Adding and Subtracting Decimals

Learn how to add and subtract decimal numbers by lining up the decimal points.

Elementary25 minLesson
Printable worksheet

Definition

To add or subtract decimals, line up the decimal points vertically and then add or subtract as you would with whole numbers.
Key steps:
  1. 1.Line up the decimal points - This ensures digits with the same place value are aligned
  2. 2.Add zeros if needed - Fill in empty places with zeros to keep columns aligned
  3. 3.Add or subtract - Work from right to left, just like with whole numbers
  4. 4.Place the decimal point - Bring the decimal point straight down into your answer
12.45+03.2015.65\begin{array}{r} 12.45 \\ + \phantom{0}3.20 \\ \hline 15.65 \end{array}

Try it now

What is 2.3+1.52.3 + 1.5?

Worked Examples

Calculate 3.45+2.313.45 + 2.31
1

Line up the decimal points

Write the numbers vertically with decimal points aligned → 3.45+2.31\begin{array}{r} 3.45 \\ +2.31 \end{array}
2

Add the hundredths column

5+1=65 + 1 = 6 → 6 hundredths
3

Add the tenths column

4+3=74 + 3 = 7 → 7 tenths
4

Add the ones column

3+2=53 + 2 = 5 → 5 ones
5

Bring down the decimal point

Place the decimal between ones and tenths → 5.765.76

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 2.5+1.252.5 + 1.25 without writing 2.502.50 can cause errors.

Correct: Add zeros at the end of decimals so all numbers have the same number of decimal places: 2.50+1.252.50 + 1.25

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

Enter a number:

12.45
Tens
10
Ones
1
Tenths
0.1
Hundredths
0.01
1245

Expanded Form:

1 × 10 + 2 × 1 + 4 × 0.1 + 5 × 0.01

Click on any place value to highlight it and see its value.

to

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 problems
Problem 1 of 15
Easy
What is 2.3+1.52.3 + 1.5?

Why It Matters

Adding and subtracting decimals is essential for everyday life:
  • 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
Without decimal operations, we couldn't handle money, measurements, or any calculations requiring precision!

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 4.99+2.50=7.494.99 + 2.50 = 7.49 dollars.

1Try It Yourself

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 28.4528.45 seconds to 27.8227.82 seconds. The improvement is 28.45−27.82=0.6328.45 - 27.82 = 0.63 seconds.

2Try It Yourself

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

Lining up decimal points ensures that digits with the same place value are in the same column. This means ones are added to ones, tenths to tenths, hundredths to hundredths, and so on.
Lining up decimal points ensures that digits with the same place value are in the same column. This means ones are added to ones, tenths to tenths, hundredths to hundredths, and so on.
Yes! Adding zeros at the end of a decimal does not change its value. 3.5=3.50=3.5003.5 = 3.50 = 3.500. This is helpful for aligning decimal places when adding or subtracting.
Add a decimal point and zeros to the whole number. For example, to add 7+2.357 + 2.35, rewrite 77 as 7.007.00, then line up and add.

Glossary

Decimal
A number that includes a decimal point to represent values less than one (e.g., 3.143.14)
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
Today's challengeOne problem, three tries

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Multiplying Decimals

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Dividing Decimals

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