Multiplying Decimals by a Whole Number — Part 2
Semester 4B · Chapter 14 · Lesson 3 · MATH-4B-C14-L03
Before you begin: prerequisite check
Recall: 14.02 and 4A partial products. Attempt these questions independently first.
Calculate 3.01 × 3.
Show answer and reasoning
Repeated addition or distribution: 301 hundredths ×3=903 hundredths=9.03.
Calculate 2.09 × 2.
Show answer and reasoning
Repeated addition or distribution: 209 hundredths ×2=418 hundredths=4.18.
Calculate 2.02 × 8.
Show answer and reasoning
Repeated addition or distribution: 202 hundredths ×8=1616 hundredths=16.16.
Key vocabulary
- factor
- number being multiplied
- product
- result of multiplication
- dividend
- quantity divided into groups
- quotient
- amount in each equal group
Understand the concept
With a two-digit whole-number multiplier, use the distributive property. For 2.40×12, find ten copies of 2.40 and two copies of 2.40: 24.00+4.80=28.80. The multiplier remains a whole number; we have not learned general decimal-times-decimal multiplication yet in this chapter. Break the multiplier into tens and ones, track hundredths accurately, and use an estimate to check the scale of the product. Write the whole-number multiplier clearly so a reader can see the tens group and the ones group being combined.
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 2.94 × 20, where 20 is a whole number.
Use (20+0) groups: 294 hundredths ×20=5880 hundredths = 58.80.
Check 1: try it yourself
Calculate 1.19 × 23, where 23 is a whole number.
Show answer and reasoning
Use (20+3) groups: 119 hundredths ×23=2737 hundredths = 27.37.
Worked example 2
Calculate 3.30 × 13, where 13 is a whole number.
Use (10+3) groups: 330 hundredths ×13=4290 hundredths = 42.90.
Check 2: try it yourself
Calculate 1.18 × 15, where 15 is a whole number.
Show answer and reasoning
Use (10+5) groups: 118 hundredths ×15=1770 hundredths = 17.70.
Worked example 3
Calculate 1.05 × 25, where 25 is a whole number.
Use (20+5) groups: 105 hundredths ×25=2625 hundredths = 26.25.
Check 3: try it yourself
Calculate 2.85 × 24, where 24 is a whole number.
Show answer and reasoning
Use (20+4) groups: 285 hundredths ×24=6840 hundredths = 68.40.
Guided practice
Calculate 2.69 × 23, where 23 is a whole number.
Show answer and reasoning
Use (20+3) groups: 269 hundredths ×23=6187 hundredths = 61.87.
Calculate 2.81 × 21, where 21 is a whole number.
Show answer and reasoning
Use (20+1) groups: 281 hundredths ×21=5901 hundredths = 59.01.
Calculate 2.68 × 12, where 12 is a whole number.
Show answer and reasoning
Use (10+2) groups: 268 hundredths ×12=3216 hundredths = 32.16.
Calculate 1.34 × 18, where 18 is a whole number.
Show answer and reasoning
Use (10+8) groups: 134 hundredths ×18=2412 hundredths = 24.12.
Calculate 2.79 × 19, where 19 is a whole number.
Show answer and reasoning
Use (10+9) groups: 279 hundredths ×19=5301 hundredths = 53.01.
Independent practice
Calculate 2.93 × 17, where 17 is a whole number.
Show answer and reasoning
Use (10+7) groups: 293 hundredths ×17=4981 hundredths = 49.81.
Calculate 1.88 × 11, where 11 is a whole number.
Show answer and reasoning
Use (10+1) groups: 188 hundredths ×11=2068 hundredths = 20.68.
Calculate 2.64 × 14, where 14 is a whole number.
Show answer and reasoning
Use (10+4) groups: 264 hundredths ×14=3696 hundredths = 36.96.
Calculate 3.25 × 16, where 16 is a whole number.
Show answer and reasoning
Use (10+6) groups: 325 hundredths ×16=5200 hundredths = 52.00.
Calculate 1.32 × 24, where 24 is a whole number.
Show answer and reasoning
Use (20+4) groups: 132 hundredths ×24=3168 hundredths = 31.68.
Calculate 1.83 × 23, where 23 is a whole number.
Show answer and reasoning
Use (20+3) groups: 183 hundredths ×23=4209 hundredths = 42.09.
Calculate 2.48 × 18, where 18 is a whole number.
Show answer and reasoning
Use (10+8) groups: 248 hundredths ×18=4464 hundredths = 44.64.
Calculate 1.57 × 11, where 11 is a whole number.
Show answer and reasoning
Use (10+1) groups: 157 hundredths ×11=1727 hundredths = 17.27.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 3.70 × 12, where 12 is a whole number. Explain how place value or a model can check your result.
Show answer and reasoning
Use (10+2) groups: 370 hundredths ×12=4440 hundredths = 44.40. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “2.35 × 12 = 2.35 × 10 + 2.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: distribute 2.35 × (10 + 2) = 23.50 + 4.70 = 28.20. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 2.38 × 14, where 14 is a whole number.
Show answer and reasoning
Use (10+4) groups: 238 hundredths ×14=3332 hundredths = 33.32.
Calculate 1.49 × 15, where 15 is a whole number.
Show answer and reasoning
Use (10+5) groups: 149 hundredths ×15=2235 hundredths = 22.35.
Calculate 1.49 × 12, where 12 is a whole number.
Show answer and reasoning
Use (10+2) groups: 149 hundredths ×12=1788 hundredths = 17.88.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.