Multiplying Tenths and Hundredths
Semester 4B · Chapter 14 · Lesson 1 · MATH-4B-C14-L01
Before you begin: prerequisite check
Recall: 12.01–12.04; 4A fraction-times-whole. Attempt these questions independently first.
Calculate 12 × 4.
Show answer and reasoning
Twelve groups of four have 48 objects.
Calculate 84 ÷ 4.
Show answer and reasoning
Four groups of 21 make 84.
Write 0.25 as a fraction in hundredths.
Show answer and reasoning
Twenty-five hundredths is 25/100.
Key vocabulary
- factor
- number being multiplied
- product
- result of multiplication
- dividend
- quantity divided into groups
- quotient
- amount in each equal group
Understand the concept
Multiplying tenths and hundredths by a whole number counts repeated equal fractional units. Four groups of 0.3 are twelve tenths, or 1.2. Six groups of 0.04 are 24 hundredths, or 0.24. A bar model can display identical sections, each containing the given decimal amount. Use place-value reasoning to explain the decimal answer instead of memorizing a rule for moving a decimal point. Ask whether an answer of twelve wholes would make sense when adding only four groups of three tenths.
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 0.2 × 7.
The displayed decimal contains 2 tenths. Multiply the number of equal units by 7: 14 tenths = 1.4.
Check 1: try it yourself
Calculate 0.5 × 3.
Show answer and reasoning
The displayed decimal contains 5 tenths. Multiply the number of equal units by 3: 15 tenths = 1.5.
Worked example 2
Calculate 0.03 × 3.
The displayed decimal contains 3 hundredths. Multiply the number of equal units by 3: 9 hundredths = 0.09.
Check 2: try it yourself
Calculate 0.05 × 8.
Show answer and reasoning
The displayed decimal contains 5 hundredths. Multiply the number of equal units by 8: 40 hundredths = 0.40.
Worked example 3
Calculate 0.7 × 3.
The displayed decimal contains 7 tenths. Multiply the number of equal units by 3: 21 tenths = 2.1.
Check 3: try it yourself
Calculate 0.3 × 9.
Show answer and reasoning
The displayed decimal contains 3 tenths. Multiply the number of equal units by 9: 27 tenths = 2.7.
Guided practice
Calculate 0.4 × 9.
Show answer and reasoning
The displayed decimal contains 4 tenths. Multiply the number of equal units by 9: 36 tenths = 3.6.
Calculate 0.07 × 3.
Show answer and reasoning
The displayed decimal contains 7 hundredths. Multiply the number of equal units by 3: 21 hundredths = 0.21.
Calculate 0.9 × 6.
Show answer and reasoning
The displayed decimal contains 9 tenths. Multiply the number of equal units by 6: 54 tenths = 5.4.
Calculate 0.08 × 5.
Show answer and reasoning
The displayed decimal contains 8 hundredths. Multiply the number of equal units by 5: 40 hundredths = 0.40.
Calculate 0.4 × 6.
Show answer and reasoning
The displayed decimal contains 4 tenths. Multiply the number of equal units by 6: 24 tenths = 2.4.
Independent practice
Calculate 0.6 × 4.
Show answer and reasoning
The displayed decimal contains 6 tenths. Multiply the number of equal units by 4: 24 tenths = 2.4.
Calculate 0.03 × 6.
Show answer and reasoning
The displayed decimal contains 3 hundredths. Multiply the number of equal units by 6: 18 hundredths = 0.18.
Calculate 0.8 × 4.
Show answer and reasoning
The displayed decimal contains 8 tenths. Multiply the number of equal units by 4: 32 tenths = 3.2.
Calculate 0.08 × 8.
Show answer and reasoning
The displayed decimal contains 8 hundredths. Multiply the number of equal units by 8: 64 hundredths = 0.64.
Calculate 0.9 × 5.
Show answer and reasoning
The displayed decimal contains 9 tenths. Multiply the number of equal units by 5: 45 tenths = 4.5.
Calculate 0.2 × 4.
Show answer and reasoning
The displayed decimal contains 2 tenths. Multiply the number of equal units by 4: 8 tenths = 0.8.
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 0.6 × 9.
Show answer and reasoning
The displayed decimal contains 6 tenths. Multiply the number of equal units by 9: 54 tenths = 5.4.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 0.8 × 4. Explain how place value or a model can check your result.
Show answer and reasoning
The displayed decimal contains 8 tenths. Multiply the number of equal units by 4: 32 tenths = 3.2. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “0.3 × 4 = 1.2 only because the 3 stays in the tenths place.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
The result is right, but 3 tenths × 4 = 12 tenths = 1 whole and 2 tenths, which explains the result. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 0.5 × 7.
Show answer and reasoning
The displayed decimal contains 5 tenths. Multiply the number of equal units by 7: 35 tenths = 3.5.
Calculate 0.02 × 6.
Show answer and reasoning
The displayed decimal contains 2 hundredths. Multiply the number of equal units by 6: 12 hundredths = 0.12.
Calculate 0.3 × 7.
Show answer and reasoning
The displayed decimal contains 3 tenths. Multiply the number of equal units by 7: 21 tenths = 2.1.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.