Proper Fractions: Problem Solving & Reasoning

Mathematics
Year 9
14 questions
~28 mins
1 views0 downloads

About This Worksheet

A worksheet focused on subtracting proper fractions with like denominators, including procedural exercises and real-world problems to develop deep understanding and reasoning skills.

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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

Introduction

Read the key concept about proper fractions below.
1.
A proper fraction has a numerator smaller than the denominator. When subtracting proper fractions with the same denominator, subtract the numerators and keep the denominator the same. For example, 3717=27 \frac{3}{7} - \frac{1}{7} = \frac{2}{7} .
[2 marks]
B

Fluency & Practice

Solve the following to practice your procedural skills.
1.
Calculate: 5929 \frac{5}{9} - \frac{2}{9} .
[2 marks]
2.
Subtract: 712412 \frac{7}{12} - \frac{4}{12} .
[2 marks]
3.
Find the difference: 815515 \frac{8}{15} - \frac{5}{15} .
[2 marks]
C

Targeted Practice

Apply your knowledge to more challenging questions.
1.
Calculate: 920420 \frac{9}{20} - \frac{4}{20} .
[2 marks]
2.
Subtract: 1118718 \frac{11}{18} - \frac{7}{18} .
[2 marks]
3.
Find the difference: 1325925 \frac{13}{25} - \frac{9}{25} .
[2 marks]
4.
Calculate: 1724924 \frac{17}{24} - \frac{9}{24} .
[2 marks]
D

Word Problems & Reasoning

Solve these multi-step problems and explain your reasoning.
1.
Sara had 710 \frac{7}{10} of a chocolate bar. She ate 210 \frac{2}{10} of it. How much of the chocolate bar does she have left? Show your working.
[3 marks]
2.
A recipe requires 34 \frac{3}{4} cup of sugar. If you use 14 \frac{1}{4} cup less than the recipe calls for, how much sugar do you use? Show your working.
[3 marks]
E

Challenge & Extension

Attempt these more difficult problems for extension.
1.
Calculate: 19301130 \frac{19}{30} - \frac{11}{30} .
[3 marks]
2.
If you subtract 49 \frac{4}{9} from 79 \frac{7}{9} , what is the result? Express your answer as a proper fraction.
[3 marks]
F

Mixed Review & Error Analysis

Review these questions on common errors. Fix the mistakes.
1.
A student calculated 5838=26 \frac{5}{8} - \frac{3}{8} = \frac{2}{6} . Is this correct? If not, identify and correct the mistake.
[3 marks]
2.
Subtract: 3727 \frac{3}{7} - \frac{2}{7} . Some students get an answer of 17 \frac{1}{7} , but others write 114 \frac{1}{14} . Which is correct? Explain why.
[3 marks]

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Details

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