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

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

In this Grade 5 Eureka Math lesson from Chapter 25, students learn to connect division by unit fractions to division by 1 tenth and 1 hundredth by rewriting decimal expressions like 7 ÷ 0.1 as fraction division problems such as 7 ÷ 1/10. Students practice reasoning about how many tenths or hundredths are in a whole number, building on prior work with dividing whole numbers by unit fractions. The lesson strengthens understanding of place value relationships and lays the groundwork for fluent division with decimal fractions.

Section 1

Divide by 0.1 by Finding the Number of Tenths

Property

Dividing a number by 0.10.1 is equivalent to finding the total number of tenths in that number. This is based on the place value relationship that 11 whole is equal to 1010 tenths.

Examples

Section 2

Divide by 0.01 Using Place Value

Property

Dividing a number by 0.010.01 is equivalent to finding the total number of hundredths in that number. This is the same as dividing by the unit fraction 1100\frac{1}{100} or multiplying by 100.

x÷0.01=x÷1100=x×100x \div 0.01 = x \div \frac{1}{100} = x \times 100

Examples

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Chapter 25: Division of Fractions and Decimal Fractions

  1. Lesson 1

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

  2. Lesson 2

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

  3. Lesson 3

    Lesson 3: Solve problems involving fraction division.

  4. Lesson 4

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

  5. Lesson 5Current

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

  6. Lesson 6

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

  7. Lesson 7

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

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Divide by 0.1 by Finding the Number of Tenths

Property

Dividing a number by 0.10.1 is equivalent to finding the total number of tenths in that number. This is based on the place value relationship that 11 whole is equal to 1010 tenths.

Examples

Section 2

Divide by 0.01 Using Place Value

Property

Dividing a number by 0.010.01 is equivalent to finding the total number of hundredths in that number. This is the same as dividing by the unit fraction 1100\frac{1}{100} or multiplying by 100.

x÷0.01=x÷1100=x×100x \div 0.01 = x \div \frac{1}{100} = x \times 100

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 1

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

  2. Lesson 2

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

  3. Lesson 3

    Lesson 3: Solve problems involving fraction division.

  4. Lesson 4

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

  5. Lesson 5Current

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

  6. Lesson 6

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

  7. Lesson 7

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