Word Problems with Decimals Division: 4th Grade Practice

Master decimal division through engaging word problems: step-by-step solutions, visual aids, and real-world applications.

Decimal Division Word Problems: 1 to 5
1 Shopping Division
Exercise 1
Emma bought 3 notebooks for $4.50. How much did each notebook cost?
Definition:

Decimal Division: Divide the total cost by the number of items to find the unit cost

Solution Method:
  1. Identify the total cost: $4.50
  2. Identify the number of items: 3 notebooks
  3. Divide total cost by number of items: $4.50 ÷ 3
Total Cost
$4.50
Number of Items
÷ 3
Cost per Item
$1.50
Step 1: Set up the division

$4.50 ÷ 3

Step 2: Divide the dollars

4 ÷ 3 = 1 remainder 1

Step 3: Bring down the 50 cents

150 cents ÷ 3 = 50 cents

Step 4: Combine results

1 dollar + 50 cents = $1.50

$4.50 ÷ 3 = $1.50
Final answer:

Each notebook cost $1.50

Applied rules:

• Unit Cost: Divide total cost by number of items

• Decimal Division: Place decimal point in quotient directly above dividend

• Verification: Multiply quotient by divisor to check answer

2 Measurement Division
Exercise 2
A 12.6-inch ribbon is cut into 3 equal pieces. How long is each piece?
Definition:

Equal Partitioning: Divide the total length by the number of pieces to find length of each piece

Total Length
12.6 in
Number of Pieces
÷ 3
Length per Piece
4.2 in
Step 1: Set up the division

12.6 ÷ 3

Step 2: Divide the whole number part

12 ÷ 3 = 4

Step 3: Bring down the decimal and continue

0.6 ÷ 3 = 0.2

Step 4: Combine results

4 + 0.2 = 4.2 inches

12.6 ÷ 3 = 4.2
Final answer:

Each piece is 4.2 inches long

Applied rules:

• Equal Partitioning: Divide total by number of equal parts

• Decimal Division: Align decimal point in quotient with dividend

• Verification: Multiply quotient by divisor to check answer

3 Money Division
Exercise 3
Alex earned $15.75 for 5 hours of work. How much did he earn per hour?
Definition:

Unit Rate: Divide the total amount by the number of units to find the rate per unit

Total Earnings
$15.75
Hours Worked
÷ 5
Hourly Rate
$3.15
Step 1: Set up the division

$15.75 ÷ 5

Step 2: Divide the dollars

15 ÷ 5 = 3

Step 3: Bring down the 75 cents

75 cents ÷ 5 = 15 cents

Step 4: Combine results

3 dollars + 15 cents = $3.15

$15.75 ÷ 5 = $3.15
Final answer:

Alex earned $3.15 per hour

Applied rules:

• Unit Rate: Divide total by number of units to find per-unit amount

• Decimal Division: Place decimal point in quotient directly above dividend

• Verification: Multiply hourly rate by hours worked to check

4 Weight Division
Exercise 4
A bag of flour weighs 2.4 kg. It is divided equally among 4 people. How much does each person get?
Definition:

Equal Sharing: Divide the total weight by the number of people to find individual share

Total Weight
2.4 kg
Number of People
÷ 4
Per Person
0.6 kg
Step 1: Set up the division

2.4 ÷ 4

Step 2: Since 2 < 4, consider 24 tenths

24 tenths ÷ 4 = 6 tenths

Step 3: Convert to decimal

6 tenths = 0.6 kg

2.4 ÷ 4 = 0.6
Final answer:

Each person gets 0.6 kg of flour

Applied rules:

• Equal Sharing: Divide total by number of recipients

• Decimal Division: When dividend is smaller than divisor, result is less than 1

• Verification: Multiply individual share by number of people to check

5 Distance Division
Exercise 5
A car traveled 187.5 miles using 7.5 gallons of gas. How many miles per gallon did the car get?
Definition:

Rate Calculation: Divide total distance by total fuel to find miles per gallon

Total Distance
187.5 mi
Total Gas
÷ 7.5 gal
Miles per Gallon
25 mpg
Step 1: Set up the division

