Operations with Fractions
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Operations with Fractions — Free MYP2 Mathematics Practice Questions

1QuestionAdding and Subtracting FractionsConcept Practice
3 marks~5 minCriterion A
Two bar models are shown. The first bar is divided into 3 equal parts with 2 parts shaded, representing 23\dfrac{2}{3}. The second bar is divided into 5 equal parts with 1 part shaded, representing 15\dfrac{1}{5}.
a
Identify the least common multiple (LCM) of 3 and 5. [1]
b
Calculate the total shaded fraction. Show your working. [1]
c
Explain why 1315\dfrac{13}{15} cannot be simplified further. [1]
Question diagram

Solutions

2QuestionAdding and Subtracting FractionsAssessment Practice
6 marks~9 minCriterion D
A student cuts a piece of length 1351\dfrac{3}{5} m from a wooden plank of length 3133\dfrac{1}{3} m. Their measuring tape is marked only in eighths of a metre.
a
Calculate the remaining length of the plank using the exact measurements. [2]
b
Calculate the remaining length after first rounding each measurement to the nearest 18\dfrac{1}{8} m. Show your rounding clearly. [2]
c
Compare the two remaining lengths from parts (a) and (b). State one limitation of using a measuring tape marked only in eighths of a metre for this task. [2]
Question diagram

Solutions

3QuestionEquivalent FractionsConcept Practice
4 marks~6 minCriterion B
Each square below is divided into equal parts. The shaded region shows a fraction of the whole square.

Diagram 12 equal parts1 shaded.
Diagram 24 equal parts2 shaded.
Diagram 36 equal parts3 shaded.
Diagram 48 equal parts4 shaded.
a
Identify the fraction of each square that is shaded. [2]
b
Explain why all four fractions represent the same value, and state the general rule that connects them. [2]
Question diagram

Solutions

4QuestionAdding and Subtracting FractionsAssessment Practice
8 marks~12 minCriterion C
Alice and Ben each calculate 34+56\dfrac{3}{4} + \dfrac{5}{6}.

Alice uses denominator 12: 34=912,56=1012,sum=1912\quad \dfrac{3}{4} = \dfrac{9}{12}, \quad \dfrac{5}{6} = \dfrac{10}{12}, \quad \text{sum} = \dfrac{19}{12}

Ben uses denominator 24: 34=1824,56=2024,sum=3824\quad \dfrac{3}{4} = \dfrac{18}{24}, \quad \dfrac{5}{6} = \dfrac{20}{24}, \quad \text{sum} = \dfrac{38}{24}
a
Identify one equivalent fraction used by either student and explain why it equals the original fraction. [2]
b
Calculate whether Ben's answer 3824\dfrac{38}{24} equals Alice's answer 1912\dfrac{19}{12}. Show your working. [2]
c
Compare the two methods. Explain which is more efficient and why, giving at least two reasons. [4]

Solutions

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