Multiplying Decimals by a Whole Number — Part 1
Semester 4B · Chapter 14 · Lesson 2 · MATH-4B-C14-L02
Before you begin: prerequisite check
Recall: 14.01; whole-number algorithms. Attempt these questions independently first.
Calculate 0.3 × 4.
Show answer and reasoning
The displayed decimal contains 3 tenths. Multiply the number of equal units by 4: 12 tenths = 1.2.
Calculate 0.04 × 4.
Show answer and reasoning
The displayed decimal contains 4 hundredths. Multiply the number of equal units by 4: 16 hundredths = 0.16.
Calculate 0.8 × 9.
Show answer and reasoning
The displayed decimal contains 8 tenths. Multiply the number of equal units by 9: 72 tenths = 7.2.
Key vocabulary
- factor
- number being multiplied
- product
- result of multiplication
- dividend
- quantity divided into groups
- quotient
- amount in each equal group
Understand the concept
Multiplication of a decimal by a whole number can be modeled as repeated addition or equal groups. For 1.25×3, add 1.25 three times to get 3.75. An area-style decomposition also works: 1×3 + 0.25×3 = 3.75. Estimate first: three groups of a little over one should give a little over three. Each partial product's unit matters, and a hundredth times an integer still counts hundredths before any regrouping.
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 2.77 × 5.
Repeated addition or distribution: 277 hundredths ×5=1385 hundredths=13.85.
Check 1: try it yourself
Calculate 3.56 × 8.
Show answer and reasoning
Repeated addition or distribution: 356 hundredths ×8=2848 hundredths=28.48.
Worked example 2
Calculate 4.39 × 7.
Repeated addition or distribution: 439 hundredths ×7=3073 hundredths=30.73.
Check 2: try it yourself
Calculate 3.31 × 6.
Show answer and reasoning
Repeated addition or distribution: 331 hundredths ×6=1986 hundredths=19.86.
Worked example 3
Calculate 2.50 × 5.
Repeated addition or distribution: 250 hundredths ×5=1250 hundredths=12.50.
Check 3: try it yourself
Calculate 3.90 × 3.
Show answer and reasoning
Repeated addition or distribution: 390 hundredths ×3=1170 hundredths=11.70.
Guided practice
Calculate 3.57 × 3.
Show answer and reasoning
Repeated addition or distribution: 357 hundredths ×3=1071 hundredths=10.71.
Calculate 4.12 × 2.
Show answer and reasoning
Repeated addition or distribution: 412 hundredths ×2=824 hundredths=8.24.
Calculate 2.67 × 4.
Show answer and reasoning
Repeated addition or distribution: 267 hundredths ×4=1068 hundredths=10.68.
Calculate 1.27 × 4.
Show answer and reasoning
Repeated addition or distribution: 127 hundredths ×4=508 hundredths=5.08.
Calculate 3.92 × 4.
Show answer and reasoning
Repeated addition or distribution: 392 hundredths ×4=1568 hundredths=15.68.
Independent practice
Calculate 1.81 × 7.
Show answer and reasoning
Repeated addition or distribution: 181 hundredths ×7=1267 hundredths=12.67.
Calculate 1.36 × 2.
Show answer and reasoning
Repeated addition or distribution: 136 hundredths ×2=272 hundredths=2.72.
Calculate 3.25 × 8.
Show answer and reasoning
Repeated addition or distribution: 325 hundredths ×8=2600 hundredths=26.00.
Calculate 3.82 × 5.
Show answer and reasoning
Repeated addition or distribution: 382 hundredths ×5=1910 hundredths=19.10.
Calculate 2.21 × 5.
Show answer and reasoning
Repeated addition or distribution: 221 hundredths ×5=1105 hundredths=11.05.
Calculate 2.76 × 6.
Show answer and reasoning
Repeated addition or distribution: 276 hundredths ×6=1656 hundredths=16.56.
Calculate 2.63 × 3.
Show answer and reasoning
Repeated addition or distribution: 263 hundredths ×3=789 hundredths=7.89.
Calculate 3.12 × 6.
Show answer and reasoning
Repeated addition or distribution: 312 hundredths ×6=1872 hundredths=18.72.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 2.58 × 7. Explain how place value or a model can check your result.
Show answer and reasoning
Repeated addition or distribution: 258 hundredths ×7=1806 hundredths=18.06. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “1.25 × 3 = 3.15.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 125 hundredths × 3 = 375 hundredths = 3.75. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 2.79 × 3.
Show answer and reasoning
Repeated addition or distribution: 279 hundredths ×3=837 hundredths=8.37.
Calculate 2.52 × 6.
Show answer and reasoning
Repeated addition or distribution: 252 hundredths ×6=1512 hundredths=15.12.
Calculate 1.98 × 3.
Show answer and reasoning
Repeated addition or distribution: 198 hundredths ×3=594 hundredths=5.94.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.