Operations with Fractions and Decimals

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Operations with Fractions and Decimals — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionConverting Between Fractions Decimals and PercentagesConcept Practice

2 marks~3 minCriterion A

A jacket is priced at 80 dollars. Store A offers a 25% discount; Store B sells the same jacket for 61 dollars with no discount.

Calculate the sale price of the jacket at Store A after the 25% discount is applied. [1]

Advise a customer which store to purchase from, justifying your recommendation with reference to the calculated sale price. [1]

Solutions

2QuestionAddition and Subtraction of FractionsAssessment Practice

6 marks~9 minCriterion D

A painter is mixing a custom shade of green for a large mural. The recipe specifies

\frac{2}{5}

of the total mixture as blue paint,

\frac{1}{3}

as yellow paint, and

\frac{1}{15}

as black paint; the remainder is white paint.

Calculate the fraction of the total mixture that is white paint. [2]

The blue paint measurement has a possible error of up to

\frac{1}{60}

of the total mixture. Analyse the effect of this error on the shade of green, considering both the case where more blue is used and the case where less blue is used. [2]

The painter considers measuring each colour by volume rather than as a fraction of the total mixture. Given that the paints have different densities, advise the painter whether this alternative method is appropriate for achieving consistent colour across the mural. [2]

Solutions

3QuestionConverting Between Fractions Decimals and PercentagesConcept Practice

3 marks~5 minCriterion C

A factory quality-control report states that

\frac{3}{8}

of a batch of components failed inspection. The supervisor needs the failure rate expressed as a decimal to enter it into a digital monitoring system that does not accept fractions.

Explain what mathematical operation

\frac{3}{8}

represents, identifying the role of the numerator and denominator. [1]

Show that

\frac{3}{8} = 0.375

by completing the long division of

3.000 \div 8

, presenting each step clearly. [1]

The monitoring system flags any batch with a failure rate above

0.4

. Advise the supervisor whether this batch requires further action, justifying your answer with reference to the decimal result. [1]

Solutions

4QuestionConverting Between Fractions Decimals and PercentagesConcept Practice

2 marks~3 minCriterion B

A currency exchange app displays repeating decimals when converting amounts. The app shows these fraction-to-decimal conversions:

\frac{1}{9} = 0.\overline{1}, \quad \frac{2}{9} = 0.\overline{2}, \quad \frac{3}{9} = 0.\overline{3}, \quad \frac{4}{9} = 0.\overline{4}

Deduce the fraction, in simplest form, that corresponds to

0.\overline{7}

. [1]

A currency conversion gives the result

0.\overline{7}

of a base amount. Justify whether this is greater than, equal to, or less than

\dfrac{3}{4}

of the same base amount, using fractions. [1]

Solutions

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