Operations with Fractions and Decimals

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

1QuestionAddition and Subtraction of FractionsConcept Practice

2 marks~3 minCriterion A

A community garden is divided into 12 equal plots. Volunteers have planted vegetables in 5 plots and flowers in 3 plots. The remaining plots are unused.

Calculate the fraction of the garden used for vegetables and flowers combined. Express your answer in simplest form. [1]

The garden committee will fund a water irrigation system only if more than $\dfrac{2}{3}$ of all plots are in use. Justify whether the committee will fund the irrigation system. [1]

Solutions

2QuestionAddition and Subtraction of FractionsAssessment Practice

2 marks~3 minCriterion D

A baker's cookie recipe requires

\dfrac{2}{3}

cup of flour and

\dfrac{1}{4}

cup of sugar. She decides to make half the recipe.

Calculate the halved quantity of sugar. Justify whether this halved measurement presents a practical challenge when using standard measuring cups, which are marked at

\dfrac{1}{4}

\dfrac{1}{3}

, and

\dfrac{1}{2}

cup intervals, and state one consequence for the finished cookies. [2]

Solutions

3QuestionOrder of Operations with Mixed Numbers and DecimalsConcept Practice

2 marks~3 minCriterion C

A student purchases 4 cinema tickets at

7.25

dollars each and applies a

6.00

dollar voucher to the total bill.

Calculate the amount the student pays, showing the correct order of operations. [1]

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]

Solutions

4QuestionConverting Between Fractions Decimals and PercentagesAssessment Practice

12 marks~18 minCriterion B

Prime numbers can produce recurring decimals when used as the denominator of a unit fraction (numerator = 1). This question investigates the relationship between a prime denominator

p

and the length of the recurring block

L

Calculate the decimal form of each unit fraction. Show your long-division working. [4]

\frac{1}{3}, \quad \frac{1}{7}, \quad \frac{1}{11}, \quad \frac{1}{13}

Deduce the length of the recurring block for each decimal in part (a), and record your results.

Denominator ( $p$ )	___	___	___	___
Length of recurring block ( $L$ )	___	___	___	___ [2]

Analyse the values in part (b) to formulate a rule for the maximum possible length

L

of the recurring block in terms of

p

. Express your rule as an equation and justify why the actual length may sometimes be shorter than this maximum. [4]

A computer-science student claims that knowing the recurring-block length of

\frac{1}{p}

tells you the minimum number of digits a computer must store to represent

\frac{1}{p}

exactly. Calculate the decimal form of

\frac{1}{17}

, determine its recurring-block length, and assess whether the student's claim is supported for this fraction, referring to your rule from part (c). [2]

Solutions

Questions 5-79

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