Introduction
Decimal numbers are everywhere in real life - from money to measurements. Being able to solve word problems with decimals is an essential math skill. In this lesson, we'll learn how to solve and create story problems involving decimal operations.
In this lesson, you will learn:
- How to analyze and solve word problems with decimals
- Strategies for working with data presented in tables
- How to create your own decimal word problems
- Common mistakes to avoid when working with decimals
Real-World Connection
Decimals appear in many everyday situations:
• Shopping: Calculating total costs and change
• Cooking: Measuring ingredients
• Sports: Timing races to hundredths of a second
• Weather: Recording temperatures and rainfall
Solving Decimal Word Problems
Problem-Solving Strategy
Use this step-by-step approach to solve any decimal word problem:
Step-by-Step Method:
- Read carefully: Understand what the problem is asking
- Identify: Find the numbers and operations needed
- Plan: Decide how to solve it (equation, diagram, etc.)
- Solve: Perform the calculations carefully
- Check: Verify if your answer makes sense
Example 1: Addition Problem
Sarah bought a book for GH₵12.50 and a pen for GH₵3.75. How much did she spend in total?
Solution:
1. We need to find the total cost → addition
2. Numbers: 12.50 and 3.75
3. Equation: 12.50 + 3.75 = ?
4. Calculation:
\[ \begin{array}{r} \phantom{0}12.50 \\ +\ \phantom{0}3.75 \\ \hline \phantom{0}16.25 \\ \end{array} \]5. Check: 12 + 4 = 16 (estimate), so GH₵16.25 is reasonable
Answer: Sarah spent GH₵16.25 in total.
Example 2: Subtraction Problem
A 2.5 liter bottle of juice has 1.75 liters remaining. How much juice was consumed?
Solution:
1. We need to find the difference → subtraction
2. Numbers: 2.5 and 1.75
3. Equation: 2.50 - 1.75 = ?
4. Calculation:
\[ \begin{array}{r} \phantom{0}2.50 \\ -\ 1.75 \\ \hline \phantom{0}0.75 \\ \end{array} \]5. Check: 2.5 - 2 = 0.5, so 0.75 is reasonable (more was drunk)
Answer: 0.75 liters of juice was consumed.
Multiplication & Division Problems
Example 3: Multiplication Problem
If one meter of fabric costs GH₵8.75, how much would 3.5 meters cost?
Solution:
1. Cost per unit × quantity → multiplication
2. Numbers: 8.75 and 3.5
3. Equation: 8.75 × 3.5 = ?
4. Calculation:
\[ \begin{array}{r} \phantom{0}8.75 \\ \times\ \phantom{0}3.5 \\ \hline \phantom{0}4375 \ \text{(875 × 5)} \\ +\ 2625\ \ \ \text{(875 × 3, shifted)} \\ \hline \phantom{0}30.625 \\ \end{array} \]Since we're dealing with money, we round to 2 decimal places: GH₵30.63
5. Check: 9 × 3.5 = 31.5, so GH₵30.63 is reasonable
Answer: 3.5 meters cost GH₵30.63.
Example 4: Division Problem
A 4.8 kg bag of rice is divided equally into 6 containers. How much rice goes in each container?
Solution:
1. Total ÷ parts → division
2. Numbers: 4.8 and 6
3. Equation: 4.8 ÷ 6 = ?
4. Calculation:
48 tenths ÷ 6 = 8 tenths (0.8)
5. Check: 6 × 0.8 = 4.8 ✔
Answer: Each container gets 0.8 kg of rice.
Practice Exercise (Word Problems)
Question 1
Kofi ran 1.75 km on Monday, 2.5 km on Tuesday, and 1.25 km on Wednesday. What was his total distance for the three days?
Solution:
This is an addition problem: 1.75 + 2.5 + 1.25
Align decimals:
\[ \begin{array}{r} 1.75 \\ 2.50 \\ +\ 1.25 \\ \hline 5.50 \\ \end{array} \]Answer: Kofi ran 5.5 km total.
Question 2
A shop bought 15.5 kg of sugar at GH₵4.20 per kg. What was the total cost?
Solution:
This is a multiplication problem: 15.5 × 4.20
Calculate:
\[ \begin{array}{r} 15.5 \\ \times\ 4.2 \\ \hline 310 \ \text{(155 × 2)} \\ +\ 620\ \ \ \text{(155 × 4, shifted)} \\ \hline 65.10 \\ \end{array} \]Answer: The total cost was GH₵65.10.
Ready for more challenges?
Full Practice SetSolving Problems with Data Tables
Working with Tables
Many real-world problems present data in tables. The key is to:
- Read the table headings carefully
- Identify which data you need
- Determine the correct operation(s) to use
Example 1: Grocery Shopping
Prices at Makola Market
| Item | Price per kg (GH₵) |
|---|---|
| Rice | 8.50 |
| Beans | 12.75 |
| Maize | 5.25 |
| Millet | 7.80 |
Question: If Ama buys 2 kg of rice and 1.5 kg of beans, how much does she spend?
