Word Problems with Decimals and Fractions Worksheets: 4th Grade Practice

Comprehensive collection of printable worksheets with step-by-step solutions, answer keys, and educational infographics for mastering decimal and fraction operations.

Worksheet Problems: 1 to 5
1 Shopping Worksheet
Worksheet Problem 1
Emma bought 1/4 kg of apples for $2.50 and 3/4 kg of oranges for $3.75. How much fruit did she buy in total? How much did she spend?
Definition:

Fraction Addition: Add numerators when denominators are the same, keep the denominator

Solution Method:
  1. Add the fractional amounts of fruit: 1/4 + 3/4
  2. Add the decimal amounts of money: $2.50 + $3.75
  3. Align decimal points when adding decimals
Fruit Amount
1 kg
Money Spent
$6.25
Step 1: Add fractions (same denominator)

1/4 + 3/4 = (1 + 3)/4 = 4/4 = 1 kg

Step 2: Add decimal amounts

$2.50

+ $3.75

------

$6.25

Step 3: Verify calculation

1 kg of fruit, $6.25 spent

Fruit: 1/4 + 3/4 = 1 kg; Money: $2.50 + $3.75 = $6.25
Final answer:

Emma bought 1 kg of fruit and spent $6.25

Applied rules:

• Fraction Addition: When denominators are the same, add numerators

• Decimal Alignment: Always align decimal points when adding

• Carrying: When sum exceeds 9, carry the excess to next column

2 Measurement Worksheet
Worksheet Problem 2
A board is 2.5 meters long. If 1/2 meter is cut off, how much board remains? Express your answer as a decimal.
Definition:

Fraction to Decimal Conversion: 1/2 = 0.5, then perform decimal subtraction

Original Length
2.5 m
Cut Off
- 0.5 m
Remaining
2.0 m
Step 1: Convert fraction to decimal

1/2 = 0.5

Step 2: Set up subtraction with aligned decimals

2.5 - 0.5 = 2.0

Step 3: Verify calculation

2.0 + 0.5 = 2.5 ✓

2.5 - 1/2 = 2.5 - 0.5 = 2.0 m
Final answer:

2.0 meters of board remains

Applied rules:

• Fraction Conversion: Convert fractions to decimals before performing operations

• Decimal Subtraction: Align decimal points before subtracting

• Verification: Check by adding the result to the subtracted amount

3 Money Worksheet
Worksheet Problem 3
Alex had $15.50. He spent 1/4 of his money on lunch and $3.75 on snacks. How much money does he have left?
Definition:

Fraction of a Whole Number: Multiply the fraction by the decimal amount to find the portion

Lunch Cost
$3.88
Total Spent
$7.63
Remaining
$7.87
Step 1: Calculate lunch cost (1/4 of $15.50)

1/4 × $15.50 = $15.50 ÷ 4 = $3.875 ≈ $3.88

Step 2: Calculate total spent

$3.88 + $3.75 = $7.63

Step 3: Calculate remaining money

$15.50 - $7.63 = $7.87

$15.50 - (1/4 × $15.50 + $3.75) = $7.87
Final answer:

Alex has $7.87 left

Applied rules:

• Fraction of Amount: Multiply fraction by decimal to find portion

• Decimal Operations: Align decimal points when adding/subtracting

• Rounding: Round monetary amounts to nearest cent

4 Weight Worksheet
Worksheet Problem 4
A bag of flour weighs 2.5 kg. If 3/4 kg is used for baking and then 0.25 kg more is added back, what is the final weight?
Definition:

Decimal-Fraction Operations: Convert fractions to decimals, then perform sequential operations

Initial Weight
2.5 kg
After Removing
1.75 kg
Final Weight
2.0 kg
Step 1: Convert fraction to decimal

3/4 = 0.75 kg

Step 2: Subtract amount used

2.5 - 0.75 = 1.75 kg

Step 3: Add amount returned

1.75 + 0.25 = 2.0 kg

2.5 - 3/4 + 0.25 = 2.5 - 0.75 + 0.25 = 2.0 kg
Final answer:

The final weight is 2.0 kg

Applied rules:

• Conversion: Convert fractions to decimals for easier operations

• Sequential Operations: Perform operations in the order they occur

• Decimal Alignment: Essential for accurate calculations

5 Distance Worksheet
Worksheet Problem 5
A car traveled 125.5 miles on Monday. On Tuesday, it traveled 1/2 as far as Monday. How many miles did it travel in total over the two days?
Definition:

Fraction of a Decimal: Multiply the decimal by the fraction to find the portion

Monday Distance
125.5 mi
Tuesday Distance
62.75 mi
Total Distance
188.25 mi
Step 1: Calculate Tuesday's distance