187.5 ÷ 7.5

Step 2: Eliminate decimal by multiplying both by 10

(187.5 × 10) ÷ (7.5 × 10) = 1875 ÷ 75

Step 3: Perform the division

1875 ÷ 75 = 25

187.5 ÷ 7.5 = 25
Final answer:

The car gets 25 miles per gallon

Applied rules:

• Rate Calculation: Divide total distance by total fuel to find rate

• Decimal Division: Multiply both numbers by 10 to eliminate decimal

• Verification: Multiply rate by fuel to check distance

Decimal Division Word Problems: 6 to 10
6 Liquid Division
Exercise 6
A container has 4.8 liters of juice. If it's divided equally into 6 glasses, how much juice is in each glass?
Definition:

Equal Distribution: Divide the total volume by the number of containers to find volume per container

Total Volume
4.8 L
Number of Glasses
÷ 6
Per Glass
0.8 L
Step 1: Set up the division

4.8 ÷ 6

Step 2: Since 4 < 6, consider 48 tenths

48 tenths ÷ 6 = 8 tenths

Step 3: Convert to decimal

8 tenths = 0.8 L

4.8 ÷ 6 = 0.8
Final answer:

Each glass contains 0.8 liters of juice

Applied rules:

• Equal Distribution: Divide total volume by number of containers

• Decimal Division: When dividend is smaller than divisor, result is less than 1

• Verification: Multiply per-glass amount by number of glasses to check

7 Savings Division
Exercise 7
Maya saved $31.20 over 8 weeks. If she saved the same amount each week, how much did she save per week?
Definition:

Periodic Rate: Divide the total amount by the number of periods to find the amount per period

Total Savings
$31.20
Number of Weeks
÷ 8
Weekly Savings
$3.90
Step 1: Set up the division

$31.20 ÷ 8

Step 2: Divide the dollars

31 ÷ 8 = 3 remainder 7

Step 3: Bring down the 20 cents

720 cents ÷ 8 = 90 cents

Step 4: Combine results

3 dollars + 90 cents = $3.90

$31.20 ÷ 8 = $3.90
Final answer:

Maya saved $3.90 per week

Applied rules:

• Periodic Rate: Divide total amount by number of periods

• Decimal Division: Place decimal point in quotient directly above dividend

• Verification: Multiply weekly amount by number of weeks to check

8 Length Division
Exercise 8
A rope 15.6 feet long is cut into pieces that are each 1.2 feet long. How many pieces can be made?
Definition:

Measurement Division: Divide the total length by the length of each piece to find the number of pieces

Total Length
15.6 ft
Length per Piece
÷ 1.2 ft
Number of Pieces
13
Step 1: Set up the division

15.6 ÷ 1.2

Step 2: Eliminate decimal by multiplying both by 10

(15.6 × 10) ÷ (1.2 × 10) = 156 ÷ 12

Step 3: Perform the division

156 ÷ 12 = 13

15.6 ÷ 1.2 = 13
Final answer:

13 pieces can be made

Applied rules:

• Measurement Division: Divide total length by length of each piece

• Decimal Division: Multiply both numbers by 10 to eliminate decimal

• Verification: Multiply number of pieces by length of each to check

9 Weight Division
Exercise 9
A bag of apples weighs 3.6 kg. If each apple weighs 0.3 kg, how many apples are in the bag?
Definition:

Count Division: Divide the total weight by the weight of each item to find the number of items

Total Weight
3.6 kg
Weight per Apple
÷ 0.3 kg
Number of Apples
12
Step 1: Set up the division

3.6 ÷ 0.3

Step 2: Eliminate decimal by multiplying both by 10

(3.6 × 10) ÷ (0.3 × 10) = 36 ÷ 3

Step 3: Perform the division

36 ÷ 3 = 12

3.6 ÷ 0.3 = 12
Final answer:

There are 12 apples in the bag

Applied rules:

