Adding Tenths with Regrouping
Semester 4B · Chapter 13 · Lesson 2 · MATH-4B-C13-L02
Before you begin: prerequisite check
Recall: 13.01; regrouping whole numbers. Attempt these questions independently first.
Calculate 2.8 + 0.5.
Show answer and reasoning
Combine 28 and 5 tenths to get 33 tenths, or 3.3.
Calculate 7.7 − 1.3.
Show answer and reasoning
Subtract 13 tenths from 77 tenths to get 6.4.
Calculate 6.5 + 0.8.
Show answer and reasoning
Combine 65 and 8 tenths to get 73 tenths, or 7.3.
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
Ten tenths make one whole. For example, 0.8 + 0.7 = 15 tenths = 1 whole and 5 tenths = 1.5. Regrouping is an equal exchange, not an arbitrary carrying rule. In 2.8+3.6, first combine two and three wholes to get five, then add 14 tenths. Exchange ten tenths for one more whole to obtain 6.4. A tenths strip or place-value chart makes the exchange visible.
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 2.9 + 2.8.
The tenths combine to 17 tenths, which makes one whole and 7 tenths. Add whole units to get 5.7.
Check 1: try it yourself
Calculate 5.8 + 1.7.
Show answer and reasoning
The tenths combine to 15 tenths, which makes one whole and 5 tenths. Add whole units to get 7.5.
Worked example 2
Calculate 3.9 + 4.6.
The tenths combine to 15 tenths, which makes one whole and 5 tenths. Add whole units to get 8.5.
Check 2: try it yourself
Calculate 3.7 + 1.5.
Show answer and reasoning
The tenths combine to 12 tenths, which makes one whole and 2 tenths. Add whole units to get 5.2.
Worked example 3
Calculate 4.9 + 4.9.
The tenths combine to 18 tenths, which makes one whole and 8 tenths. Add whole units to get 9.8.
Check 3: try it yourself
Calculate 2.7 + 0.7.
Show answer and reasoning
The tenths combine to 14 tenths, which makes one whole and 4 tenths. Add whole units to get 3.4.
Guided practice
Calculate 4.7 + 1.5.
Show answer and reasoning
The tenths combine to 12 tenths, which makes one whole and 2 tenths. Add whole units to get 6.2.
Calculate 1.6 + 2.5.
Show answer and reasoning
The tenths combine to 11 tenths, which makes one whole and 1 tenths. Add whole units to get 4.1.
Calculate 5.7 + 3.7.
Show answer and reasoning
The tenths combine to 14 tenths, which makes one whole and 4 tenths. Add whole units to get 9.4.
Calculate 1.6 + 4.7.
Show answer and reasoning
The tenths combine to 13 tenths, which makes one whole and 3 tenths. Add whole units to get 6.3.
Calculate 3.8 + 3.5.
Show answer and reasoning
The tenths combine to 13 tenths, which makes one whole and 3 tenths. Add whole units to get 7.3.
Independent practice
Calculate 3.6 + 2.5.
Show answer and reasoning
The tenths combine to 11 tenths, which makes one whole and 1 tenths. Add whole units to get 6.1.
Calculate 1.7 + 3.9.
Show answer and reasoning
The tenths combine to 16 tenths, which makes one whole and 6 tenths. Add whole units to get 5.6.
Calculate 4.9 + 1.8.
Show answer and reasoning
The tenths combine to 17 tenths, which makes one whole and 7 tenths. Add whole units to get 6.7.
Calculate 3.6 + 0.7.
Show answer and reasoning
The tenths combine to 13 tenths, which makes one whole and 3 tenths. Add whole units to get 4.3.
Calculate 3.9 + 2.7.
Show answer and reasoning
The tenths combine to 16 tenths, which makes one whole and 6 tenths. Add whole units to get 6.6.
Calculate 3.9 + 3.9.
Show answer and reasoning
The tenths combine to 18 tenths, which makes one whole and 8 tenths. Add whole units to get 7.8.
Calculate 5.7 + 0.7.
Show answer and reasoning
The tenths combine to 14 tenths, which makes one whole and 4 tenths. Add whole units to get 6.4.
Calculate 2.9 + 2.7.
Show answer and reasoning
The tenths combine to 16 tenths, which makes one whole and 6 tenths. Add whole units to get 5.6.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 1.7 + 4.9. Explain how place value or a model can check your result.
Show answer and reasoning
The tenths combine to 16 tenths, which makes one whole and 6 tenths. Add whole units to get 6.6. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “2.8 + 1.7 = 3.15.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 8 tenths + 7 tenths = 15 tenths = 1 whole 5 tenths, so 2.8 + 1.7 = 4.5. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 4.8 + 1.8.
Show answer and reasoning
The tenths combine to 16 tenths, which makes one whole and 6 tenths. Add whole units to get 6.6.
Calculate 2.8 + 0.9.
Show answer and reasoning
The tenths combine to 17 tenths, which makes one whole and 7 tenths. Add whole units to get 3.7.
Calculate 2.9 + 0.7.
Show answer and reasoning
The tenths combine to 16 tenths, which makes one whole and 6 tenths. Add whole units to get 3.6.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.