Proper Fractions: Problem Solving & Reasoning
Mathematics
Year 9
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on adding proper fractions with like denominators, designed to develop procedural skills, reasoning, and real-world problem solving for Year 9 students.
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Proper Fractions: Problem Solving & Reasoning
Subject: MathematicsGrade: Year 9
Name:
Date:
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Solve the following questions by performing the calculations. Show your working in the grid spaces.
1.
Calculate: 3/7 + 2/7
[2 marks]2.
Add the fractions: 5/9 + 2/9
[2 marks]3.
Simplify the sum: 4/11 + 6/11
[2 marks]4.
What is 7/13 + 4/13?
[2 marks]B
Problem Solving & Reasoning
Solve the problems below. Show detailed reasoning for each step.
1.
A recipe requires 2/8 cups of sugar. If you want to make half of the recipe, how much sugar will you need? Explain your reasoning.
[4 marks]2.
A race track is 3/7 miles long. Two runners complete the track, one in 3/7 miles and another in 2/7 miles. What is the total distance run? Show your calculations.
[4 marks]3.
If you add 5/12 and 4/12, what is the total? Why is the sum a proper fraction?
[3 marks]C
Real-world Applications
Apply your understanding to these real-life scenarios.
1.
Jamie eats 3/8 of a pizza and her friend eats 2/8 of the same pizza. How much of the pizza did they eat together? Show your work.
[3 marks]2.
A container holds 7/10 liters of juice. If you pour out 3/10 liters, how much remains? Express your answer as a proper fraction.
[3 marks]D
Challenge & Extension
Tackle these advanced problems to extend your understanding.
1.
Construct a visual representation on the grid for 4/9 + 3/9. Label the parts clearly.
[4 marks]2.
A cyclist travels 5/8 miles each day. If they cycle for 5 days, what total distance do they cover? Explain the calculation.
[4 marks]E
Mixed Review
Answer these questions to review various aspects of proper fractions.
1.
Express the sum: 9/15 + 4/15 in simplest form.
[2 marks]2.
Add 2/5 and 3/5. Is the result a proper fraction? Justify your answer.
[3 marks]F
Error Analysis
Identify and correct the common mistake in the following problem.
1.
Student's solution: 3/8 + 5/8 = 8/8 = 1. Is this correct? If not, explain the mistake and provide the correct answer.
[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