Dividing Decimals by a Whole Number — Part 1
Semester 4B · Chapter 14 · Lesson 5 · MATH-4B-C14-L05
Before you begin: prerequisite check
Recall: 14.05. Attempt these questions independently first.
Calculate 0.10 ÷ 5.
Show answer and reasoning
Share 10 hundredths equally among 5 groups: 2 hundredths each = 0.02.
Calculate 0.65 ÷ 5.
Show answer and reasoning
Share 65 hundredths equally among 5 groups: 13 hundredths each = 0.13.
Calculate 0.27 ÷ 3.
Show answer and reasoning
Share 27 hundredths equally among 3 groups: 9 hundredths each = 0.09.
Key vocabulary
- factor
- number being multiplied
- product
- result of multiplication
- dividend
- quantity divided into groups
- quotient
- amount in each equal group
Understand the concept
Divide a decimal by a whole number using place-value groups. For 8.4÷4, split eight ones into four groups of two and four tenths into four groups of one tenth: each group gets 2.1. Check by multiplying 2.1×4=8.4. When the tenths do not divide evenly, exchange one tenth for ten hundredths before continuing. The divisor here is a positive whole number; choose a quotient that matches the original magnitude.
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
Calculate 3.20 ÷ 2.
320 hundredths ÷2=160 hundredths = 1.60. Verify by multiplying.
Check 1: try it yourself
Calculate 7.60 ÷ 5.
Show answer and reasoning
760 hundredths ÷5=152 hundredths = 1.52. Verify by multiplying.
Worked example 2
Calculate 6.84 ÷ 6.
684 hundredths ÷6=114 hundredths = 1.14. Verify by multiplying.
Check 2: try it yourself
Calculate 6.80 ÷ 4.
Show answer and reasoning
680 hundredths ÷4=170 hundredths = 1.70. Verify by multiplying.
Worked example 3
Calculate 3.15 ÷ 3.
315 hundredths ÷3=105 hundredths = 1.05. Verify by multiplying.
Check 3: try it yourself
Calculate 5.70 ÷ 3.
Show answer and reasoning
570 hundredths ÷3=190 hundredths = 1.90. Verify by multiplying.
Guided practice
Calculate 6.08 ÷ 4.
Show answer and reasoning
608 hundredths ÷4=152 hundredths = 1.52. Verify by multiplying.
Calculate 4.16 ÷ 4.
Show answer and reasoning
416 hundredths ÷4=104 hundredths = 1.04. Verify by multiplying.
Calculate 8.60 ÷ 5.
Show answer and reasoning
860 hundredths ÷5=172 hundredths = 1.72. Verify by multiplying.
Calculate 3.10 ÷ 2.
Show answer and reasoning
310 hundredths ÷2=155 hundredths = 1.55. Verify by multiplying.
Calculate 6.30 ÷ 7.
Show answer and reasoning
630 hundredths ÷7=90 hundredths = 0.90. Verify by multiplying.
Independent practice
Calculate 4.45 ÷ 5.
Show answer and reasoning
445 hundredths ÷5=89 hundredths = 0.89. Verify by multiplying.
Calculate 4.17 ÷ 3.
Show answer and reasoning
417 hundredths ÷3=139 hundredths = 1.39. Verify by multiplying.
Calculate 1.86 ÷ 3.
Show answer and reasoning
186 hundredths ÷3=62 hundredths = 0.62. Verify by multiplying.
Calculate 8.12 ÷ 7.
Show answer and reasoning
812 hundredths ÷7=116 hundredths = 1.16. Verify by multiplying.
Calculate 5.05 ÷ 5.
Show answer and reasoning
505 hundredths ÷5=101 hundredths = 1.01. Verify by multiplying.
Calculate 9.80 ÷ 5.
Show answer and reasoning
980 hundredths ÷5=196 hundredths = 1.96. Verify by multiplying.
Calculate 8.45 ÷ 5.
Show answer and reasoning
845 hundredths ÷5=169 hundredths = 1.69. Verify by multiplying.
Calculate 3.92 ÷ 2.
Show answer and reasoning
392 hundredths ÷2=196 hundredths = 1.96. Verify by multiplying.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 6.54 ÷ 6. Explain how place value or a model can check your result.
Show answer and reasoning
654 hundredths ÷6=109 hundredths = 1.09. Verify by multiplying. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “8.4 ÷ 4 = 21 because 84 ÷ 4 = 21.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 84 tenths ÷ 4 = 21 tenths = 2.1. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 11.48 ÷ 7.
Show answer and reasoning
1148 hundredths ÷7=164 hundredths = 1.64. Verify by multiplying.
Calculate 7.50 ÷ 6.
Show answer and reasoning
750 hundredths ÷6=125 hundredths = 1.25. Verify by multiplying.
Calculate 4.80 ÷ 4.
Show answer and reasoning
480 hundredths ÷4=120 hundredths = 1.20. Verify by multiplying.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.