1/2 × 125.5 = 125.5 ÷ 2 = 62.75 miles

Step 2: Add distances for both days

125.5 + 62.75 = 188.25 miles

Step 3: Verify calculation

62.75 × 2 = 125.5 ✓

125.5 + (1/2 × 125.5) = 125.5 + 62.75 = 188.25 mi
Final answer:

The car traveled 188.25 miles in total

Applied rules:

• Fraction of Decimal: Multiply decimal by fraction to find portion

• Decimal Addition: Align decimal points when adding

• Verification: Check that half of Monday's distance equals Tuesday's

Worksheet Problems: 6 to 10
6 Liquid Measurement Worksheet
Worksheet Problem 6
A container had 3.75 liters of juice. After pouring out 1/4 liter, how much juice remains?
Definition:

Decimal-Fraction Subtraction: Convert fraction to decimal, then subtract

Initial Amount
3.75 L
Removed
- 0.25 L
Remaining
3.50 L
Step 1: Convert fraction to decimal

1/4 = 0.25 L

Step 2: Align decimals and subtract

3.75 - 0.25 = 3.50 L

Step 3: Verify calculation

3.50 + 0.25 = 3.75 ✓

3.75 - 1/4 = 3.75 - 0.25 = 3.50 L
Final answer:

3.50 liters of juice remains

Applied rules:

• Conversion: Convert fractions to decimals before operations

• Decimal Subtraction: Align decimal points when subtracting

• Verification: Check by adding the result to the subtracted amount

7 Savings Worksheet
Worksheet Problem 7
Maya saved $24.50 last month. This month, she saved 3/4 as much as last month. How much did she save in total over the two months?
Definition:

Fraction of Decimal Amount: Multiply decimal by fraction to find portion

Last Month
$24.50
This Month
$18.38
Total
$42.88
Step 1: Calculate this month's savings

3/4 × $24.50 = $73.50 ÷ 4 = $18.375 ≈ $18.38

Step 2: Add both months' savings

$24.50 + $18.38 = $42.88

Step 3: Verify calculation

$18.38 ÷ $24.50 ≈ 0.75 = 3/4 ✓

$24.50 + (3/4 × $24.50) = $24.50 + $18.38 = $42.88
Final answer:

Maya saved $42.88 in total

Applied rules:

• Fraction of Amount: Multiply decimal by fraction to find portion

• Decimal Operations: Align decimal points when adding

• Rounding: Round monetary amounts to nearest cent

8 Length Worksheet
Worksheet Problem 8
A wooden board is 12.8 inches long. A piece 1/2 inch long is cut off, then another piece 0.75 inch long is cut off. What is the length of the remaining board?
Definition:

Sequential Decimal-Fraction Operations: Convert fractions to decimals, then perform sequential subtractions

Original Length
12.80 in
First Cut
- 0.50 in
Second Cut
- 0.75 in
Remaining
11.55 in
Step 1: Convert fraction to decimal

1/2 = 0.50 inch

Step 2: Subtract first cut

12.80 - 0.50 = 12.30 inches

Step 3: Subtract second cut

12.30 - 0.75 = 11.55 inches

12.80 - 1/2 - 0.75 = 12.80 - 0.50 - 0.75 = 11.55 in
Final answer:

The remaining board is 11.55 inches long

Applied rules:

• Sequential Operations: Perform operations in order from left to right

• Conversion: Convert all fractions to decimals for consistency

• Decimal Alignment: Maintain alignment during subtraction

9 Weight Comparison Worksheet
Worksheet Problem 9
A bag of apples weighs 5.25 kg. A bag of oranges weighs 3/4 kg less than the apples. How much do the oranges weigh?
Definition:

Subtracting Fraction from Decimal: Convert fraction to decimal, then subtract

Apple Weight
5.25 kg
Difference
- 0.75 kg
Orange Weight
4.50 kg
Step 1: Convert fraction to decimal

3/4 = 0.75 kg

Step 2: Subtract the difference from apple weight

5.25 - 0.75 = 4.50 kg

Step 3: Verify calculation

4.50 + 0.75 = 5.25 ✓

5.25 - 3/4 = 5.25 - 0.75 = 4.50 kg
Final answer:

The oranges weigh 4.50 kg

Applied rules:

• Conversion: Convert fractions to decimals before operations

• Subtraction: When subtracting a smaller value from a larger one

• Verification: Check by adding the result to the subtracted amount

10 Budget Worksheet
Worksheet Problem 10
Sarah budgeted $40.00 for groceries. She spent 1/4 of her budget on vegetables, $8.50 on fruit, and $15.25 on meat. How much of her budget remains?
Definition:

