Learn on PengienVision, Mathematics, Grade 5Chapter 6: Use Models and Strategies to Divide Decimals

Lesson 5: Divide by a Decimal

In this Grade 5 lesson from enVision Mathematics Chapter 6, students learn how to divide a decimal by another decimal using strategies such as converting decimals to equivalent whole-number relationships, applying the inverse relationship between multiplication and division, and using place value reasoning with hundredths. The lesson connects decimal division to familiar whole-number division methods, helping students understand why the dividend and divisor can be scaled equally without changing the quotient. Real-world money contexts, such as finding the number of items purchased at a given unit price, ground the skill in practical problem-solving.

Section 1

Dividing Decimals by Converting to Whole Numbers

Property

If we multiply both numbers by the same number, the result of the division is the same. So, we can multiply both numbers by 10 as many times as we need to to make the divisor a whole number.
Then we proceed as with whole number division.

Examples

  • To solve 24.5÷0.524.5 \div 0.5, move the decimal one place in both numbers to get the equivalent problem 245÷5245 \div 5, which equals 4949.
  • To solve 8.82÷1.48.82 \div 1.4, move the decimal one place in both numbers to get 88.2÷1488.2 \div 14, which equals 6.36.3.

Book overview

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Chapter 6: Use Models and Strategies to Divide Decimals

  1. Lesson 1

    Lesson 1: Patterns for Dividing with Decimals

  2. Lesson 2

    Lesson 2: Estimate Decimal Quotients

  3. Lesson 3

    Lesson 3: Use Models to Divide by a 1-Digit Whole Number

  4. Lesson 4

    Lesson 4: Divide by a 2-Digit Whole Number

  5. Lesson 5Current

    Lesson 5: Divide by a Decimal

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Dividing Decimals by Converting to Whole Numbers

Property

If we multiply both numbers by the same number, the result of the division is the same. So, we can multiply both numbers by 10 as many times as we need to to make the divisor a whole number.
Then we proceed as with whole number division.

Examples

  • To solve 24.5÷0.524.5 \div 0.5, move the decimal one place in both numbers to get the equivalent problem 245÷5245 \div 5, which equals 4949.
  • To solve 8.82÷1.48.82 \div 1.4, move the decimal one place in both numbers to get 88.2÷1488.2 \div 14, which equals 6.36.3.

Book overview

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

Continue this chapter

Chapter 6: Use Models and Strategies to Divide Decimals

  1. Lesson 1

    Lesson 1: Patterns for Dividing with Decimals

  2. Lesson 2

    Lesson 2: Estimate Decimal Quotients

  3. Lesson 3

    Lesson 3: Use Models to Divide by a 1-Digit Whole Number

  4. Lesson 4

    Lesson 4: Divide by a 2-Digit Whole Number

  5. Lesson 5Current

    Lesson 5: Divide by a Decimal