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 examplemaking the divisor a whole number

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

How many 0.4-liter cups can be filled from 9.6 liters of juice?

  1. The divisor 0.4 is not whole, so slide its point one place right to make it 4.
  2. Slide the dividend's point the same one place: 9.6 becomes 96.
  3. Divide the equivalent problem 96 ÷ 4 with the usual algorithm.
  4. Sliding both points multiplies both numbers by ten, so the quotient does not change.

Answer: 24 cups can be filled, because 9.6 ÷ 0.4 and 96 ÷ 4 have the same quotient.

Now you trySame steps, your turn

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

How many 0.25-meter ribbons can be cut from 8.5 meters of ribbon?

  1. Is the divisor whole? Slide its point places right to get
  2. Slide the dividend the same number of places:
  3. Divide the new whole-number problem: ÷
  4. Number of ribbons: Check by multiplying.
Answer:number of ribbons

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 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 2.7Dividing 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:
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:
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:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help