Mixed Decimal-Fraction Operations: Calculate fraction of amount, then add and subtract

Budget
$40.00
Vegetables
- $10.00
Fruit
- $8.50
Meat
- $15.25
Remaining
$6.25
Step 1: Calculate vegetable cost

1/4 × $40.00 = $40.00 ÷ 4 = $10.00

Step 2: Calculate total expenses

$10.00 + $8.50 + $15.25 = $33.75

Step 3: Calculate remaining budget

$40.00 - $33.75 = $6.25

$40.00 - (1/4 × $40.00 + $8.50 + $15.25) = $6.25
Final answer:

Sarah has $6.25 remaining in her budget

Applied rules:

• Fraction of Amount: Multiply decimal by fraction to find portion

• Multi-step Operations: Follow order of operations

• Verification: Check that remaining + spent = original budget

Worksheet Operations Infographic

Worksheet Guide

📋
Fraction Addition
Same denominators: add numerators

• Add numerators when denominators match

• Keep the denominator the same

• Simplify if possible

• Example: 1/4 + 2/4 = 3/4

Conversion
Fraction to decimal: divide numerator by denominator

• 1/2 = 1 ÷ 2 = 0.5

• 1/4 = 1 ÷ 4 = 0.25

• 3/4 = 3 ÷ 4 = 0.75

• 1/5 = 1 ÷ 5 = 0.2

Worksheet Steps
1
Read
2
Identify
3
Convert
4
Calculate
5
Check
Common Mistakes

• Adding numerators and denominators

• Not converting fractions to decimals

• Misaligning decimal points

• Forgetting to verify reasonableness

Key Tips

• Always convert fractions to decimals for mixed operations

• Use estimation to check reasonableness

Common Conversions:

• 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75

• Align decimal points when adding/subtracting

Fraction-Decimal Equivalents
1/2 = 0.5
1/4 = 0.25
3/4 = 0.75
1/5 = 0.2
Practice Worksheets!
Worksheet Concepts, Methods, and Rules
a/b + c.d = (a÷b) + c.d
Fraction-Decimal Operation
Key definitions:

Decimal: A number system based on 10, using a decimal point to separate whole numbers from fractional parts

Fraction: A number representing part of a whole, expressed as numerator/denominator

Numerator: The top number in a fraction, indicating how many parts are taken

Denominator: The bottom number in a fraction, indicating how many equal parts the whole is divided into

Equivalent Fractions: Fractions that represent the same value (e.g., 1/2 = 2/4)

Worksheet Problem-Solving Methodology:
  1. Read: Carefully read the entire problem to understand what is being asked
  2. Identify: Determine which numbers are fractions and which are decimals
  3. Convert: Change fractions to decimals for easier operations
  4. Plan: Decide which operations to perform and in what order
  5. Calculate: Perform the required operations with proper alignment
  6. Check: Verify that your answer makes sense in context
Tip 1: Convert fractions to decimals before performing mixed operations.
Tip 2: Memorize common fraction-to-decimal conversions (1/2=0.5, 1/4=0.25, 3/4=0.75).
Tip 3: Always align decimal points when adding or subtracting decimals.
Tip 4: Estimate your answer first to check if the final result is reasonable.
Common errors: Adding numerators and denominators separately, misaligning decimal points, not converting fractions before operations.
Success strategies: Convert to same format (decimals), align decimal points, verify with estimation.
Essential Rules:

• Fraction Addition: When denominators are the same, add numerators and keep denominator

• Decimal Alignment: Always line up decimal points vertically

• Conversion: Divide numerator by denominator to convert fraction to decimal

• Order of Operations: Perform operations in the order they occur

• Verification: Check your answer by estimating or reversing the operation

Worksheet Practice Sheets

Basic Fraction-Decimal Operations

Skills Covered: Basic conversion, addition, and subtraction

Problems: 10 basic problems with simple fractions and decimals

Difficulty: Beginner level

Time Required: 15-20 minutes

Money Word Problems

Skills Covered: Real-world applications with money

Problems: 12 problems involving shopping and budgeting

Difficulty: Intermediate level

Time Required: 20-25 minutes

Measurement Problems

Skills Covered: Length, weight, and capacity problems

Problems: 8 problems with various measurement units

Difficulty: Intermediate level

Time Required: 15-20 minutes

Multi-Step Operations

Skills Covered: Sequential operations with fractions and decimals

Problems: 6 complex problems with multiple steps

Difficulty: Advanced level

Time Required: 25-30 minutes

Mixed Operations Review

Skills Covered: Comprehensive review of all concepts

Problems: 15 mixed problems of varying difficulty

Difficulty: All levels

Time Required: 30-35 minutes

Challenge Problems

Skills Covered: Advanced applications and critical thinking

Problems: 5 challenging problems requiring multiple concepts

Difficulty: Advanced level

Time Required: 20-25 minutes

Decimal and Fraction Operations Summary

Definitions & Concepts

Decimal: A number system based on 10, using a decimal point to separate whole numbers from fractional parts

