Subtracting Hundredths
Semester 4B · Chapter 13 · Lesson 6 · MATH-4B-C13-L06
Before you begin: prerequisite check
Recall: 13.05–13.06. Attempt these questions independently first.
Calculate 1.00 − 0.11.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 11 hundredths to get 89 hundredths.
Calculate 0.10 − 0.09.
Show answer and reasoning
Rename 0.10 as 10 hundredths; subtract 9 hundredths to get 1 hundredths.
Calculate 1.00 − 0.79.
Show answer and reasoning
Rename 1.00 as 100 hundredths; subtract 79 hundredths to get 21 hundredths.
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
Subtract decimals with hundredths by aligning decimal points and regrouping whenever a place has too few units. For example, 5.04−2.78 can be viewed as 504 hundredths minus 278 hundredths: 226 hundredths, or 2.26. This exact-integer strategy is a useful independent check. If the answer has fewer decimal places, trailing zeros may be omitted without changing value. Subtraction should never rely on subtracting whichever digit happens to be larger.
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 5.63 − 1.28.
563 hundredths minus 128 hundredths = 435 hundredths = 4.35.
Check 1: try it yourself
Calculate 3.93 − 2.71.
Show answer and reasoning
393 hundredths minus 271 hundredths = 122 hundredths = 1.22.
Worked example 2
Calculate 7.13 − 2.76.
713 hundredths minus 276 hundredths = 437 hundredths = 4.37.
Check 2: try it yourself
Calculate 4.11 − 1.35.
Show answer and reasoning
411 hundredths minus 135 hundredths = 276 hundredths = 2.76.
Worked example 3
Calculate 4.35 − 2.33.
435 hundredths minus 233 hundredths = 202 hundredths = 2.02.
Check 3: try it yourself
Calculate 6.30 − 1.34.
Show answer and reasoning
630 hundredths minus 134 hundredths = 496 hundredths = 4.96.
Guided practice
Calculate 4.08 − 1.88.
Show answer and reasoning
408 hundredths minus 188 hundredths = 220 hundredths = 2.20.
Calculate 3.11 − 1.91.
Show answer and reasoning
311 hundredths minus 191 hundredths = 120 hundredths = 1.20.
Calculate 3.15 − 2.69.
Show answer and reasoning
315 hundredths minus 269 hundredths = 46 hundredths = 0.46.
Calculate 7.87 − 1.50.
Show answer and reasoning
787 hundredths minus 150 hundredths = 637 hundredths = 6.37.
Calculate 5.05 − 1.81.
Show answer and reasoning
505 hundredths minus 181 hundredths = 324 hundredths = 3.24.
Independent practice
Calculate 7.48 − 1.81.
Show answer and reasoning
748 hundredths minus 181 hundredths = 567 hundredths = 5.67.
Calculate 3.38 − 2.26.
Show answer and reasoning
338 hundredths minus 226 hundredths = 112 hundredths = 1.12.
Calculate 8.93 − 2.42.
Show answer and reasoning
893 hundredths minus 242 hundredths = 651 hundredths = 6.51.
Calculate 6.75 − 2.88.
Show answer and reasoning
675 hundredths minus 288 hundredths = 387 hundredths = 3.87.
Calculate 6.78 − 2.74.
Show answer and reasoning
678 hundredths minus 274 hundredths = 404 hundredths = 4.04.
Calculate 4.21 − 2.40.
Show answer and reasoning
421 hundredths minus 240 hundredths = 181 hundredths = 1.81.
Calculate 6.12 − 1.31.
Show answer and reasoning
612 hundredths minus 131 hundredths = 481 hundredths = 4.81.
Calculate 9.45 − 1.90.
Show answer and reasoning
945 hundredths minus 190 hundredths = 755 hundredths = 7.55.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Calculate 4.76 − 2.68. Explain how place value or a model can check your result.
Show answer and reasoning
476 hundredths minus 268 hundredths = 208 hundredths = 2.08. A correct explanation should name the relevant fractional place values and verify the answer.
A learner claims: “4.05 - 1.27 = 3.22.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: regroup one whole into 100 hundredths as necessary; 4.05 - 1.27 = 2.78. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Calculate 7.62 − 2.48.
Show answer and reasoning
762 hundredths minus 248 hundredths = 514 hundredths = 5.14.
Calculate 5.19 − 2.57.
Show answer and reasoning
519 hundredths minus 257 hundredths = 262 hundredths = 2.62.
Calculate 8.84 − 1.11.
Show answer and reasoning
884 hundredths minus 111 hundredths = 773 hundredths = 7.73.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.