Operations with Fractions and Decimals
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Operations with Fractions and Decimals — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionMultiplication and Division of FractionsConcept Practice
2 marks~3 minCriterion A
A nutritionist is scaling down a granola recipe. The full batch requires 34\dfrac{3}{4} cup of rolled oats, but she is making 13\dfrac{1}{3} of the batch.
a
Calculate the amount of rolled oats needed. [1]
b
Standard dry measuring cups come in sizes 14\dfrac{1}{4} cup and 18\dfrac{1}{8} cup. Justify whether the calculated amount can be measured exactly using these cups. [1]
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Solutions

2QuestionOrder of Operations with Mixed Numbers and DecimalsAssessment Practice
2 marks~3 minCriterion C
A student purchases 4 cinema tickets at 7.257.25 dollars each and applies a 6.006.00 dollar voucher to the total bill.
a
Calculate the amount the student pays, showing the correct order of operations. [1]
b
The student's friend argues that the voucher should be subtracted from one ticket price before multiplying. Justify whether the friend's interpretation is mathematically valid, referring to the real-world transaction. [1]
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Solutions

3QuestionMultiplication and Division of FractionsAssessment Practice
4 marks~6 minCriterion D
A baker is halving a recipe that requires 2132\dfrac{1}{3} cups of flour. The baker mistakenly calculates 213×2=4232\dfrac{1}{3} \times 2 = 4\dfrac{2}{3} cups instead of halving correctly.
a
Show that the correct amount of flour needed is 1161\dfrac{1}{6} cups. [2]
b
The baker measures 1161\dfrac{1}{6} cups using a set of cups marked in increments of 18\dfrac{1}{8} cup. Advise the baker whether fraction arithmetic remains a reliable method for scaling this recipe, given the measurement tools available. [2]
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Solutions

4QuestionAddition and Subtraction of FractionsAssessment Practice
5 marks~8 minCriterion B
A pharmacist mixes two liquid medicines in equal parts. Medicine A is administered at 1n\frac{1}{n} of a standard dose per millilitre, and Medicine B at 1n+1\frac{1}{n+1} of a standard dose per millilitre, where nn is a positive integer. The combined concentration per millilitre is 1n+1n+1\frac{1}{n} + \frac{1}{n+1}.
a
Calculate each sum for n=2,3,4,5,6n = 2, 3, 4, 5, 6, expressing each result as a single fraction in simplest form.

12+13,13+14,14+15,15+16,16+17\frac{1}{2}+\frac{1}{3}, \quad \frac{1}{3}+\frac{1}{4}, \quad \frac{1}{4}+\frac{1}{5}, \quad \frac{1}{5}+\frac{1}{6}, \quad \frac{1}{6}+\frac{1}{7} [2]
b
Explain the pattern you observe in the numerators and denominators of your results. [1]
c
Deduce the combined concentration when n=9n = 9, without performing the full calculation. [1]
d
A safe combined concentration must remain below 14\frac{1}{4} of a standard dose per millilitre. Using the general rule 1n+1n+1=2n+1n(n+1)\frac{1}{n}+\frac{1}{n+1} = \frac{2n+1}{n(n+1)}, advise the pharmacist whether the mixture is safe for all values of n≥4n \geq 4, and state the smallest value of nn for which it becomes safe. [1]

Solutions

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