Decimal Operations
Master adding, subtracting, multiplying, and dividing decimals! Learn the key rules that make decimal math easy and accurate.
Understanding Decimal Place Value
The Decimal Point is Your Guide
The decimal point separates whole numbers from parts of a whole. Everything to the LEFT is ones, tens, hundreds... Everything to the RIGHT is tenths, hundredths, thousandths...
| Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | . | 4 | 5 | 6 |
123.456 = 100 + 20 + 3 + 0.4 + 0.05 + 0.006
Adding and Subtracting Decimals
The key to adding and subtracting decimals is lining up the decimal points!
1 Line up the decimal points vertically
Write the numbers so decimal points are directly above each other.
2 Add zeros as placeholders if needed
Make the numbers the same length by adding zeros after the last digit.
3 Add or subtract as you would with whole numbers
Work from right to left, carrying or borrowing as needed.
4 Bring down the decimal point
The decimal point in your answer goes directly below the other decimal points.
Addition Example: 12.5 + 3.75
Notice: Added a zero to make 12.50
Subtraction Example: 8.3 - 2.47
Notice: Added a zero to make 8.30
When you line up decimal points, you're making sure you add things of the same value together:
- Tenths line up with tenths
- Hundredths line up with hundredths
- Ones line up with ones
It's like adding apples to apples and oranges to oranges!
Multiplying Decimals
Multiplying decimals is different - you DON'T need to line up decimal points!
The Multiplication Rule
Multiply as if there are no decimals, then count the total decimal places in both factors. Put that many decimal places in your answer!
1 Ignore the decimals and multiply
Pretend the numbers are whole numbers and multiply normally.
2 Count decimal places in both factors
Add up all the digits after the decimal points.
3 Place the decimal in your answer
Count from the right and place the decimal point.
Step 1: Multiply 25 x 13 = 325
Step 2: 1 + 1 = 2 decimal places needed
Step 3: 325 becomes 3.25
4 x 3 = 12, but we need 2 decimal places, so 0.12
Dividing Decimals
Division with decimals requires making the divisor (the number you divide BY) a whole number.
1 Make the divisor a whole number
Move the decimal point in the divisor to the right until it's a whole number.
2 Move the dividend's decimal the same amount
Move the decimal in the number you're dividing the same number of places.
3 Divide normally
Now divide as you would with whole numbers.
4 Place the decimal point directly above
The decimal point in your answer goes directly above where it is in the dividend.
Step 1: Make 0.3 a whole number: move decimal 1 place right = 3
Step 2: Move 6.3's decimal too: 6.3 becomes 63
Step 3: Now solve: 63 ÷ 3 = 21
Step 1: Move 0.12's decimal 2 places right = 12
Step 2: Move 4.56's decimal 2 places right = 456
Step 3: Now solve: 456 ÷ 12 = 38
Decimal Calculator
Practice decimal operations! Enter two decimals, choose an operation, and see the step-by-step solution.
Calculate with Decimals
Practice Problems
Solve these problems. Click the correct answer!
Problem 1: Addition
Problem 2: Subtraction
Problem 3: Multiplication
Problem 4: Multiplication
Problem 5: Division
Problem 6: Division
Problem 7: Word Problem
Problem 8: Word Problem
Check Your Understanding
When adding decimals, what must you do first?
How many decimal places are in the answer to 0.25 x 0.4?
When dividing by a decimal, what do you do to the divisor?
What We Learned
Add/Subtract
Line up decimal points, add zeros as needed
Multiply
Count decimal places in both numbers, put that many in answer
Divide
Make divisor a whole number, move dividend's decimal too
Key Rule
The decimal point keeps place values aligned!
Next Steps
- Practice lining up decimals with different length numbers
- Try multiplication problems with 3+ decimal places
- Work on word problems involving money (dollars and cents)
- Move on to learn about converting between decimals and fractions!