Proper Fractions: Error Analysis & Misconceptions

Mathematics
GCSE Foundation
11 questions
~22 mins
1 views0 downloads

About This Worksheet

A worksheet focusing on proper fractions, highlighting common errors and misconceptions related to adding fractions with the same denominator. Designed for GCSE Foundation students to develop procedural fluency and reasoning skills.

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Proper Fractions: Error Analysis & Misconceptions

Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet

Grade GCSE Foundation
A

Fluency & Practice

Answer the following questions to practice adding proper fractions with the same denominator. Show your working in the grid spaces provided.
1.
Calculate: 37+27 \frac{3}{7} + \frac{2}{7}
[2 marks]
2.
Calculate: 59+39 \frac{5}{9} + \frac{3}{9}
[2 marks]
3.
Add: 411+611 \frac{4}{11} + \frac{6}{11}
[2 marks]
4.
Add: 713+513 \frac{7}{13} + \frac{5}{13}
[2 marks]
B

Problem Solving & Reasoning

Solve the following multi-step problems involving proper fractions. Explain your reasoning clearly.
1.
A recipe requires 25 \frac{2}{5} of a cup of sugar and 15 \frac{1}{5} of a cup of flour. How much of these ingredients are used in total? Show your working.
[4 marks]
2.
Emma has 38 \frac{3}{8} of a chocolate bar and gives away 18 \frac{1}{8} . How much does she have left? Show your working.
[4 marks]
C

Real-world Applications

Read the scenario and solve the problem related to proper fractions in real-life contexts.
1.
Liam drank 37 \frac{3}{7} of a litre of juice in the morning and 27 \frac{2}{7} in the afternoon. How much juice did he drink altogether? Show your working.
[3 marks]
D

Challenge & Extension

Attempt these more challenging problems that involve proper fractions and reasoning.
1.
A pizza is cut into 8 equal slices. If 38 \frac{3}{8} of the pizza is eaten, what fraction remains? How does this compare to 58 \frac{5}{8} ? Explain your reasoning.
[4 marks]
2.
Construct a diagram showing the sum of 49 \frac{4}{9} and 29 \frac{2}{9} . Confirm the total in simplest form.
[3 marks]
E

Mixed Review & Error Analysis

Review the following common mistakes and identify/fix errors.
1.
A student adds 27+37 \frac{2}{7} + \frac{3}{7} and writes the answer as 58 \frac{5}{8} . Identify the mistake and correct it.
[3 marks]
2.
A student claims 49+49=89 \frac{4}{9} + \frac{4}{9} = \frac{8}{9} . Is this correct? If not, explain and correct the mistake.
[3 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet