Subtracting Tenths with Regrouping
Semester 4B · Chapter 13 · Lesson 3 · MATH-4B-C13-L03
Before you begin: prerequisite check
Recall: 13.01–13.02. Attempt these questions independently first.
Calculate 4.8 + 3.5.
Show answer and reasoning
The tenths combine to 13 tenths, which makes one whole and 3 tenths. Add whole units to get 8.3.
Calculate 2.9 + 4.5.
Show answer and reasoning
The tenths combine to 14 tenths, which makes one whole and 4 tenths. Add whole units to get 7.4.
Calculate 1.9 + 0.8.
Show answer and reasoning
The tenths combine to 17 tenths, which makes one whole and 7 tenths. Add whole units to get 2.7.
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
If the minuend has too few tenths, rename one whole as ten tenths before subtracting. For 3.2−1.7, rewrite 3 wholes and 2 tenths as 2 wholes and 12 tenths. Subtract one whole and seven tenths to get 1.5. You have not changed the value of 3.2; you have only changed its units. Check by adding the difference to the amount subtracted: 1.5+1.7=3.2. If the result seems bigger than the original amount even though you subtracted a positive quantity, your work needs another look.
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 2.4 − 1.5.
Rename 2.4 as 1 wholes and 14 tenths. Subtract 1 whole and 5 tenths; result 0.9.
Check 1: try it yourself
Calculate 5.4 − 1.8.
Show answer and reasoning
Rename 5.4 as 4 wholes and 14 tenths. Subtract 1 whole and 8 tenths; result 3.6.
Worked example 2
Calculate 7.2 − 1.8.
Rename 7.2 as 6 wholes and 12 tenths. Subtract 1 whole and 8 tenths; result 5.4.
Check 2: try it yourself
Calculate 3.4 − 1.5.
Show answer and reasoning
Rename 3.4 as 2 wholes and 14 tenths. Subtract 1 whole and 5 tenths; result 1.9.
Worked example 3
Calculate 3.2 − 1.6.
Rename 3.2 as 2 wholes and 12 tenths. Subtract 1 whole and 6 tenths; result 1.6.
Check 3: try it yourself
Calculate 9.1 − 1.5.
Show answer and reasoning
Rename 9.1 as 8 wholes and 11 tenths. Subtract 1 whole and 5 tenths; result 7.6.
Guided practice
Calculate 8.1 − 1.9.
Show answer and reasoning
Rename 8.1 as 7 wholes and 11 tenths. Subtract 1 whole and 9 tenths; result 6.2.
Calculate 4.2 − 1.8.
Show answer and reasoning
Rename 4.2 as 3 wholes and 12 tenths. Subtract 1 whole and 8 tenths; result 2.4.
Calculate 5.3 − 1.8.
Show answer and reasoning
Rename 5.3 as 4 wholes and 13 tenths. Subtract 1 whole and 8 tenths; result 3.5.
Calculate 4.2 − 1.7.
Show answer and reasoning
Rename 4.2 as 3 wholes and 12 tenths. Subtract 1 whole and 7 tenths; result 2.5.
Calculate 3.2 − 1.5.
Show answer and reasoning
Rename 3.2 as 2 wholes and 12 tenths. Subtract 1 whole and 5 tenths; result 1.7.
Independent practice
Calculate 2.1 − 1.9.
Show answer and reasoning
Rename 2.1 as 1 wholes and 11 tenths. Subtract 1 whole and 9 tenths; result 0.2.
Calculate 2.2 − 1.6.
Show answer and reasoning
Rename 2.2 as 1 wholes and 12 tenths. Subtract 1 whole and 6 tenths; result 0.6.
Calculate 5.2 − 1.9.
Show answer and reasoning
Rename 5.2 as 4 wholes and 12 tenths. Subtract 1 whole and 9 tenths; result 3.3.
Calculate 4.1 − 1.9.
Show answer and reasoning
Rename 4.1 as 3 wholes and 11 tenths. Subtract 1 whole and 9 tenths; result 2.2.
Calculate 4.3 − 1.5.
Show answer and reasoning
Rename 4.3 as 3 wholes and 13 tenths. Subtract 1 whole and 5 tenths; result 2.8.
Calculate 2.2 − 1.8.
Show answer and reasoning
Rename 2.2 as 1 wholes and 12 tenths. Subtract 1 whole and 8 tenths; result 0.4.
Calculate 4.3 − 1.8.
Show answer and reasoning
Rename 4.3 as 3 wholes and 13 tenths. Subtract 1 whole and 8 tenths; result 2.5.
Calculate 9.2 − 1.9.
Show answer and reasoning
Rename 9.2 as 8 wholes and 12 tenths. Subtract 1 whole and 9 tenths; result 7.3.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 2.1 − 1.7. Explain how place value or a model can check your result.
Show answer and reasoning
Rename 2.1 as 1 wholes and 11 tenths. Subtract 1 whole and 7 tenths; result 0.4. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “3.2 - 1.7 = 2.5.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: exchange one whole for ten tenths, then subtract to get 1.5. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 4.3 − 1.6.
Show answer and reasoning
Rename 4.3 as 3 wholes and 13 tenths. Subtract 1 whole and 6 tenths; result 2.7.
Calculate 2.3 − 1.7.
Show answer and reasoning
Rename 2.3 as 1 wholes and 13 tenths. Subtract 1 whole and 7 tenths; result 0.6.
Calculate 2.4 − 1.8.
Show answer and reasoning
Rename 2.4 as 1 wholes and 14 tenths. Subtract 1 whole and 8 tenths; result 0.6.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.