Curriculum›4B›Chapter 14

Dividing Decimals by a Whole Number — Part 3

Semester 4B · Chapter 14 · Lesson 7 · MATH-4B-C14-L07

Learning goal: Solve multidigit decimal division problems and contextual applications.

Before you begin: prerequisite check

Recall: 14.06–14.07. Attempt these questions independently first.

Question 1 · application

Divide 22.80 equally among 8 people. How much does each receive?

Show answer and reasoning

2.85

Convert to hundredths: 2280÷8=285 hundredths = 2.85. Exchange hundreds/tenths when needed.

Question 2 · application

Divide 8.96 equally among 7 people. How much does each receive?

Show answer and reasoning

1.28

Convert to hundredths: 896÷7=128 hundredths = 1.28. Exchange hundreds/tenths when needed.

Question 3 · application

Divide 4.64 equally among 2 people. How much does each receive?

Show answer and reasoning

2.32

Convert to hundredths: 464÷2=232 hundredths = 2.32. Exchange hundreds/tenths when needed.

Key vocabulary

factor: number being multiplied
product: result of multiplication
dividend: quantity divided into groups
quotient: amount in each equal group

Understand the concept

Longer decimal division follows the same equal-sharing and regrouping rules as whole-number division. For 12.48÷6, share twelve ones to get two ones per group, then divide four tenths and eight hundredths after exchanging as needed. The answer is 2.08, because 2.08×6=12.48. Word problems require interpreting the quotient's unit: dollars per person, meters per section, or liters per container. Use multiplication to verify. A zero in a quotient may be necessary to mark an empty tenths place while the hundredths place has a nonzero amount.

Common misunderstanding to avoid: Unverified quotient scale

Fully worked examples and immediate checks

Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.

Worked example 1

Question 1 · application

28.25 liters of juice are shared equally into 5 containers. How many liters per container?

Answer: 5.65 L

2825 hundredths ÷5=565 hundredths = 5.65 liters. Check 5.65×5=28.25.

Check 1: try it yourself

Question 1 · application

11.16 liters of juice are shared equally into 6 containers. How many liters per container?

Show answer and reasoning

1.86 L

1116 hundredths ÷6=186 hundredths = 1.86 liters. Check 1.86×6=11.16.

Worked example 2

Question 2 · application

3.88 liters of juice are shared equally into 2 containers. How many liters per container?

Answer: 1.94 L

388 hundredths ÷2=194 hundredths = 1.94 liters. Check 1.94×2=3.88.

Check 2: try it yourself

Question 2 · application

5.38 liters of juice are shared equally into 2 containers. How many liters per container?

Show answer and reasoning

2.69 L

538 hundredths ÷2=269 hundredths = 2.69 liters. Check 2.69×2=5.38.

Worked example 3

Question 3 · application

13.76 liters of juice are shared equally into 4 containers. How many liters per container?

Answer: 3.44 L

1376 hundredths ÷4=344 hundredths = 3.44 liters. Check 3.44×4=13.76.

Check 3: try it yourself

Question 3 · application

29.46 liters of juice are shared equally into 6 containers. How many liters per container?

Show answer and reasoning

4.91 L

2946 hundredths ÷6=491 hundredths = 4.91 liters. Check 4.91×6=29.46.

Guided practice

Question 1 · application

2.36 liters of juice are shared equally into 2 containers. How many liters per container?

Show answer and reasoning

1.18 L

236 hundredths ÷2=118 hundredths = 1.18 liters. Check 1.18×2=2.36.

Question 2 · application

5.74 liters of juice are shared equally into 2 containers. How many liters per container?

Show answer and reasoning

2.87 L

574 hundredths ÷2=287 hundredths = 2.87 liters. Check 2.87×2=5.74.

Question 3 · application

18.40 liters of juice are shared equally into 5 containers. How many liters per container?

Show answer and reasoning

3.68 L

1840 hundredths ÷5=368 hundredths = 3.68 liters. Check 3.68×5=18.40.