• Count Division: Divide total weight by weight of each item

• Decimal Division: Multiply both numbers by 10 to eliminate decimal

• Verification: Multiply number of apples by weight of each to check

10 Budget Division
Exercise 10
Sarah has $24.00 to spend on 5 friends' gifts. If she spends the same amount on each gift, how much can she spend per gift?
Definition:

Equal Allocation: Divide the total budget by the number of recipients to find per-person allocation

Total Budget
$24.00
Number of Friends
÷ 5
Per Gift
$4.80
Step 1: Set up the division

$24.00 ÷ 5

Step 2: Divide the dollars

24 ÷ 5 = 4 remainder 4

Step 3: Bring down the 00 cents

400 cents ÷ 5 = 80 cents

Step 4: Combine results

4 dollars + 80 cents = $4.80

$24.00 ÷ 5 = $4.80
Final answer:

Sarah can spend $4.80 per gift

Applied rules:

• Equal Allocation: Divide total budget by number of recipients

• Decimal Division: Place decimal point in quotient directly above dividend

• Verification: Multiply per-gift amount by number of gifts to check

Decimal Division Infographic

Decimal Division Guide

➗
Division Process
Place decimal point in quotient

• Place decimal point in quotient directly above dividend

• When divisor has decimals, multiply both by 10, 100, etc.

• Divide as with whole numbers

• Add zeros to dividend if needed

Decimal Elimination
Multiply both numbers to eliminate decimals

• If divisor has 1 decimal place, multiply both by 10

• If divisor has 2 decimal places, multiply both by 100

• If divisor has 3 decimal places, multiply both by 1000

• Dividend and divisor must be multiplied by same number

Division Steps
1
Set Up
2
Eliminate Decimals
3
Divide
4
Place Decimal
5
Verify
Common Mistakes

• Forgetting to place decimal point in quotient

• Only multiplying divisor by 10, not dividend

• Placing decimal point incorrectly

• Not checking reasonableness of answer

Key Tips

• Always place decimal point in quotient first

• When divisor has decimals, eliminate them by multiplying both

• Estimate first to check reasonableness

• Verify by multiplying quotient by divisor

Decimal Division Examples
4.8 ÷ 2 = 2.4
12.6 ÷ 3 = 4.2
7.5 ÷ 0.5 = 15
3.6 ÷ 0.4 = 9
Practice Division!
Key Concepts, Methods, and Rules
a.b ÷ c.d = (a.b × 100) ÷ (c.d × 100)
Decimal Division
Key definitions:

Dividend: The number being divided

Divisor: The number that divides the dividend

Quotient: The result of the division

Unit Rate: A rate with denominator of 1, expressing quantity per single unit

Equal Partitioning: Dividing a quantity into equal parts

Decimal Division Methodology:
  1. Identify: Determine which number is the dividend and which is the divisor
  2. Eliminate decimals: If divisor has decimals, multiply both numbers by 10, 100, etc.
  3. Place decimal: Put decimal point in quotient directly above dividend
  4. Divide: Perform division as with whole numbers
  5. Verify: Multiply quotient by divisor to check your answer
Tip 1: Always place the decimal point in the quotient directly above the dividend's decimal point.
Tip 2: When the divisor has decimals, multiply both numbers by 10, 100, or 1000 to eliminate decimals.
Tip 3: Estimate your answer first to check if the final result is reasonable.
Tip 4: Remember to verify your answer by multiplying the quotient by the divisor.
Common errors: Misplacing the decimal point in the quotient, forgetting to multiply both numbers when eliminating decimals, not checking the reasonableness of the answer.
Success strategies: Always place the decimal point first, multiply both numbers by the same value when eliminating decimals, verify your answer by multiplication.
Essential Rules:

• Decimal Placement: Place decimal point in quotient directly above dividend's decimal point

• Decimal Elimination: Multiply both numbers by 10, 100, or 1000 to eliminate divisor decimals

• Verification: Multiply quotient by divisor to check your answer

• Estimation: Round to estimate and verify your answer

• Reasonableness: Check that your answer makes sense in the context of the problem

