Back to Lesson

Teacher Guide: Dividing Decimals

Learn how to divide decimal numbers using place value understanding and the standard algorithm.

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
  • 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
Prerequisites
  • • Understanding of place value in decimals
  • • Long division with whole numbers
  • • Multiplying decimals by powers of 10
Discussion Starters
  • 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?
Common Misconceptions

Dividing always makes numbers smaller

Remediation: Show counterexamples: 6÷0.5=126 \div 0.5 = 12. Explain that dividing by a number less than 1 is like asking 'how many small pieces fit in this amount?'

Moving the decimal changes the value of the answer

Remediation: Demonstrate that multiplying both divisor and dividend by the same number keeps the quotient the same. Use fraction equivalence: 20.4=204=5\frac{2}{0.4} = \frac{20}{4} = 5

Differentiation Ideas

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
Standards Alignment
  • 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

Lesson Resources
  • 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.

Definition

Dividing decimals follows the same process as dividing whole numbers, with careful attention to decimal point placement.
Key strategies:
  1. 1.Dividing by a whole number: Divide normally, then place the decimal point in the quotient directly above where it appears in the dividend.
  1. 2.Dividing by a decimal: Multiply both the divisor and dividend by a power of 10 to make the divisor a whole number, then divide.
12.63=4.28.40.4=844=21\frac{12.6}{3} = 4.2 \quad\quad \frac{8.4}{0.4} = \frac{84}{4} = 21

Worked Examples

Calculate 12.48÷412.48 \div 4
1

Set up the division

Place 12.4812.48 under the division symbol with 44 outside → 4)12.48‾4 \overline{)12.48}
2

Divide the whole number part

12÷4=312 \div 4 = 3 → Write 33 above the 22
3

Place the decimal point

Put the decimal directly above where it appears in 12.4812.48 → 3.3.
4

Divide the tenths

4÷4=14 \div 4 = 1 → 3.13.1
5

Divide the hundredths

8÷4=28 \div 4 = 2 → 3.123.12

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: 8.4÷0.48.4 \div 0.4: Multiply BOTH by 10 to get 84÷4=2184 \div 4 = 21

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 12.48÷412.48 \div 4, place the decimal after the 33: 3.123.12, not 31.231.2 or 0.3120.312

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: 7÷47 \div 4: Don't stop at 11 R33. Add zeros: 7.00÷4=1.757.00 \div 4 = 1.75

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 0.50.5s fit into 33? Six!

Correct: 3÷0.5=63 \div 0.5 = 6 (larger than 3, not smaller)

Why It Matters

Decimal division is essential in everyday life:
  • 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
Without decimal division, we couldn't solve many practical problems involving precise measurements!

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 4.50÷6=0.754.50 \div 6 = 0.75 euros.

1Try It Yourself

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: 87.50÷5=17.5087.50 \div 5 = 17.50 euros each.

2Try It Yourself

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?

Multiplying the numerator and denominator of a fraction by the same number keeps the value the same. 8.40.4=844\frac{8.4}{0.4} = \frac{84}{4} because both top and bottom were multiplied by 10.

How do I know when to stop dividing?

Stop when: (1) there is no remainder, (2) you reach a repeating pattern, or (3) you have enough decimal places for your purpose (often 2 for money).

Why is 3÷0.5=63 \div 0.5 = 6 instead of a smaller number?

Think of it as: 'How many halves fit into 3?' Six halves make 3 wholes. Dividing by a fraction or decimal less than 1 asks how many small pieces fit into the whole.

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

a.bc÷na.bc \div n

Place decimal in quotient directly above decimal in dividend

Dividing by a decimal

a0.b=a×10b\frac{a}{0.b} = \frac{a \times 10}{b}

Multiply both numbers by $10^n$ to make divisor whole, then divide

More in This Topic

Adding and Subtracting Decimals

Elementary25 min

Multiplying Decimals

Intermediate25 min