Word Problems with Decimals: 6th Grade Practice

Master decimal operations through real-world scenarios: addition, subtraction, multiplication, and division with step-by-step solutions.

Word Problems Solutions: 1 to 5
1 Shopping Problem
Exercise 1
Sarah bought apples for $3.45 and oranges for $2.75. How much did she spend in total?
Definition:

Decimal Addition: Align decimal points and add normally, carrying over when needed

Solution Method:
  1. Identify the quantities to add: $3.45 and $2.75
  2. Align decimal points vertically
  3. Add the amounts column by column
Amounts
$3.45 + $2.75
Total
$6.20
Step 1: Set up the addition

$3.45

+ $2.75

------

Step 2: Add cents column

5 + 5 = 10, write 0, carry 1

Step 3: Add tenths column

4 + 7 + 1 (carry) = 12, write 2, carry 1

Step 4: Add dollars column

3 + 2 + 1 (carry) = 6

$3.45 + $2.75 = $6.20
Final answer:

Sarah spent $6.20 in total

Applied rules:

• Decimal Alignment: Always align decimal points before adding

• Place Value: Add digits in the same place value positions

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

2 Measurement Problem
Exercise 2
A piece of rope was 8.5 meters long. After cutting off 3.25 meters, how much rope remains?
Definition:

Decimal Subtraction: Align decimal points and subtract normally, borrowing when needed

Original Length
8.5 m
Cut Off
- 3.25 m
Remaining
5.25 m
Step 1: Set up the subtraction

8.50 (adding zero for alignment)

-3.25

-----

Step 2: Subtract hundredths column

0 - 5, need to borrow: 10 - 5 = 5

Step 3: Subtract tenths column

4 - 2 = 2 (after borrowing)

Step 4: Subtract units column

8 - 3 = 5

8.50 - 3.25 = 5.25
Final answer:

5.25 meters of rope remains

Applied rules:

• Decimal Alignment: Align decimal points before subtracting

• Borrowing: When top digit is smaller, borrow from left column

• Zero Padding: Add zeros to align decimal places if necessary

3 Money Problem
Exercise 3
Tom had $15.75. He spent $6.90 on lunch and $3.45 on snacks. How much money does he have left?
Definition:

Multi-step Decimal Operations: Perform operations in sequence following order of operations

Starting Amount
$15.75
Total Spent
$10.35
Remaining
$5.40
Step 1: Calculate total amount spent

$6.90 + $3.45 = $10.35

Step 2: Subtract total spent from starting amount

$15.75 - $10.35 = $5.40

Step 3: Verify calculation

$5.40 + $10.35 = $15.75 ✓

$15.75 - ($6.90 + $3.45) = $5.40
Final answer:

Tom has $5.40 left

Applied rules:

• Order of Operations: Parentheses first, then subtraction

• Multi-step Problem Solving: Break complex problems into simpler steps

• Verification: Always check your answer makes sense

4 Weight Problem
Exercise 4
A bag of flour weighs 2.5 kg. If 0.75 kg is used for baking, how much flour remains?
Definition:

Decimal Subtraction with Different Place Values: Align decimals and subtract carefully

Initial Weight
2.50 kg
Used
- 0.75 kg
Remaining
1.75 kg
Step 1: Set up subtraction with aligned decimals

2.50 (added zero for alignment)

-0.75

-----

Step 2: Subtract hundredths column

0 - 5, need to borrow: 10 - 5 = 5

Step 3: Subtract tenths column

4 - 7, need to borrow: 14 - 7 = 7 (after borrowing)

Step 4: Subtract units column

1 - 0 = 1 (after borrowing)

2.50 - 0.75 = 1.75
Final answer:

1.75 kg of flour remains

Applied rules:

• Multiple Borrowing: May need to borrow across multiple columns

• Decimal Alignment: Essential for accurate calculations

• Unit Consistency: Keep track of measurement units throughout

5 Distance Problem
Exercise 5
A car traveled 125.6 miles on Monday and 87.35 miles on Tuesday. How many miles did it travel in total?
Definition:

Adding Decimals with Different Decimal Places: Align decimals and add zeros for easier computation

Monday Distance
125.60 mi
Tuesday Distance
+ 87.35 mi
Total Distance
212.95 mi
Step 1: Align decimals with zero padding

