BananaLearnLearning LibraryGamesFind 20.00 − 7.85.
- Hundredths: 10 − 5 = 5. Tenths: 9 − 8 = 1.
- Ones: 9 − 7 = 2. Tens: 1 − 0 = 1. The result is 12.15.
- Check 12.15 + 7.85 = 20.00.
Start with the value, then write the subtraction
Suppose a ribbon measures 5.2 m and a project uses 1.76 m. Before calculating, notice that the answer must be less than 5.2 m and greater than 3 m. A metre is the whole unit; a tenth of a metre is 10 cm, while a hundredth is 1 cm. Writing 5.20 m makes the centimetre-sized parts visible. It does not add any ribbon.
Set the numbers in a place-value chart. Put ones under ones, tenths under tenths and hundredths under hundredths. The decimal point is a separator between places, so aligning it aligns the units. Lining up the final digits instead would put the 2 tenths above 6 hundredths.
| Stage | Ones | Tenths | Hundredths | Value |
|---|---|---|---|---|
| Start | 5 | 2 | 0 | 5.20 |
| Exchange one one | 4 | 12 | 0 | 4 + 1.2 = 5.20 |
| Exchange one tenth | 4 | 11 | 10 | 4 + 1.1 + 0.10 = 5.20 |
| Subtract 1.76 | 3 | 4 | 4 | 3.44 |
Why the exchanged digits still describe the same number
The 12 tenths in the second row include the original 2 tenths and 10 new tenths exchanged from one whole. After giving one tenth to the hundredths column, 11 tenths remain. You are not borrowing an extra amount from somewhere else; you are renaming the amount you already have.
Read each row aloud as a sum. This is especially useful with zeros: 10.00 can become 9 ones, 9 tenths and 10 hundredths. A child who can explain that exchange is less likely to cross out digits mechanically and lose track of their value.
A second method: find the distance by counting up
Subtraction also measures the distance between two amounts. For 10.00 − 9.68, go from 9.68 to 9.70 (+0.02), then to 10.00 (+0.30). The distance is 0.32. This can be easier than exchanging through several zeros when the numbers are close.
For a money problem, keep the units visible: ₹10 − ₹9.68 = ₹0.32. For a length problem, do not replace metres with rupees just because both use decimals. The calculation method transfers, but the meaning and unit come from the question.
Find and repair a wrong method
A learner writes 7.03 − 4.8 = 3.77 by subtracting whichever digit is smaller from whichever is larger. Ask them to check the proposed answer: 4.80 + 3.77 = 8.57, not 7.03. The failed check identifies a method problem, not just untidy working.
Rewrite 4.8 as 4.80. Exchange one whole from 7 to obtain 6 ones and 10 tenths. Subtract: 3 hundredths, 2 tenths and 2 ones remain, giving 2.23. Because 7 − 5 is about 2, the size of the corrected answer is also sensible.
Worked examples: follow each decision
A ribbon is 5.2 m long. Cut away 1.76 m. What remains?
- Write 5.20 − 1.76 so the columns match.
- Regroup: 4 ones, 11 tenths and 10 hundredths. Subtract to get 3.44 m.
- Check 3.44 + 1.76 = 5.20; retain metres in the answer.
Two lengths, 1.275 m and 0.86 m, are cut from a 3 m roll. What remains?
- Add the cuts: 1.275 + 0.860 = 2.135 m.
- Subtract 3.000 − 2.135 = 0.865 m.
- Check 0.865 + 1.275 + 0.860 = 3.000 m. This is a two-step problem; subtracting only one cut is incomplete.
13 questions with explained answers
Attempt a short group of questions before opening the solutions. Use a drawing or written method where helpful. Explain the answer, then try a similar question with a detail changed.
8.40 − 2.15
Show answer and reasoning
6.25
Regroup a tenth into ten hundredths; 6.25 + 2.15 = 8.40.
10 − 0.68
Show answer and reasoning
9.32
Write 10.00 and exchange through the zero columns.
7.03 − 4.8
Show answer and reasoning
2.23
Write 4.80; the 8 represents tenths.
A jug has 2.5 L. Pour out 0.875 L.
Show answer and reasoning
1.625 L
Use 2.500 − 0.875. The thousandths must align.
Why is 6.5 − 2.35 not 4.30?
Show answer and reasoning
6.5 − 2.35 = 4.15
Treat 6.5 as 6.50, not 6.65 or 6.05.
4.60 − 2.18
Show answer and reasoning
2.42
Rename 4.60 as 4 ones, 5 tenths and 10 hundredths.
6.00 − 2.47
Show answer and reasoning
3.53
Use 5 ones, 9 tenths and 10 hundredths, then subtract.
3.4 − 0.85
Show answer and reasoning
2.55
Write 3.40. Check 2.55 + 0.85 = 3.40.
12.005 − 0.87
Show answer and reasoning
11.135
Write 0.870. Match thousandths, not the last written digit.
A 4.75 L container holds 2.9 L. How much more fits?
Show answer and reasoning
1.85 L
The difference is 4.75 − 2.90.
Find 15 − 14.96 by counting up.
Show answer and reasoning
0.04
Four hundredths bridge 14.96 to 15.00.
Is 8.2 − 3.47 greater than 5? Explain without finishing the calculation.
Show answer and reasoning
No
8.2 − 3.2 = 5; subtracting the larger 3.47 leaves less than 5.
Write a subtraction whose answer is 0.75.
Show answer and reasoning
For example 2.00 − 1.25
Many answers work. Verify by adding the difference to the smaller number.
Check what you can now explain
- Can you rename 6.00 without changing its value?
- Can you decide when counting up is easier than columns?
- Does your answer, added to the amount removed, restore the starting amount?
Keep these distinctions clear
- Do not subtract the smaller digit from the larger digit in each column regardless of order. Regroup from the top number.
- Adding a zero at the right of a decimal is safe; inserting one inside the number changes it.
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Keep the ideas connected
- Decimal place value: tenths, hundredths and thousandths
- Adding decimals by matching place values
- Choose a Maths practice game by skill
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Original explanations, examples, visual models and practice by BananaLearn. This guide is not an official textbook extract, exam paper or endorsed assessment resource.
The examples teach the stated concept; check your school’s terminology and sequence when using the guide alongside a course.