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Academy11+

📝 Fraction & Percentage Word Problems

Learn to solve real-world problems involving fractions and percentages. Master the problem-solving strategies and apply your knowledge.

Advanced Level
50-60 minutes
Problem Solving

What are Word Problems?

Word problems help us apply math to real situations! 📝

Word problems are mathematical questions written in everyday language. They require you to identify the relevant information, choose the right operation, and solve step-by-step. This is essential for real-world applications.

Read Carefully
Understand the problem

Read the problem multiple times to understand what's being asked. Identify key information and what you need to find.

Plan Your Solution
Choose the right method

Decide which mathematical operations to use. Convert between fractions, decimals, and percentages as needed.

Check Your Answer
Verify the solution

Always check if your answer makes sense in the context of the problem. Does it answer the question asked?

Key Concepts

Problem Analysis

Read carefully, identify key information, understand what's being asked, and determine what you need to find.

Mathematical Operations

Choose the right operations: addition, subtraction, multiplication, division, and conversions between forms.

Solution Verification

Check if your answer makes sense, verify calculations, and ensure you've answered the question correctly.

Detailed Examples

Example 1: Fraction Word Problem

Problem: A class has 30 students. 2/3 of them are girls. How many girls are in the class?

Step 1: Understand the problem
Total students = 30
Fraction of girls = 2/3
Step 2: Calculate 2/3 of 30
2/3 × 30 = 60/3 = 20
Answer: 20 girls

Problem-Solving Steps

• Read the problem carefully
• Identify key information
• Choose the right operation
• Perform the calculation
• Check your answer

Example 2: Percentage Word Problem

Problem: A shirt costs £40. It's on sale for 25% off. What is the sale price?

Step 1: Understand the problem
Original price = £40
Discount = 25% off
Step 2: Find 25% of £40
25% = 0.25, so 0.25 × £40 = £10
Step 3: Subtract discount
Sale price = £40 - £10 = £30
Answer: £30

Alternative Method

• 25% off means 75% of original price
• 75% = 0.75
• 0.75 × £40 = £30
• This gives the same answer
• Always check your answer

Example 3: Mixed Operations

Problem: A pizza is cut into 8 slices. Tom eats 3 slices. What fraction of the pizza did he eat?

Step 1: Understand the problem
Total slices = 8
Slices eaten = 3
Step 2: Write as fraction
Fraction eaten = 3/8
Step 3: Check if it can be simplified
3/8 is already in simplest form
Answer: 3/8 of the pizza

Fraction Word Problems

• Identify the whole (denominator)
• Identify the part (numerator)
• Write as fraction
• Simplify if possible
• Always check your answer

Interactive Activities

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Activity 1: Problem Analyzer

Learn to identify key information in word problems.

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Activity 2: Operation Chooser

Practice choosing the right mathematical operations.

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Activity 3: Shopping Problems

Solve real-world shopping and money problems.

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Activity 4: Word Problem Quiz

Test your word problem solving skills.

Practice Questions

Practise this with a free account

4 practice questions on this topic, from easy to 11+ level. Reading the guide is free for everyone; practice is for members, and signing up is free.

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Tips and Tricks

Problem Analysis

  • • Read the problem multiple times
  • • Underline key information
  • • Identify what you need to find
  • • Draw a diagram if helpful
  • • Always check your answer

Mathematical Operations

  • • Choose the right operation
  • • Convert between forms as needed
  • • Use mental math when possible
  • • Show your work step-by-step
  • • Always check your answer

Common Problem Types

  • • Shopping and discounts
  • • Sharing and dividing
  • • Percentages of amounts
  • • Fractions of groups
  • • Time and distance problems

Memory Tricks

  • • "Read, Plan, Solve, Check"
  • • "What do I know? What do I need?"
  • • "Does my answer make sense?"
  • • "Show your work"
  • • "Always check your answer"