Decimal Division Summary

Definitions & Concepts

Dividend: The number being divided

Divisor: The number that divides the dividend

Quotient: The result of the division

Unit Rate: A rate with denominator of 1, expressing quantity per single unit

Equal Partitioning: Dividing a quantity into equal parts

Core Rules & Principles

• Always place decimal point in quotient directly above dividend's decimal point

• When divisor has decimals, multiply both numbers by 10, 100, or 1000 to eliminate decimals

• When dividend is smaller than divisor, result is less than 1

• The quotient represents how many times the divisor fits into the dividend

• Verify by multiplying quotient by divisor to get original dividend

Methods & Procedures

1. Identify: Determine dividend and divisor in the problem

2. Eliminate Decimals: If divisor has decimals, multiply both by 10, 100, or 1000

3. Place Decimal: Put decimal point in quotient directly above dividend

4. Divide: Perform division as with whole numbers

5. Verify: Multiply quotient by divisor to check your answer

Examples & Applications

Simple Division: 4.8 ÷ 2 = 2.4

With Decimals: 7.5 ÷ 0.5 = 15 (multiply both by 10: 75 ÷ 5 = 15)

Unit Rate: $15.75 ÷ 5 hours = $3.15 per hour

Partitioning: 12.6 inches ÷ 3 pieces = 4.2 inches per piece

Real-world: 187.5 miles ÷ 7.5 gallons = 25 miles per gallon

Tips & Tricks

• Place the decimal point in the quotient first

• When divisor has decimals, eliminate them by multiplying both numbers

• Estimate first to check reasonableness

• Remember: smaller ÷ larger = result less than 1

• Always verify by multiplying quotient by divisor

Memory Aids

• "Decimal point in quotient goes directly above dividend's decimal point"

• "To eliminate decimals, multiply both numbers by the same power of 10"

• "Dividend ÷ Divisor = Quotient (the answer)"

• "Check by multiplying: Quotient × Divisor = Dividend"

• "If dividend is smaller than divisor, answer is less than 1"

Questions & Answers

Question: I always get confused about where to put the decimal point when dividing decimals. Any tips?

Answer: Great question! Here's a foolproof method for decimal placement in division:

  1. Place the decimal point first: Put the decimal point in the quotient directly above the dividend's decimal point
  2. Eliminate decimals in divisor: If the divisor has decimals, multiply both numbers by 10, 100, or 1000 to make the divisor a whole number
  3. Divide as usual: Perform the division with the decimal point already in place

Example: For 4.8 ÷ 2
1. Place decimal point: 4.8 ÷ 2 = _._
2. Divide: 4 ÷ 2 = 2, 8 ÷ 2 = 4
3. Result: 2.4

The key is putting the decimal point in the quotient BEFORE you start dividing!

Question: How can I help my child practice decimal division at home?

Answer: Real-world contexts make decimal division meaningful! Try these activities:

  • Shopping: Calculate unit prices (cost per item, per pound, per liter)
  • Cooking: Divide recipes, measure ingredients equally among servings
  • Travel: Calculate miles per gallon, average speed, or distance per day
  • Budgeting: Divide allowance or earnings into equal parts

Also practice with problems that involve sharing or partitioning: "If 3 friends share $7.50 equally, how much does each get?"

Start with simple problems and gradually increase complexity as skills develop.

Question: What do I do when the divisor has decimals? It confuses me!

Answer: When the divisor has decimals, eliminate them by multiplying both numbers by the same power of 10! Here's the method:

  1. Count decimal places in divisor: How many digits after the decimal point?
  2. Multiply both numbers by 10, 100, or 1000: Based on the count from step 1
  3. Divide as normal: With a whole number divisor
  4. Place decimal point: In quotient directly above where it appears in the new dividend

Example: 7.5 ÷ 0.5
Divisor has 1 decimal place, so multiply both by 10:
(7.5 × 10) ÷ (0.5 × 10) = 75 ÷ 5 = 15

This method turns any decimal division into whole number division!