Question 4 · application

11.15 liters of juice are shared equally into 5 containers. How many liters per container?

Show answer and reasoning

2.23 L

1115 hundredths ÷5=223 hundredths = 2.23 liters. Check 2.23×5=11.15.

Question 5 · application

22.95 liters of juice are shared equally into 5 containers. How many liters per container?

Show answer and reasoning

4.59 L

2295 hundredths ÷5=459 hundredths = 4.59 liters. Check 4.59×5=22.95.

Independent practice

Question 1 · application

48.60 liters of juice are shared equally into 9 containers. How many liters per container?

Show answer and reasoning

5.40 L

4860 hundredths ÷9=540 hundredths = 5.40 liters. Check 5.40×9=48.60.

Question 2 · application

3.12 liters of juice are shared equally into 2 containers. How many liters per container?

Show answer and reasoning

1.56 L

312 hundredths ÷2=156 hundredths = 1.56 liters. Check 1.56×2=3.12.

Question 3 · application

41.52 liters of juice are shared equally into 8 containers. How many liters per container?

Show answer and reasoning

5.19 L

4152 hundredths ÷8=519 hundredths = 5.19 liters. Check 5.19×8=41.52.

Question 4 · application

33.53 liters of juice are shared equally into 7 containers. How many liters per container?

Show answer and reasoning

4.79 L

3353 hundredths ÷7=479 hundredths = 4.79 liters. Check 4.79×7=33.53.

Question 5 · application

14.70 liters of juice are shared equally into 6 containers. How many liters per container?

Show answer and reasoning

2.45 L

1470 hundredths ÷6=245 hundredths = 2.45 liters. Check 2.45×6=14.70.

Question 6 · application

27.84 liters of juice are shared equally into 6 containers. How many liters per container?

Show answer and reasoning

4.64 L

2784 hundredths ÷6=464 hundredths = 4.64 liters. Check 4.64×6=27.84.

Question 7 · application

16.48 liters of juice are shared equally into 4 containers. How many liters per container?

Show answer and reasoning

4.12 L

1648 hundredths ÷4=412 hundredths = 4.12 liters. Check 4.12×4=16.48.

Question 8 · application

9.52 liters of juice are shared equally into 4 containers. How many liters per container?

Show answer and reasoning

2.38 L

952 hundredths ÷4=238 hundredths = 2.38 liters. Check 2.38×4=9.52.

Challenge and transfer

Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.

Question 1 · reasoning

10.96 liters of juice are shared equally into 4 containers. How many liters per container? Explain how place value or a model can check your result.

Show answer and reasoning

2.74 L

1096 hundredths ÷4=274 hundredths = 2.74 liters. Check 2.74×4=10.96. A correct explanation should name the relevant fractional place values and verify the answer.

Question 2 · error analysis

A learner claims: “12.48 ÷ 6 = 2.8 because the zero in the tenths place is unnecessary.” Identify what is wrong or incomplete and give a mathematically correct explanation.

Show answer and reasoning

False: the correct quotient is 2.08; omitting the zero changes the value.

False: the correct quotient is 2.08; omitting the zero changes the value. Explain the relevant quantities or properties, not merely the final answer.

Exit check

Question 1 · application

39.96 liters of juice are shared equally into 9 containers. How many liters per container?

Show answer and reasoning

4.44 L

3996 hundredths ÷9=444 hundredths = 4.44 liters. Check 4.44×9=39.96.

Question 2 · application

13.30 liters of juice are shared equally into 7 containers. How many liters per container?

Show answer and reasoning

1.90 L

1330 hundredths ÷7=190 hundredths = 1.90 liters. Check 1.90×7=13.30.

Question 3 · application

51.48 liters of juice are shared equally into 9 containers. How many liters per container?

Show answer and reasoning

5.72 L

5148 hundredths ÷9=572 hundredths = 5.72 liters. Check 5.72×9=51.48.

Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.

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