Dividing Decimals
Learn how to divide decimal numbers using place value understanding and the standard algorithm.
Definition
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Worked Examples
Calculate
Set up the division
Place under the division symbol with outside →
Divide the whole number part
→ Write above the
Place the decimal point
Put the decimal directly above where it appears in →
Divide the tenths
→
Divide the hundredths
→
Answer:
Common Mistakes
Forgetting to move the decimal point in the dividend when making the divisor whole
Why it's wrong: When you multiply the divisor by 10 (or 100), you must do the same to the dividend to keep the division equivalent.
Correct: : Multiply BOTH by 10 to get
Placing the decimal point in the wrong position in the quotient
Why it's wrong: The decimal in the quotient must align directly above where it appears in the dividend.
Correct: In , place the decimal after the : , not or
Stopping the division too early when there is a remainder
Why it's wrong: If there is a remainder, add zeros after the decimal and continue dividing.
Correct: : Don't stop at R. Add zeros:
Thinking dividing by a decimal less than 1 makes the answer smaller
Why it's wrong: Dividing by a number less than 1 actually makes the answer larger. Think: how many s fit into ? Six!
Correct: (larger than 3, not smaller)
Interactive Visual
Place Value Chart
| Tens 10 | Ones 1 | Tenths 0.1 | Hundredths 0.01 |
|---|---|---|---|
| 1 | 2 | 4 | 8 |
Expanded Form:
1 × 10 + 2 × 1 + 4 × 0.1 + 8 × 0.01
Click on any place value to highlight it and see its value.
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
15 problemsWhat is ?
Why It Matters
- Shopping: Calculating unit prices (1.89 euros for 3 items = 0.63 euros each)
- Cooking: Scaling recipes up or down (0.75 liters shared among 3 servings)
- Finance: Splitting costs equally among friends
- Science: Converting measurements and analyzing data
- Sports: Calculating batting averages and other statistics
Real World Applications
Unit Price Calculation
Stores use decimal division to calculate the price per item or per unit weight.
Example:
A pack of 6 yogurts costs 4.50 euros. Each yogurt costs euros.
A 2.5 kg bag of apples costs 3.75 euros.
What is the price per kilogram?
Step 1: Write the mathematical expression
Divide total price by weight:
Splitting Costs
Friends often need to divide costs equally, including amounts with decimals.
Example:
A dinner bill of 87.50 euros split 5 ways: euros each.
Four friends share a taxi fare of 23.60 euros equally.
How much does each person pay?
Step 1: Write the mathematical expression
Divide the fare by the number of friends:
Key Takeaways
- 1To divide by a whole number, divide normally and place the decimal point in the quotient directly above where it appears in the dividend
- 2To divide by a decimal, multiply both the divisor and dividend by 10, 100, etc. to make the divisor a whole number
- 3Add zeros after the decimal point if needed to continue dividing when there is a remainder
- 4Dividing by a number less than 1 gives a quotient larger than the dividend
Frequently Asked Questions
Glossary
- Dividend
- The number being divided (the number inside or under the division symbol)
- Divisor
- The number you are dividing by (the number outside the division symbol)
- Quotient
- The result of a division
- Remainder
- The amount left over when a division does not come out evenly
Formula Card
Dividing by a whole number
Place decimal in quotient directly above decimal in dividend
Dividing by a decimal
Multiply both numbers by $10^n$ to make divisor whole, then divide