Solution:
1. Find prices from table: Rice = GH₵8.50/kg, Beans = GH₵12.75/kg
2. Calculate costs:
Rice: 2 × 8.50 = GH₵17.00
Beans: 1.5 × 12.75 = GH₵19.125 → GH₵19.13
3. Total: 17.00 + 19.13 = GH₵36.13
Answer: Ama spends GH₵36.13.
Multi-Step Table Problems
Example 2: Sports Records
100m Dash Times (seconds)
| Athlete | Heat 1 | Heat 2 | Heat 3 |
|---|---|---|---|
| Kwame | 11.45 | 11.32 | 11.28 |
| Ama | 11.89 | 11.75 | 11.82 |
| Yaw | 11.53 | 11.47 | 11.39 |
Question: What is the difference between Kwame's fastest and Ama's slowest times?
Solution:
1. Find Kwame's fastest time: 11.28 (Heat 3)
2. Find Ama's slowest time: 11.89 (Heat 1)
3. Calculate difference: 11.89 - 11.28 = 0.61 seconds
Answer: The difference is 0.61 seconds.
Practice Exercise (Table Problems)
Question 1
Classroom Supplies
| Item | Price | Quantity Needed |
|---|---|---|
| Pencils | GH₵0.75 each | 24 |
| Notebooks | GH₵3.50 each | 15 |
| Rulers | GH₵1.25 each | 10 |
What is the total cost for all the pencils and notebooks?
Solution:
Pencils: 24 × 0.75 = GH₵18.00
Notebooks: 15 × 3.50 = GH₵52.50
Total: 18.00 + 52.50 = GH₵70.50
Answer: The total cost is GH₵70.50.
Question 2
Water Consumption
| Day | Amount Used (liters) |
|---|---|
| Monday | 125.5 |
| Tuesday | 118.75 |
| Wednesday | 132.25 |
| Thursday | 140.0 |
| Friday | 127.8 |
What is the average daily water consumption for these five days?
Solution:
Total consumption: 125.5 + 118.75 + 132.25 + 140.0 + 127.8 = 644.3 liters
Average: 644.3 ÷ 5 = 128.86 liters/day
Answer: The average is 128.86 liters per day.
Ready for more challenges?
Full Practice SetCreating Decimal Word Problems
How to Create Good Problems
Creating your own word problems helps deepen your understanding. Follow these guidelines:
Creating Effective Problems:
- Choose a real-world context: Shopping, sports, cooking, etc.
- Decide the operation: Addition, subtraction, multiplication, or division
- Use reasonable numbers: Appropriate decimal places for the context
- Make it clear: Ensure the question is understandable
- Include all needed information: But don't add unnecessary details
Example 1: Creating an Addition Problem
Context: Cooking recipe
Operation: Addition of ingredient amounts
Problem:
"A cake recipe requires 1.5 cups of flour, 0.75 cups of sugar, and 0.25 cups of cocoa powder. How many cups of dry ingredients are needed in total?"
Solution: 1.5 + 0.75 + 0.25 = 2.5 cups
Example 2: Creating a Table Problem
Context: Weekly savings
Operation: Multi-step with subtraction and addition
Problem:
Kofi's Weekly Savings (GH₵)
| Week | Amount Saved | Amount Spent |
|---|---|---|
| 1 | 15.50 | 8.25 |
| 2 | 12.75 | 10.50 |
| 3 | 18.00 | 7.75 |
"How much did Kofi save in total after three weeks, considering what he spent each week?"
Solution:
Week 1: 15.50 - 8.25 = 7.25
Week 2: 12.75 - 10.50 = 2.25
Week 3: 18.00 - 7.75 = 10.25
Total saved: 7.25 + 2.25 + 10.25 = 19.75
Answer: Kofi saved GH₵19.75 total.
Create Your Own Problems
Exercise 1
Create a word problem involving decimal multiplication with a money context.
Exercise 2
Design a table showing prices of three items at a market, then write a question requiring two operations to solve.
Common Mistakes to Avoid
Frequent Errors
Misaligned Decimal Points
Forgetting to line up decimals when adding/subtracting
Wrong:
\[ \begin{array}{r} 12.5 \\ +\ 3.75 \\ \hline 16.0 \text{✗} \\ \end{array} \]Right:
\[ \begin{array}{r} 12.50 \\ +\ \phantom{0}3.75 \\ \hline 16.25 \text{✓} \\ \end{array} \]Incorrect Place Value
Counting decimal places wrong in multiplication
Wrong:
2.5 × 1.3 = 3.25 (correct), but sometimes written as 32.5 or 0.325
Misreading Tables
Using wrong data from tables or misinterpreting headings
Wrong:
Using price instead of quantity when calculating totals
Unrealistic Answers
Not checking if answers make sense in context
Wrong:
Calculating a person's height as 15.2 meters
Pro Tips for Success
- Always write decimals with the same number of places when adding/subtracting
- Count decimal places in multiplication (total places in factors = places in product)
- Double-check which data you're using from tables
- Estimate first to see if your final answer is reasonable
- When creating problems, test them to make sure they work
Math Challenge
Timed Test: 7 Levels
Test your multiplication and division skills!