Adding and Subtracting Tenths
Semester 4B · Chapter 13 · Lesson 1 · MATH-4B-C13-L01
Before you begin: prerequisite check
Recall: 12.01–12.04. Attempt these questions independently first.
Write 7 tenths as a fraction.
Show answer and reasoning
Seven of ten equal parts is 7/10.
Write 0.5 as a fraction in tenths.
Show answer and reasoning
The tenths digit is 5, or five of ten equal parts.
How many hundredths make one tenth?
Show answer and reasoning
1/10 = 10/100.
Key vocabulary
- decimal point
- separator between whole units and fractional place values
- regroup
- exchange equivalent place-value units
- hundredth
- one hundredth of a whole
- exact amount
- quantity without rounding
Understand the concept
Adding tenths means combining equal-size tenth units. Three tenths plus four tenths is seven tenths, or 0.7. When whole numbers are present, keep whole units separate from tenths and combine like place values. For subtraction, remove tenths from tenths, using a number line to check the result. Align decimal points in a written algorithm because they mark the same place values. An estimate can catch answers that are clearly too big or too small.
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 6.1 + 1.2.
Combine 61 and 12 tenths to get 73 tenths, or 7.3.
Check 1: try it yourself
Calculate 7.8 + 1.0.
Show answer and reasoning
Combine 78 and 10 tenths to get 88 tenths, or 8.8.
Worked example 2
Calculate 5.6 − 0.9.
Subtract 9 tenths from 56 tenths to get 4.7.
Check 2: try it yourself
Calculate 3.6 − 1.1.
Show answer and reasoning
Subtract 11 tenths from 36 tenths to get 2.5.
Worked example 3
Calculate 6.4 + 0.3.
Combine 64 and 3 tenths to get 67 tenths, or 6.7.
Check 3: try it yourself
Calculate 6.5 + 1.0.
Show answer and reasoning
Combine 65 and 10 tenths to get 75 tenths, or 7.5.
Guided practice
Calculate 4.6 + 0.6.
Show answer and reasoning
Combine 46 and 6 tenths to get 52 tenths, or 5.2.
Calculate 3.5 − 0.6.
Show answer and reasoning
Subtract 6 tenths from 35 tenths to get 2.9.
Calculate 3.4 + 0.9.
Show answer and reasoning
Combine 34 and 9 tenths to get 43 tenths, or 4.3.
Calculate 2.4 − 0.2.
Show answer and reasoning
Subtract 2 tenths from 24 tenths to get 2.2.
Calculate 1.9 + 0.5.
Show answer and reasoning
Combine 19 and 5 tenths to get 24 tenths, or 2.4.
Independent practice
Calculate 7.9 + 0.8.
Show answer and reasoning
Combine 79 and 8 tenths to get 87 tenths, or 8.7.
Calculate 7.1 − 0.5.
Show answer and reasoning
Subtract 5 tenths from 71 tenths to get 6.6.
Calculate 5.7 + 0.3.
Show answer and reasoning
Combine 57 and 3 tenths to get 60 tenths, or 6.0.
Calculate 7.3 − 0.6.
Show answer and reasoning
Subtract 6 tenths from 73 tenths to get 6.7.
Calculate 7.4 + 0.4.
Show answer and reasoning
Combine 74 and 4 tenths to get 78 tenths, or 7.8.
Calculate 6.3 + 0.3.
Show answer and reasoning
Combine 63 and 3 tenths to get 66 tenths, or 6.6.
Calculate 6.7 − 0.5.
Show answer and reasoning
Subtract 5 tenths from 67 tenths to get 6.2.
Calculate 2.6 + 0.6.
Show answer and reasoning
Combine 26 and 6 tenths to get 32 tenths, or 3.2.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 7.9 + 0.5. Explain how place value or a model can check your result.
Show answer and reasoning
Combine 79 and 5 tenths to get 84 tenths, or 8.4. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “0.4 + 0.3 = 0.7 because we add two unrelated digits.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
The answer 0.7 is correct, but the reason is not: four tenths plus three tenths equals seven tenths, so aligned units justify it. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 6.6 + 1.1.
Show answer and reasoning
Combine 66 and 11 tenths to get 77 tenths, or 7.7.
Calculate 1.7 − 0.7.
Show answer and reasoning
Subtract 7 tenths from 17 tenths to get 1.0.
Calculate 6.0 + 1.1.
Show answer and reasoning
Combine 60 and 11 tenths to get 71 tenths, or 7.1.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.