Learn on PengiEureka Math, Grade 5Chapter 25: Division of Fractions and Decimal Fractions

Lesson 1: Divide a whole number by a unit fraction.

In this Grade 5 Eureka Math lesson from Chapter 25, students learn to divide a whole number by a unit fraction using tape diagrams and area models to build conceptual understanding. Through hands-on problems, such as determining how many one-third or one-fourth pound bags can be made from a whole number of pounds, students discover the relationship between division by a unit fraction and multiplication by its reciprocal. The lesson connects prior knowledge of fraction and decimal operations to this new division concept.

Section 1

Whole Number ÷ Unit Fraction

Property

Dividing a whole number, aa, by a unit fraction, 1b\frac{1}{b}, is a way of asking: "How many groups of size 1b\frac{1}{b} are in aa?"
This can be modeled visually to find the total number of fractional parts.

Examples

Section 2

Connecting Division by a Unit Fraction to Multiplication

Property

We noticed in the previous visual models that dividing by a unit fraction (1b\frac{1}{b}) produces the same result as multiplying by the denominator (bb).
To solve a÷1ba \div \frac{1}{b}, you can ask: "aa is 1b\frac{1}{b} of what number?". The shortcut is to multiply the whole number by the denominator:

a÷1b=a×ba \div \frac{1}{b} = a \times b

Examples

Book overview

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Chapter 25: Division of Fractions and Decimal Fractions

  1. Lesson 1Current

    Lesson 1: Divide a whole number by a unit fraction.

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  2. Lesson 2

    Lesson 2: Divide a unit fraction by a whole number.

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  3. Lesson 3

    Lesson 3: Solve problems involving fraction division.

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  4. Lesson 4

    Lesson 4: Write equations and word problems corresponding to tape and number line diagrams.

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  5. Lesson 5

    Lesson 5: Connect division by a unit fraction to division by 1 tenth and 1 hundredth.

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  6. Lesson 6

    Lesson 6: Divide decimal dividends by non-unit decimal divisors.

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  7. Lesson 7

    Lesson 7: Divide decimal dividends by non-unit decimal divisors.

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Lesson overview

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Section 1

Whole Number ÷ Unit Fraction

Property

Dividing a whole number, aa, by a unit fraction, 1b\frac{1}{b}, is a way of asking: "How many groups of size 1b\frac{1}{b} are in aa?"
This can be modeled visually to find the total number of fractional parts.

Examples

Section 2

Connecting Division by a Unit Fraction to Multiplication

Property

We noticed in the previous visual models that dividing by a unit fraction (1b\frac{1}{b}) produces the same result as multiplying by the denominator (bb).
To solve a÷1ba \div \frac{1}{b}, you can ask: "aa is 1b\frac{1}{b} of what number?". The shortcut is to multiply the whole number by the denominator:

a÷1b=a×ba \div \frac{1}{b} = a \times b

Examples

Book overview

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

Continue this chapter

Chapter 25: Division of Fractions and Decimal Fractions

  1. Lesson 1Current

    Lesson 1: Divide a whole number by a unit fraction.

    LearnPractice
  2. Lesson 2

    Lesson 2: Divide a unit fraction by a whole number.

    LearnPractice
  3. Lesson 3

    Lesson 3: Solve problems involving fraction division.

    LearnPractice
  4. Lesson 4

    Lesson 4: Write equations and word problems corresponding to tape and number line diagrams.

    LearnPractice
  5. Lesson 5

    Lesson 5: Connect division by a unit fraction to division by 1 tenth and 1 hundredth.

    LearnPractice
  6. Lesson 6

    Lesson 6: Divide decimal dividends by non-unit decimal divisors.

    LearnPractice
  7. Lesson 7

    Lesson 7: Divide decimal dividends by non-unit decimal divisors.

    LearnPractice