Dividing Decimals by a Whole Number — Part 2
Semester 4B · Chapter 14 · Lesson 6 · MATH-4B-C14-L06
Before you begin: prerequisite check
Recall: 14.06. Attempt these questions independently first.
Calculate 9.00 ÷ 6.
Show answer and reasoning
900 hundredths ÷6=150 hundredths = 1.50. Verify by multiplying.
Calculate 4.80 ÷ 3.
Show answer and reasoning
480 hundredths ÷3=160 hundredths = 1.60. Verify by multiplying.
Calculate 7.20 ÷ 4.
Show answer and reasoning
720 hundredths ÷4=180 hundredths = 1.80. Verify by multiplying.
Key vocabulary
- factor
- number being multiplied
- product
- result of multiplication
- dividend
- quantity divided into groups
- quotient
- amount in each equal group
Understand the concept
A quotient may require exchanging units after starting the division. For 5.4÷4, divide five ones among four groups to give one each, then exchange the remaining one into ten tenths. Fourteen tenths shared among four groups gives three tenths each and two tenths remaining. Exchange those two tenths into twenty hundredths: five hundredths per group. Thus the quotient is 1.35. Every exchange preserves the total measured amount.
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
Divide 11.48 equally among 7 people. How much does each receive?
Convert to hundredths: 1148÷7=164 hundredths = 1.64. Exchange hundreds/tenths when needed.
Check 1: try it yourself
Divide 12.32 equally among 7 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1232÷7=176 hundredths = 1.76. Exchange hundreds/tenths when needed.
Worked example 2
Divide 8.16 equally among 3 people. How much does each receive?
Convert to hundredths: 816÷3=272 hundredths = 2.72. Exchange hundreds/tenths when needed.
Check 2: try it yourself
Divide 4.02 equally among 3 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 402÷3=134 hundredths = 1.34. Exchange hundreds/tenths when needed.
Worked example 3
Divide 6.84 equally among 3 people. How much does each receive?
Convert to hundredths: 684÷3=228 hundredths = 2.28. Exchange hundreds/tenths when needed.
Check 3: try it yourself
Divide 3.28 equally among 2 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 328÷2=164 hundredths = 1.64. Exchange hundreds/tenths when needed.
Guided practice
Divide 5.76 equally among 3 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 576÷3=192 hundredths = 1.92. Exchange hundreds/tenths when needed.
Divide 15.78 equally among 6 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1578÷6=263 hundredths = 2.63. Exchange hundreds/tenths when needed.
Divide 7.83 equally among 3 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 783÷3=261 hundredths = 2.61. Exchange hundreds/tenths when needed.
Divide 11.68 equally among 4 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1168÷4=292 hundredths = 2.92. Exchange hundreds/tenths when needed.
Divide 11.90 equally among 7 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1190÷7=170 hundredths = 1.70. Exchange hundreds/tenths when needed.
Independent practice
Divide 10.80 equally among 8 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1080÷8=135 hundredths = 1.35. Exchange hundreds/tenths when needed.
Divide 12.60 equally among 5 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1260÷5=252 hundredths = 2.52. Exchange hundreds/tenths when needed.
Divide 8.08 equally among 4 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 808÷4=202 hundredths = 2.02. Exchange hundreds/tenths when needed.
Divide 12.66 equally among 6 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1266÷6=211 hundredths = 2.11. Exchange hundreds/tenths when needed.
Divide 6.30 equally among 3 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 630÷3=210 hundredths = 2.10. Exchange hundreds/tenths when needed.
Divide 9.84 equally among 6 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 984÷6=164 hundredths = 1.64. Exchange hundreds/tenths when needed.
Divide 8.45 equally among 5 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 845÷5=169 hundredths = 1.69. Exchange hundreds/tenths when needed.
Divide 14.40 equally among 6 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1440÷6=240 hundredths = 2.40. Exchange hundreds/tenths when needed.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Divide 4.44 equally among 4 people. How much does each receive? Explain how place value or a model can check your result.
Show answer and reasoning
Convert to hundredths: 444÷4=111 hundredths = 1.11. Exchange hundreds/tenths when needed. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “5.4 ÷ 4 = 1.3 with 2 left over, so the division is finished.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 5.4 ÷ 4 = 1.35; exchange the remaining tenths for hundredths and continue. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Divide 10.15 equally among 5 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1015÷5=203 hundredths = 2.03. Exchange hundreds/tenths when needed.
Divide 8.58 equally among 3 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 858÷3=286 hundredths = 2.86. Exchange hundreds/tenths when needed.
Divide 15.76 equally among 8 people. How much does each receive?
Show answer and reasoning
Convert to hundredths: 1576÷8=197 hundredths = 1.97. Exchange hundreds/tenths when needed.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.