Teacher Guide: Dividing Decimals
Learn how to divide decimal numbers using place value understanding and the standard algorithm.
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Class quiz
10 questions on Decimal Operations. Students join with a name, you see everyone's score.
For Teachers
- Divide decimals by whole numbers using place value understanding
- Convert division by a decimal to division by a whole number
- Apply decimal division to solve real-world problems
- Estimate quotients to check reasonableness of answers
- • Understanding of place value in decimals
- • Long division with whole numbers
- • Multiplying decimals by powers of 10
- 1. When you divide a number by a decimal less than 1, is the answer bigger or smaller than the original number? Why?
- 2. How is dividing 24 by 0.3 related to dividing 240 by 3?
- 3. In what real-life situations have you needed to divide amounts that include decimals?
- 4. Why is it helpful to estimate before you calculate a decimal division?
Dividing always makes numbers smaller
Moving the decimal changes the value of the answer
For Struggling Students:
- • Use place value charts to visualize decimal positions
- • Start with division by whole numbers only
- • Provide estimation practice before computing
- • Use money contexts (dividing dollars and cents)
For On-Level Students:
- • Practice division by one-digit decimal divisors
- • Solve word problems involving unit rates
- • Connect to fraction division concepts
For Advanced Students:
- • Explore repeating decimals in division
- • Calculate multi-step problems with decimal operations
- • Investigate when decimal division produces terminating vs repeating decimals
- 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
- 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
- visualPlace Value Chart
Interactive chart showing decimal place values during division
- activityUnit Price Challenge
Calculate and compare unit prices from store advertisements
- worksheetDecimal Division Practice
Progressive practice from basic to complex problems
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
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)
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
Why do we multiply both numbers by 10 when dividing by a decimal?
How do I know when to stop dividing?
Why is instead of a smaller number?
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