Back to Lesson

Teacher Guide: Adding and Subtracting Decimals

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

Present LessonShare to ClassroomView Student Page

Use this lesson with your class

Free, no student accounts needed.

Share with students

Students open the lesson and practise with instant feedback.

Printable worksheet

All practice problems on paper, with a separate answer key.

Worksheet Answer key

Class quiz

10 questions on Decimal Operations. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Add decimal numbers by aligning decimal points vertically
  • Subtract decimal numbers using borrowing when necessary
  • Use placeholder zeros to align decimals with different numbers of decimal places
  • Apply decimal addition and subtraction to real-world problems
Prerequisites
  • • Understanding of place value (ones, tens, hundreds)
  • • Knowledge of decimal place values (tenths, hundredths)
  • • Ability to add and subtract whole numbers with regrouping
Discussion Starters
  • 1. Why is it important to line up decimal points when adding or subtracting?
  • 2. Can you think of a time when you added or subtracted decimals in real life?
  • 3. What happens if you forget to put the decimal point in your answer?
  • 4. How is adding decimals similar to adding whole numbers? How is it different?
Common Misconceptions

Treating decimals like separate whole numbers (adding 2.3 + 1.45 as 23 + 145)

Remediation: Emphasize place value by using a place value chart. Show that 2.3 means 2 ones and 3 tenths, not 23.

Thinking more decimal places means a larger number

Remediation: Compare on a number line: 2.5=2.50=2.5002.5 = 2.50 = 2.500. The number of zeros after the last non-zero digit doesn't change the value.

Differentiation Ideas

For Struggling Students:

  • • Use grid paper to help line up decimal points
  • • Start with decimals that have the same number of decimal places
  • • Provide place value charts with color-coded columns

For On-Level Students:

  • • Practice with different numbers of decimal places
  • • Solve word problems involving money and measurement
  • • Check answers using estimation

For Advanced Students:

  • • Work with three or more addends
  • • Estimate first, then calculate exact answers
  • • Create their own word problems for classmates
Standards Alignment
  • 5.NBT.B.7 (CCSS.MATH.CONTENT.5.NBT.B.7)

    Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value

  • 6.NS.B.3 (CCSS.MATH.CONTENT.6.NS.B.3)

    Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation

Lesson Resources
  • visualPlace Value Chart

    Interactive chart showing decimal place values

  • activityShopping Simulation

    Calculate totals and change with decimal prices

  • worksheetDecimal Operations Practice

    Mixed addition and subtraction problems with varying decimal places

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

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}

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.

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

Why do we need to line up the decimal points?

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.

Can I add zeros at the end of a decimal without changing its value?

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.

What if one number has no decimal and the other does?

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

More in This Topic

Multiplying Decimals

Intermediate25 min

Dividing Decimals

Intermediate25 min