Dividing Decimals

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

Intermediate25 minLesson

Definition

Dividing decimals follows the same process as dividing whole numbers, with careful attention to decimal point placement.

Key strategies:

1.Dividing by a whole number: Divide normally, then place the decimal point in the quotient directly above where it appears in the dividend.

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.

\frac{12.6}{3} = 4.2 \quad\quad \frac{8.4}{0.4} = \frac{84}{4} = 21

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What is

6.4 \div 2

Worked Examples

Calculate $12.48 \div 4$

Set up the division

Place $12.48$ under the division symbol with $4$ outside → $4 \overline{)12.48}$

Divide the whole number part

$12 \div 4 = 3$ → Write $3$ above the $2$

Place the decimal point

Put the decimal directly above where it appears in $12.48$ → $3.$

Divide the tenths

$4 \div 4 = 1$ → $3.1$

Divide the hundredths

$8 \div 4 = 2$ → $3.12$

Answer: $12.48 \div 4 = 3.12$

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: $8.4 \div 0.4$ : Multiply BOTH by 10 to get $84 \div 4 = 21$

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 $12.48 \div 4$ , place the decimal after the $3$ : $3.12$ , not $31.2$ or $0.312$

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: $7 \div 4$ : Don't stop at $1$ R $3$ . Add zeros: $7.00 \div 4 = 1.75$

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 $0.5$ s fit into $3$ ? Six!

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

Interactive Visual

Place Value Chart

Enter a number:

12.48

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 problems

Problem 1 of 15

Easy

What is $6.4 \div 2$ ?

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 $4.50 \div 6 = 0.75$ 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: $87.50 \div 5 = 17.50$ 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

Multiplying the numerator and denominator of a fraction by the same number keeps the value the same.

\frac{8.4}{0.4} = \frac{84}{4}

because both top and bottom were multiplied by 10.

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 \div n

Place decimal in quotient directly above decimal in dividend

Dividing by a decimal

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

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