Fraction: A number representing part of a whole, expressed as numerator/denominator

Numerator: The top number in a fraction, indicating how many parts are taken

Denominator: The bottom number in a fraction, indicating how many equal parts the whole is divided into

Equivalent Fractions: Fractions that represent the same value (e.g., 1/2 = 2/4)

Core Rules & Principles

• When denominators are the same, add numerators and keep the denominator

• Always align decimal points when adding or subtracting decimals

• To convert fraction to decimal, divide numerator by denominator

• When multiplying fraction by decimal, convert to same format first

• The decimal point in the answer goes directly below the aligned decimal points

Methods & Procedures

1. Identify: Determine which numbers are fractions and which are decimals

2. Convert: Change fractions to decimals for easier operations

3. Align: Line up decimal points for addition/subtraction

4. Operate: Perform the required operations

5. Verify: Check that your answer makes sense in context

Examples & Applications

Fraction Addition: 1/4 + 2/4 = 3/4

Decimal-Fraction Conversion: 1/2 = 0.5

Mixed Operation: 2.5 + 1/4 = 2.5 + 0.25 = 2.75

Real-world: 3/4 kg + 1.25 kg = 0.75 + 1.25 = 2.0 kg

Word Problem: $5.50 - 1/2 of $4.00 = $5.50 - $2.00 = $3.50

Tips & Tricks

• Convert fractions to decimals before mixed operations

• Memorize common conversions: 1/2=0.5, 1/4=0.25, 3/4=0.75

• Draw vertical lines to align decimal points

• Use estimation to check reasonableness

• Check your answer by doing the opposite operation

Memory Aids

• "Fractions to decimals: divide top by bottom"

• "Same denominators: add tops, keep bottom"

• "Decimal points line up like soldiers in a row"

• "Convert to same format before operating"

• "Check your answer makes sense"

Questions & Answers

Question: I get confused when I have to add a fraction and a decimal. What should I do?

Answer: The easiest way is to convert the fraction to a decimal first! Here's the step-by-step approach:

  1. Convert the fraction to a decimal: Divide the numerator by the denominator
  2. Align the decimal points: Write both numbers with decimal points lined up
  3. Add as usual: Add the decimal numbers together

Example: Adding 1/4 and 2.5
Step 1: Convert 1/4 to decimal: 1 ÷ 4 = 0.25
Step 2: Align decimals: 0.25 + 2.50
Step 3: Add: 0.25 + 2.50 = 2.75

Memorizing common conversions (1/2=0.5, 1/4=0.25, 3/4=0.75) will make this faster!

Question: How can I help my child practice decimal and fraction operations at home?

Answer: Real-world contexts make mixed operations meaningful! Try these activities:

  • Cooking: Measuring ingredients using cups (1/2 cup, 0.75 cup) and weighing in grams
  • Shopping: Comparing prices like $2.50 vs 1/4 of $10
  • Measuring: Using rulers marked in both inches and fractional inches
  • Budgeting: Tracking allowance with both dollar bills and coins

Also practice common fraction-decimal equivalences regularly. Start with simple conversions and gradually increase complexity as skills develop.

Focus on memorizing: 1/2=0.5, 1/4=0.25, 3/4=0.75, 1/5=0.2

Question: What if I have to subtract a fraction from a decimal? How do I do that?

Answer: The process is similar to addition - convert the fraction to a decimal first! Here's how:

  1. Convert the fraction to a decimal: Divide numerator by denominator
  2. Align decimal points: Write both numbers with aligned decimal points
  3. Subtract as usual: Subtract the decimal numbers
  4. Check your answer: Add the result to the subtracted amount to verify

Example: 3.5 - 1/4
Step 1: Convert 1/4 to decimal: 1 ÷ 4 = 0.25
Step 2: Align decimals: 3.50 - 0.25
Step 3: Subtract: 3.50 - 0.25 = 3.25
Step 4: Check: 3.25 + 0.25 = 3.50 ✓

Remember to add zeros to make decimal places equal for easier subtraction!