Divide Decimals Using an Algorithm

Use place-value reasoning and the standard algorithm to divide decimals fluently.

6.NOS.B.3 · Compute Fluently with Multi-Digit Decimals
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W

Warm-Up

2 questions
Warm-Up 1
What is 8.4 ÷ 2?
Vocabulary: A decimal is a number with a dot that separates whole and fractional parts. When dividing decimals, use place value to keep the decimal point in the right spot.
Hint: 8 ÷ 2 = 4, and 0.4 ÷ 2 = 0.2. Add them together.
✓Correct! 8.4 ÷ 2 = 4.2. The decimal point stays aligned in the quotient.
✗Divide step by step: 8 ÷ 2 = 4, then 4 tenths ÷ 2 = 2 tenths. The answer is B: 4.2.
Warm-Up 2
When you divide 6.3 by 0.7, the first step is to move the decimal point. What do both numbers become?
Key idea: When the divisor is a decimal, multiply both the dividend and divisor by 10 (or 100) to make the divisor a whole number.
✓Correct! Multiply both by 10: 6.3 becomes 63 and 0.7 becomes 7. Then divide: 63 ÷ 7 = 9.
✗To make the divisor a whole number, multiply both numbers by 10. 6.3 × 10 = 63, and 0.7 × 10 = 7. The answer is A.
P

Practice

5 questions
Practice 1
What is 15.6 ÷ 4?
Strategy: Set up long division. Place the decimal point in the quotient directly above where it is in the dividend. Then divide as with whole numbers.
15.6 ÷ 4 =
Show your steps:

Sentence frame: "I divided ___ by ___ and got ___. I placed the decimal point ___."

✓Correct! 15.6 ÷ 4 = 3.9. Check: 3.9 × 4 = 15.6.
✗15 ÷ 4 = 3 R3. Bring down 6 to get 36 tenths ÷ 4 = 9 tenths. The answer is 3.9.
Practice 2
What is 7.56 ÷ 0.6?
First step: Multiply both numbers by 10 so the divisor becomes a whole number: 75.6 ÷ 6. Then use the algorithm.
Show your work:

Sentence frame: "I multiplied both by ___ to get ___ ÷ ___. The quotient is ___."

✓Correct! 7.56 ÷ 0.6 = 12.6. Move decimal: 75.6 ÷ 6 = 12.6.
✗Multiply both by 10: 75.6 ÷ 6 = 12.6. The answer is B.
Practice 3
Match each decimal division problem with its quotient.
Tip: For each problem, decide if you need to move the decimal point first. Then divide carefully.
0.8
3.5
14
4.0 ÷ 5 =
14.0 ÷ 4 =
8.4 ÷ 0.6 =
✓All correct! 4.0÷5 = 0.8, 14.0÷4 = 3.5, 8.4÷0.6 = 14.
✗Some matches are off. Check each division carefully, especially where you need to move the decimal.
Practice 4
A ribbon that is 9.45 meters long is cut into pieces that are each 0.35 meters. How many pieces are there?
Key words: "Cut into pieces" means divide. The dividend is 9.45 and the divisor is 0.35.
Step 1: Multiply both by 100 to get 945 ÷ 35.
Number of pieces:
Show your work:

Sentence frame: "I divided ___ by ___ to find that there are ___ pieces."

✓Correct! 9.45 ÷ 0.35 = 27 pieces. (945 ÷ 35 = 27)
✗Move the decimal: 945 ÷ 35 = 27. There are 27 pieces.
Practice 5
Jamal says 4.32 ÷ 1.2 = 0.36. Is he correct?
How to check: Multiply both by 10 to get 43.2 ÷ 12. Then divide. Does your answer match 0.36?
Explain the correct answer:

Sentence frame: "Jamal is incorrect because 4.32 ÷ 1.2 = ___, not ___."

✓Correct! Jamal made an error. 4.32 ÷ 1.2 = 3.6, not 0.36. He likely misplaced the decimal point.
✗Check: 43.2 ÷ 12 = 3.6. Jamal's answer of 0.36 is wrong — the correct answer is 3.6. He is not correct.
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Challenge

1 question
Challenge
A store sells trail mix for $4.75 per pound. You spend $23.75. How many pounds of trail mix did you buy?
Think about it: Total cost ÷ price per pound = number of pounds. Set up 23.75 ÷ 4.75. Multiply both by 100 first: 2375 ÷ 475.
You bought pounds.
Show your division work:

Sentence frame: "I divided ___ by ___ and got ___. You bought ___ pounds of trail mix."

✓Excellent! $23.75 ÷ $4.75 = 5 pounds. Check: 5 × $4.75 = $23.75.
✗Divide: 2375 ÷ 475 = 5. You bought 5 pounds. Check: 5 × 4.75 = 23.75.