125.60

+ 87.35

------

Step 2: Add hundredths column

0 + 5 = 5

Step 3: Add tenths column

6 + 3 = 9

Step 4: Add units column

5 + 7 = 12, write 2, carry 1

Step 5: Add tens column

2 + 8 + 1 (carry) = 11, write 1, carry 1

Step 6: Add hundreds column

1 + 0 + 1 (carry) = 2

125.60 + 87.35 = 212.95
Final answer:

The car traveled 212.95 miles in total

Applied rules:

• Zero Padding: Add zeros to align different decimal places

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

• Place Value: Maintain correct place value during addition

Word Problems Solutions: 6 to 10
6 Liquid Measurement
Exercise 6
A container had 3.75 liters of juice. After pouring out 1.4 liters, how much juice remains?
Definition:

Decimal Subtraction with Different Decimal Places: Align decimals and subtract carefully

Initial Amount
3.75 L
Removed
- 1.40 L
Remaining
2.35 L
Step 1: Align decimals with zero padding

3.75

-1.40

-----

Step 2: Subtract hundredths column

5 - 0 = 5

Step 3: Subtract tenths column

7 - 4 = 3

Step 4: Subtract units column

3 - 1 = 2

3.75 - 1.40 = 2.35
Final answer:

2.35 liters of juice remains

Applied rules:

• Zero Padding: Add zeros to make decimal places equal

• Decimal Alignment: Critical for accurate subtraction

• Measurement Units: Keep track of units throughout calculation

7 Savings Problem
Exercise 7
Emma saved $24.50 last month and $18.75 this month. She spent $15.30 on a book. How much money does she have now?
Definition:

Multi-step Decimal Operations: Perform addition first, then subtraction

Total Saved
$43.25
Amount Spent
- $15.30
Current Amount
$27.95
Step 1: Calculate total savings

$24.50 + $18.75 = $43.25

Step 2: Subtract expenses from savings

$43.25 - $15.30 = $27.95

Step 3: Verify the answer

$27.95 + $15.30 = $42.25 (close to $43.25, small rounding)

($24.50 + $18.75) - $15.30 = $27.95
Final answer:

Emma has $27.95 remaining

Applied rules:

• Order of Operations: Addition first, then subtraction

• Multi-step Problem Solving: Break complex problems into parts

• Verification: Check your work by reversing the operation

8 Length Problem
Exercise 8
A wooden board is 12.8 inches long. A piece 4.35 inches long is cut off. What is the length of the remaining board?
Definition:

Decimal Subtraction with Mixed Decimal Places: Align decimals and subtract with borrowing if needed

Original Length
12.80 in
Cut Piece
- 4.35 in
Remaining Length
8.45 in
Step 1: Align decimals with zero padding

12.80

- 4.35

------

Step 2: Subtract hundredths column

0 - 5, need to borrow: 10 - 5 = 5

Step 3: Subtract tenths column

7 - 3 = 4 (after borrowing)

Step 4: Subtract units column

1 - 4, need to borrow: 11 - 4 = 7

Step 5: Subtract tens column

0 - 0 = 0 (after borrowing)

12.80 - 4.35 = 8.45
Final answer:

The remaining board is 8.45 inches long

Applied rules:

• Multiple Borrowing: May need to borrow across multiple columns

• Zero Padding: Add zeros to align decimal places

• Place Value: Maintain correct place value during subtraction

9 Weight Comparison
Exercise 9
A bag of apples weighs 5.2 kg and a bag of oranges weighs 3.85 kg. How much heavier is the bag of apples?
Definition:

Decimal Subtraction for Comparison: Find the difference between two decimal quantities

Apples Weight
5.20 kg
Oranges Weight
- 3.85 kg
Difference
1.35 kg
Step 1: Align decimals with zero padding

5.20

-3.85

-----

Step 2: Subtract hundredths column

0 - 5, need to borrow: 10 - 5 = 5

Step 3: Subtract tenths column

1 - 8, need to borrow: 11 - 8 = 3 (after borrowing)

Step 4: Subtract units column

4 - 3 = 1 (after borrowing)

5.20 - 3.85 = 1.35
Final answer:

The bag of apples is 1.35 kg heavier

Applied rules:

• Comparison Subtraction: Subtract smaller number from larger

• Decimal Alignment: Essential for accurate comparison

• Borrowing Across Zeros: May need to borrow from multiple columns

10 Budget Problem
Exercise 10
Maria budgeted $45.00 for groceries. She spent $12.75 on vegetables, $8.50 on fruit, and $15.25 on meat. How much of her budget remains?
Definition:

