Mixed Numbers and Improper Fractions
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Mixed Numbers and Improper Fractions — Free MYP3 Mathematics Practice Questions

1QuestionAdding and Subtracting Mixed NumbersConcept Practice
2 marks~3 minCriterion A
The diagram shows two rectangles of equal size.

Rectangle A is divided into 5 equal parts, with 3 parts shaded.
Rectangle B is divided into 3 equal parts, with 2 parts shaded.

Calculate the total shaded area from both rectangles, expressing your answer as a mixed number. [2]
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Solutions

2QuestionAdding and Subtracting Mixed NumbersAssessment Practice
6 marks~9 minCriterion D
A baker has 3133\frac{1}{3} cups of flour, adds 2342\frac{3}{4} cups for a large batch, then removes 1151\frac{1}{5} cups to make a smaller batch. Each measurement has a possible error of ±18\pm\frac{1}{8} cup.
a
Calculate the final amount of flour as a simplified mixed number. [2]
b
Explain how the measurement error affects the reliability of your answer in part (a). [2]
c
A recipe requires exactly 4344\frac{3}{4} cups of flour. Analyse whether the baker's final amount is sufficient, taking into account the maximum possible measurement error. [2]
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Solutions

3QuestionApplications in Geometry and MeasurementAssessment Practice
6 marks~9 minCriterion C
A room has a rectangular section measuring 4124\dfrac{1}{2} m by 3133\dfrac{1}{3} m, and a semi-circular bay window of radius 1141\dfrac{1}{4} m. A student claims the total floor area is 181818\dfrac{1}{8} m2^2.
a
Calculate the correct total floor area of the room. Show all working. [3]
b
Explain one reason why the rectangular section area alone may not be exact in a real room. [1]
c
The student's answer differs from the correct value by approximately 0.670.67 m2^2. Interpret what this difference suggests about the reliability of the student's method. [2]
Question diagram

Solutions

4QuestionAdding and Subtracting Mixed NumbersAssessment Practice
8 marks~12 minCriterion B
When two mixed numbers are added, their fractional parts sometimes sum to exactly 1.

113+223214+134315+245116+256438+3581\tfrac{1}{3} + 2\tfrac{2}{3} \qquad 2\tfrac{1}{4} + 1\tfrac{3}{4} \qquad 3\tfrac{1}{5} + 2\tfrac{4}{5} \qquad 1\tfrac{1}{6} + 2\tfrac{5}{6} \qquad 4\tfrac{3}{8} + 3\tfrac{5}{8}
a
Calculate the first four sums. Express each result as a whole number. [4]
b
Describe the rule that determines when the sum of the fractional parts of two mixed numbers equals exactly 1. [2]
c
A student claims the fifth sum equals 8 without working out the fractions separately. Justify whether the student is correct. [2]

Solutions

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