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

Lesson 2.7Divide Decimals Using an Algorithm

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 84.6 ÷ 6, it is 84.6
DivisorSpanish: Divisor The number of equal groups you are dividing into (the number outside the division bracket). In 84.6 ÷ 6, it is 6
QuotientSpanish: Cociente The answer when you divide. 84.6 ÷ 6 = 14.1
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. 7.56 ÷ 0.12 = 756 ÷ 12 = 63 (both multiplied by 100)
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 exampledividing a decimal by a whole number

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

A ribbon 82.2 meters long is cut into 4 equal pieces. How long is each piece?

  1. Write 82.2 inside the bracket with 4 outside. The divisor is already a whole number.
  2. Put the quotient's decimal point straight above the point in 82.2, then start dividing.
  3. Divide, multiply, subtract, bring down — one place-value column at a time.
  4. An amount is still left over, so annex a zero to 82.2 and keep dividing.

Answer: Each piece is 20.55 meters long.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A load weighing 57.6 kilograms is split evenly into 3 boxes. How much does each box hold?

  1. Write inside the bracket and outside. Is the divisor whole?
  2. Place the quotient's decimal point directly above the point in the dividend.
  3. Divide, multiply, subtract, bring down until no digits are left.
  4. Each box holds kilograms. Check by multiplying your quotient.
Answer:kilograms in each box

Say it and write itSentence starters

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

  • The dividend is and the divisor is .
  • I placed the decimal point because .
  • When a remainder appeared I .
  • I checked my quotient by .

Word bank dividenddivisorquotientdecimal pointalgorithmannexbring downplace valueestimatecheckmultiplysubtract

Watch outA 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 2.7Divide Decimals Using an Algorithm

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 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Rewrite each problem by making the divisor a whole number, then solve.

    OriginalMultiply Both ByNew ProblemQuotient
    4.5 ÷ 0.910
    3.6 ÷ 0.410

    Hint The 'Multiply Both By' column is the key move: choose 10 or 100 based on how many decimal places the DIVISOR has.

    Show your work
Part 2Practice the skillshow every step
  1. 2Circle the letter of the best answer. Show how you know.

    What is 14.4 ÷ 1.2?

    1. A0.12
    2. B1.2
    3. C12
    4. D120

    Hint Dividing by a decimal is awkward — notice the divisor 1.2 has one decimal place. There's a move that makes it whole.

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    What is 3.78 ÷ 0.6?

    1. A0.063
    2. B0.63
    3. C6.3
    4. D63

    Hint The divisor 0.6 has one decimal place — shifting both numbers one place makes the divisor a whole number.

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    What is 8.4 ÷ 0.7?

    1. A0.12
    2. B1.2
    3. C12
    4. D120

    Hint Ask yourself: how many groups of 0.7 fit inside 8.4? Since 0.7 is less than 1, expect MORE groups than 8.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    What is 15.6 ÷ 1.3?

    1. A1.2
    2. B12
    3. C13
    4. D120

    Hint The divisor 1.3 isn't a whole number — shift both numbers before you divide anything.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1ProblemSolve 6.4 ÷ 0.8.
    2. 2Move the divisor's decimal0.8 becomes 8 (moved 1 place right).
    3. 3Divide without moving the dividend6.4 ÷ 8 = 0.8

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint When you moved 0.8 to 8, what did you have to do to 6.4 as well?

    Correct work
    Correct answer:

Explain your thinkingWhy does moving the point the same number of places in both numbers give you the same quotient — and why is it worth doing before you start the divide, multiply, subtract, bring down cycle?

Sentence starter Multiplying both numbers by ___ doesn't change the quotient because ___.

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 2.7Divide Decimals Using an Algorithm

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 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Solve each decimal division problem.

    Division ProblemQuotient
    9.6 ÷ 0.8
    15.6 ÷ 1.3
    24.5 ÷ 3.5
    5.76 ÷ 0.24
    11.34 ÷ 0.9
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each decimal division to its quotient.

    1. 7.2 ÷ 0.8
    2. 4.56 ÷ 0.6
    3. 13.2 ÷ 1.2
    4. 3.6 ÷ 0.12
    5. 10.5 ÷ 1.5
    6. 0.96 ÷ 0.8
    • A9
    • B7.6
    • C11
    • D30
    • E7
    • F1.2
  3. 3Write the name of the correct group on each line.

    Sort: should you multiply both numbers by 10 or by 100 to make the divisor a whole number?

    Groups: Multiply Both by 10 Multiply Both by 100
    • 6.3 ÷ 0.7 → multiply by 10
    • 8.4 ÷ 2.1 → multiply by 10
    • 13.6 ÷ 1.7 → multiply by 10
    • 7.56 ÷ 0.12 → multiply by 100
    • 8.28 ÷ 0.36 → multiply by 100
    • 9.45 ÷ 0.15 → multiply by 100
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A water tank holds 19.2 liters. It is poured into bottles that each hold 1.6 liters. How many bottles can be filled?

    1. A1.2 bottles
    2. B11 bottles
    3. C12 bottles
    4. D13 bottles
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1ProblemSolve 9.6 ÷ 0.12.
    2. 2Count how far to move0.12 has 2 decimal places, so BOTH numbers move 2 places right. The divisor: 0.12 → 12.
    3. 3Move the dividend the same 2 places9.6 only has one digit after the point, so the student moved it just 1 place: 9.6 → 96. New problem: 96 ÷ 12 = 8.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingWhy does moving the point the same number of places in both numbers give you the same quotient — and why is it worth doing before you start the divide, multiply, subtract, bring down cycle?

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 2.7Divide Decimals Using an Algorithm

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 1Understand the ideamodels and meaning
  1. 1Decide whether each pair balances. Check Yes or No, then explain.

    Verify each division by showing that quotient × divisor = dividend. Are the two sides balanced?

    Left sideRight sideBalanced?
    19.6 ÷ 0.8=?12 × 0.8 = 9.6☐ Yes ☐ No
    27.56 ÷ 0.12=?63 × 0.12 = 7.56☐ Yes ☐ No
    35.4 ÷ 0.9=?5 × 0.9 = 4.5☐ Yes ☐ No
    Explain your choice
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find Derek's Mistake

    1. 1Problem7.2 ÷ 0.45
    2. 2Multiply divisor by 100.45 × 10 = 4.5
    3. 3Multiply dividend by 107.2 × 10 = 72
    4. 4Divide72 ÷ 4.5 = 16

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A gas station sells fuel at $3.45 per gallon. A customer pays $27.60 total. How many gallons did the customer buy? Set up the decimal division, show how to convert it to whole-number division, and solve.

    Write your answer

Explain your thinkingWhy does moving the point the same number of places in both numbers give you the same quotient — and why is it worth doing before you start the divide, multiply, subtract, bring down cycle?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help