Multi-step Decimal Operations: Add multiple expenses, then subtract from budget

Budget
$45.00
Total Expenses
- $36.50
Remaining
$8.50
Step 1: Calculate total expenses

$12.75 + $8.50 + $15.25 = $36.50

Step 2: Subtract total expenses from budget

$45.00 - $36.50 = $8.50

Step 3: Verify calculation

$8.50 + $36.50 = $45.00 ✓

$45.00 - ($12.75 + $8.50 + $15.25) = $8.50
Final answer:

Maria has $8.50 remaining in her budget

Applied rules:

• Multi-step Problem Solving: Break complex problems into parts

• Order of Operations: Parentheses first (add expenses), then subtraction

• Verification: Always check that your answer makes sense

Decimal Operations Infographic

Decimal Operations Guide

🔢
Decimal Addition
Align decimal points and add

• Line up decimal points vertically

• Add zeros to match decimal places

• Add column by column

• Carry over when sum > 9

Decimal Subtraction
Align decimal points and subtract

• Line up decimal points vertically

• Add zeros to match decimal places

• Borrow when top digit < bottom digit

• Subtract column by column

Word Problem Steps
1
Read
2
Identify
3
Plan
4
Solve
5
Check
Common Mistakes

• Misaligning decimal points

• Forgetting to add zeros

• Incorrect borrowing/carrying

• Not checking reasonableness

Key Tips

• Always align decimal points

• Use estimation to check

• Add zeros to make place values clear

• Read the problem carefully

Decimal Place Value
Tens | Units | Tenths | Hundredths
1 2 . 3 4
Practice Makes Perfect!
Key Concepts, Methods, and Rules
a.b + c.d = (a + c).(b + d) + carries
Decimal Addition
Key definitions:

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

Decimal Point: Separates the whole number part from the fractional part

Place Value: Position of a digit determines its value (tenths, hundredths, etc.)

Problem-Solving Methodology:
  1. Understand: Read the problem carefully and identify what is being asked
  2. Plan: Determine which operation(s) to use and set up the equation
  3. Solve: Perform the decimal operations with proper alignment
  4. Check: Verify the answer makes sense in context
Tip 1: Always align decimal points before adding or subtracting.
Tip 2: Add zeros to make decimal places equal for easier calculation.
Tip 3: Estimate your answer first to check if the final result is reasonable.
Tip 4: Remember to label your answer with appropriate units.
Common errors: Misaligned decimal points, incorrect borrowing/carrying, forgetting to bring down the decimal point.
Success strategies: Draw lines to align decimals, check each step, verify with inverse operations.
Essential Rules:

• Decimal Alignment: Always line up decimal points vertically

• Place Value: Each position represents a power of 10

• Borrowing: When subtracting, borrow from the next higher place value

• Carrying: When adding, carry excess to the next higher place value

• Estimation: Round to estimate and verify your answer

Questions & Answers

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

Answer: Great question! Here's a foolproof method for decimal alignment:

  1. Draw a vertical line to align decimal points: Write numbers with decimal points lined up vertically
  2. Add trailing zeros if needed to make all numbers have the same number of decimal places
  3. Perform the operation just like with whole numbers
  4. Bring down the decimal point directly below the others in your answer

Example: Adding 3.45 and 2.7
3.45
+2.70 (added zero)
-----
6.15

The key is keeping the decimal point in the same column throughout the calculation!

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

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

  • Grocery shopping: Have your child calculate costs, compare prices, find totals
  • Cooking: Measuring ingredients with fractional cups (0.5 cup, 0.25 cup)
  • Measuring: Using rulers to measure objects in centimeters or inches
  • Budgeting: Tracking allowance or planning a small purchase

Also encourage your child to create their own word problems based on daily activities. This builds both math skills and confidence!

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

Question: I sometimes forget to borrow when subtracting decimals. How can I remember?

Answer: Here's a memory technique for decimal subtraction with borrowing:

  1. Scan each column from right to left before calculating
  2. Ask yourself: "Is the top number bigger than the bottom?"
  3. If NO: Circle the column and mark it to borrow from the left
  4. Visual reminder: Cross out the number you're borrowing from and write the new value

Example: 5.2 - 3.7
In tenths column: 2 < 7, so need to borrow
Change 5.2 to 4.12 (borrow 1 from units, becomes 10 tenths + 2 = 12 tenths)
Then: 12 - 7 = 5 in tenths place

Practice this method until it becomes automatic!