Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.7Dividing by a Decimal

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can divide with decimals by making the divisor a whole number first.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
DividendSpanish: Dividendo The total number being divided into equal groups (the number inside the division bracket). In 8.4 ÷ 0.2, it is 8.4
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 8.4 ÷ 0.2, it is 0.2
QuotientSpanish: Cociente The answer when you divide. 8.4 ÷ 0.2 = 42
Decimal Division AlgorithmSpanish: Algoritmo de división decimal The steps for dividing decimals: slide the divisor's decimal point right until the divisor is a whole number, slide the dividend's point right the same number of places, then divide. 8.4 ÷ 2.1 → move the point in both → 84 ÷ 21 → divide, multiply, subtract, bring down → 4
Equivalent divisionSpanish: División equivalente Multiplying both numbers by 10 or 100 gives the same answer. 8.4 ÷ 0.2 → 84 ÷ 2
Annex a zeroSpanish: Agregar un cero Write a zero after the last decimal digit without changing the value. 7.2 → 7.20

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

How many 0.7-liter bottles can be filled from 8.4 liters?

  1. Write 8.4 ÷ 0.7.
  2. Multiply both by 10: 0.7 × 10 = 7 and 8.4 × 10 = 84.
  3. 84 ÷ 7 = 12. Check: 12 × 0.7 = 8.4.

Answer: 12 bottles

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The divisor is not a whole number, so I slid its point places.
  • I slid the dividend the same way, turning into .
  • The equivalent problem is ÷ .
  • The quotient stays the same because .

Word bank divisordividendquotientslidedecimal pointequivalentpower of tenwhole numberplacesestimatecheckmultiply

Watch out!A common mistake

A common mistake in Divide Decimals is moving the decimal point in the divisor but forgetting to move it the same number of places in the dividend. For example, in 6.4 ÷ 0.8 a student changes 0.8 to 8 but leaves the dividend as 6.4, then divides 6.4 ÷ 8 = 0.8 instead of moving both points to get 64 ÷ 8 = 8. A second version of this mistake happens when the divisor has two decimal places, like 0.12: students move both points only 1 place instead of 2, turning 9.6 ÷ 0.12 into 96 ÷ 1.2 instead of the correct 960 ÷ 12. Count the divisor's decimal places first, then move BOTH points that same number of places.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.7Dividing by a Decimal

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can divide with decimals by making the divisor a whole number first.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    Find 4.2 ÷ 0.6.

    Show your work

    Hint Move both points 1 place right. Then find 42 ÷ 6.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Find 12.5 ÷ 2.5.

    Show your work

    Hint Move both points 1 place right. Then find 125 ÷ 25.

    Final answer:
Part 2Apply itreal-world problems
  1. 3Complete each step, then write the final answer.

    A rope is 3.2 meters long. Each piece is 0.4 meter long. How many pieces can you cut?

    Show your work

    Hint Move both points 1 place right. Then find 32 ÷ 4.

    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.7Dividing by a Decimal

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can divide with decimals by making the divisor a whole number first.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    Find 0.84 ÷ 0.07.

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Find 9.6 ÷ 0.8.

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 3Complete each step, then write the final answer.

    Leo finds 4.8 ÷ 0.6. He moves the point in 0.6 but not in 4.8. He gets 0.8. What is the correct quotient?

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.7Dividing by a Decimal

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can divide with decimals by making the divisor a whole number first.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    Find 2.8 ÷ 0.35.

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Find 18.9 ÷ 6.3 using the decimal division algorithm.

    1. A0.3
    2. B2.8
    3. C3
    4. D30
    Show your work
  2. 3Complete each step, then write the final answer.

    Ana says 6.3 ÷ 0.07 is 9. She changed the problem to 63 ÷ 7. What is the correct quotient?

    Show your work
    Final answer:
3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help