Adding and Subtracting Decimals
Learn how to add and subtract decimal numbers by lining up the decimal points.
Definition
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Worked Examples
Calculate
Line up the decimal points
Write the numbers vertically with decimal points aligned →
Add the hundredths column
→ 6 hundredths
Add the tenths column
→ 7 tenths
Add the ones column
→ 5 ones
Bring down the decimal point
Place the decimal between ones and tenths →
Answer:
Common Mistakes
Not lining up the decimal points
Why it's wrong: When decimals are not aligned, you end up adding digits with different place values, like adding tenths to hundredths.
Correct: Always write the numbers vertically with decimal points directly above each other before calculating.
Forgetting to add zero placeholders
Why it's wrong: Without placeholders, it's easy to misalign digits. For example, adding without writing can cause errors.
Correct: Add zeros at the end of decimals so all numbers have the same number of decimal places:
Forgetting to bring down the decimal point
Why it's wrong: The answer looks correct but is actually 10, 100, or 1000 times too large!
Correct: Always place the decimal point in your answer directly below the decimal points in the problem.
Interactive Visual
Place Value Chart
| Tens 10 | Ones 1 | Tenths 0.1 | Hundredths 0.01 |
|---|---|---|---|
| 1 | 2 | 4 | 5 |
Expanded Form:
1 × 10 + 2 × 1 + 4 × 0.1 + 5 × 0.01
Click on any place value to highlight it and see its value.
Click on numbers to select them. Adjust the range to explore different values.
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
15 problemsWhat is ?
Why It Matters
- Shopping: Calculating the total cost of items or determining how much change you should receive
- Cooking: Adjusting recipe measurements when you need more or less than the original amount
- Sports: Comparing race times or calculating total scores in events like gymnastics
- Science: Measuring and recording precise data in experiments
Real World Applications
Shopping and Money
Every time you buy multiple items or calculate change, you use decimal addition and subtraction.
Example:
A notebook costs 4.99 dollars and a pen costs 2.50 dollars. The total is dollars.
You buy a sandwich for 6.75 dollars and a drink for 2.49 dollars. You pay with a 20 dollar bill.
How much change should you receive?
Step 1: Write the mathematical expression
First find total, then subtract from 20:
Sports and Timing
In racing events, times are measured in decimals of seconds. Athletes compare times to see improvement.
Example:
A swimmer's time dropped from seconds to seconds. The improvement is seconds.
In a relay race, the first runner finishes their leg in 12.35 seconds and the second runner in 11.87 seconds.
What is their combined time?
Step 1: Write the mathematical expression
Add the two times:
Key Takeaways
- 1Always line up the decimal points vertically before adding or subtracting
- 2Add zeros as placeholders when numbers have different decimal places
- 3Add or subtract from right to left, borrowing or carrying when needed
- 4Bring the decimal point straight down into your answer
Frequently Asked Questions
Glossary
- Decimal
- A number that includes a decimal point to represent values less than one (e.g., )
- Decimal point
- The dot that separates whole numbers from fractional parts
- Place value
- The value of a digit based on its position (ones, tenths, hundredths, etc.)
- Placeholder zero
- A zero added to fill empty decimal places without changing the number's value