Mixed Numbers: Error Analysis & Misconceptions
Mathematics
Year 9
11 questions
~22 mins
1 views0 downloads
About This Worksheet
This worksheet explores common errors and misconceptions when subtracting mixed numbers with unlike denominators, offering practice, reasoning, and challenge questions.
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Mixed Numbers: Error Analysis & Misconceptions
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
Read the key concept about subtracting mixed numbers below:
1.
To subtract mixed numbers, first convert each mixed number to an improper fraction, find a common denominator, perform the subtraction, and then convert back to a mixed number if needed.
[2 marks]B
Fluency & Practice
Answer the following procedural questions. Show all working in the grid spaces below.
1.
Subtract 3 1/4 - 1 2/3. Show your working.
[3 marks]2.
Calculate 5 2/5 - 2 3/10.
[3 marks]3.
Compute 4 3/8 - 2 5/12.
[3 marks]C
Problem Solving & Reasoning
Solve multi-step problems involving mixed numbers. Explain your reasoning.
1.
A recipe requires 2 3/4 cups of sugar. If you accidentally subtract 1 5/8 cups, how much sugar remains? Show your working.
[4 marks]2.
A builder needs to subtract 7 1/2 meters from a length of 12 2/3 meters. How much length is left? Justify your answer.
[4 marks]D
Real-world Applications
Work through these contextual problems involving mixed numbers.
1.
A cyclist rides 5 2/3 miles in the morning and 3 3/4 miles in the afternoon. If they decide to rest, how many miles did they cycle in total? Then, subtract the 2 1/2 miles they covered during a quick ride. What is the remaining distance traveled? Show all steps.
[4 marks]E
Challenge & Extension
Attempt the more difficult problems below. Provide detailed calculations.
1.
Subtract 9 5/8 - 4 7/12. Use the most efficient method and justify each step.
[4 marks]2.
A diver starts at a depth of 12 1/2 meters and ascends by 4 2/3 meters, then descends by 3 5/8 meters. What is the diver's final depth? Show detailed working.
[4 marks]F
Mixed Review & Error Analysis
Identify the common errors in the following incorrect solutions and correct them.
1.
Student's solution: 2 1/2 - 1 3/4 = 1 2/4. Error? Fix it and explain.
[3 marks]2.
Another student's solution: Convert 3 2/3 to 11/3, 1 1/4 to 5/4, then subtract: 11/3 - 5/4 = 6/12 or 1/2. What's wrong? Correct the mistake.
[3 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