Mixed Numbers: Real-world Applications in Travel & Maps
Mathematics
Year 9
20 questions
~40 mins
1 views0 downloads
About This Worksheet
A worksheet exploring subtraction of mixed numbers with unlike denominators within real-world travel contexts, focusing on practical map scales and distances.
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Mixed Numbers: Real-world Applications in Travel & Maps
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Solve the following questions to practice subtracting mixed numbers. Show your working in the grid spaces provided.
1.
Calculate: 3 1/4 - 1 2/3
[3 marks]2.
Subtract: 5 3/5 - 2 4/5
[3 marks]3.
Find: 4 2/7 - 1 5/7
[3 marks]4.
Calculate the difference: 6 1/2 - 3 3/4
[3 marks]B
Problem Solving & Reasoning
Apply your knowledge to solve these multi-step problems related to travel distances and map scales.
1.
A hiker travels 4 3/4 miles on Monday and 2 2/3 miles on Tuesday. How much farther did the hiker travel on Monday than on Tuesday?
[4 marks]2.
A map uses a scale of 1 1/2 inches representing 3 miles. If a route on the map measures 5 1/4 inches, what is the actual distance?
[4 marks]3.
A cyclist covers 7 2/3 miles and then pedals back 3 1/4 miles. What is the total distance traveled?
[3 marks]4.
A boat travels 12 1/2 miles downstream and then 5 2/3 miles back upstream. Find the net distance from start to end point.
[4 marks]5.
A traveler walks 3 3/4 miles and then takes a taxi for 2 2/3 miles. How much distance has the traveler covered in total?
[3 marks]C
Real-world Applications
Solve these contextual word problems related to travel distances, map scales, and navigation.
1.
A city map shows a river that is 2 1/2 inches long, representing 5 miles in real distance. How long is the river in miles?
[3 marks]2.
A hiker plans a trail that covers 8 1/4 miles. If she has already hiked 3 2/3 miles, how much farther does she need to go?
[3 marks]3.
A cyclist travels 9 3/4 miles but then takes a detour of 2 1/2 miles. What is the total distance traveled?
[3 marks]4.
A boat travels 15 1/2 miles downstream and then 7 3/4 miles upstream. What is the net distance from the starting point?
[4 marks]D
Challenge & Extension
Attempt these more difficult problems involving mixed numbers and real-world contexts.
1.
A runner completes 10 2/3 miles in the morning and 7 5/8 miles in the evening. How much more miles did he run in the morning than in the evening?
[4 marks]2.
A train travels 45 1/4 miles at one speed and then 32 3/8 miles at a different speed. What is the total distance covered?
[3 marks]E
Mixed Review
Answer these questions of various types to review your understanding of mixed numbers.
1.
Express 3 4/5 as an improper fraction.
[2 marks]2.
Simplify: 10 4/6 - 7 1/3
[3 marks]3.
Convert 2 2/3 to an improper fraction.
[2 marks]F
Error Analysis
Below are common mistakes made in subtracting mixed numbers. Identify the mistake and correct it.
1.
Student subtracts: 2 1/2 - 1 3/4 = 0 5/4. What mistake did they make and what is the correct answer?
[4 marks]2.
A student subtracts : 4 2/3 - 2 1/2 = 2 1/6, but the actual answer is different. Identify the error.
[4 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet