Subtracting from 1 and 0.1
Semester 4B · Chapter 13 · Lesson 5 · MATH-4B-C13-L05
Before you begin: prerequisite check
Recall: 13.03 and 12.04. Attempt these questions independently first.
Calculate 5.08 + 2.08.
Show answer and reasoning
Add 508+208 exact hundredths = 716 hundredths = 7.16.
Calculate 7.23 + 2.55.
Show answer and reasoning
Add 723+255 exact hundredths = 978 hundredths = 9.78.
Calculate 1.68 + 3.13.
Show answer and reasoning
Add 168+313 exact hundredths = 481 hundredths = 4.81.
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
To subtract a decimal from one whole, rename 1 as 0.99 plus 0.01 or more simply as 100 hundredths. Thus 1−0.37 means 100−37=63 hundredths, or 0.63. To subtract from one tenth, rename 0.1 as ten hundredths: 0.10−0.07=0.03. The zeros in 1.00 and 0.10 make place-value exchanges explicit. Always check by adding the difference back to the amount subtracted. Explain why zero in the hundredths column is a placeholder, not a reason to ignore that column.
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 1.00 − 0.74.
Rename 1.00 as 100 hundredths; subtract 74 hundredths to get 26 hundredths.
Check 1: try it yourself
Calculate 1.00 − 0.14.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 14 hundredths to get 86 hundredths.
Worked example 2
Calculate 0.10 − 0.07.
Rename 0.10 as 10 hundredths; subtract 7 hundredths to get 3 hundredths.
Check 2: try it yourself
Calculate 0.10 − 0.09.
Show answer and reasoning
Rename 0.10 as 10 hundredths; subtract 9 hundredths to get 1 hundredths.
Worked example 3
Calculate 1.00 − 0.24.
Rename 1.00 as 100 hundredths; subtract 24 hundredths to get 76 hundredths.
Check 3: try it yourself
Calculate 1.00 − 0.85.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 85 hundredths to get 15 hundredths.
Guided practice
Calculate 1.00 − 0.86.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 86 hundredths to get 14 hundredths.
Calculate 0.10 − 0.03.
Show answer and reasoning
Rename 0.10 as 10 hundredths; subtract 3 hundredths to get 7 hundredths.
Calculate 1.00 − 0.47.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 47 hundredths to get 53 hundredths.
Calculate 0.10 − 0.01.
Show answer and reasoning
Rename 0.10 as 10 hundredths; subtract 1 hundredths to get 9 hundredths.
Calculate 1.00 − 0.23.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 23 hundredths to get 77 hundredths.
Independent practice
Calculate 1.00 − 0.75.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 75 hundredths to get 25 hundredths.
Calculate 1.00 − 0.52.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 52 hundredths to get 48 hundredths.
Calculate 1.00 − 0.46.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 46 hundredths to get 54 hundredths.
Calculate 0.10 − 0.04.
Show answer and reasoning
Rename 0.10 as 10 hundredths; subtract 4 hundredths to get 6 hundredths.
Calculate 1.00 − 0.38.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 38 hundredths to get 62 hundredths.
Calculate 1.00 − 0.50.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 50 hundredths to get 50 hundredths.
Calculate 0.10 − 0.02.
Show answer and reasoning
Rename 0.10 as 10 hundredths; subtract 2 hundredths to get 8 hundredths.
Calculate 1.00 − 0.94.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 94 hundredths to get 6 hundredths.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 1.00 − 0.55. Explain how place value or a model can check your result.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 55 hundredths to get 45 hundredths. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “0.1 - 0.04 = 0.06 because 0.1 is one hundredth.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
The result 0.06 is correct, but 0.1 is ten hundredths, not one; 10/100 - 4/100 = 6/100. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 1.00 − 0.05.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 5 hundredths to get 95 hundredths.
Calculate 1.00 − 0.92.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 92 hundredths to get 8 hundredths.
Calculate 1.00 − 0.66.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 66 hundredths to get 34 hundredths.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.