whole Number: Use Models

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  3. Lesson 3Current

    Lesson 3: Multiply a Fraction by a Whole Number: Use Symbols

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  4. Lesson 4

    Lesson 4: Solve Time Problems

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Lesson overview

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Section 1

Justifying the Rule with the Associative Property

Property

To multiply a whole number nn by a fraction ab\frac{a}{b}, you can decompose the fraction, apply the associative property, and then multiply the whole number by the numerator.
This demonstrates the rule n×ab=n×abn \times \frac{a}{b} = \frac{n \times a}{b}.

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

Examples

Section 2

Multiplying a Whole Number by a Fraction

Property

To multiply a whole number (nn) by a fraction (ab\frac{a}{b}), multiply the whole number by the numerator (aa) and keep the denominator (bb) the same.

n×ab=n×abn \times \frac{a}{b} = \frac{n \times a}{b}

Examples

Book overview

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

Continue this chapter

Chapter 10: Extend Multiplication Concepts to Fractions

  1. Lesson 1

    Lesson 1: Fractions as Multiples of Unit Fractions

    LearnPractice
  2. Lesson 2

    Lesson 2: Multiply a Fraction by a Whole Number: Use Models

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Multiply a Fraction by a Whole Number: Use Symbols

    LearnPractice
  4. Lesson 4

    Lesson 4: Solve Time Problems

    LearnPractice