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Solve problems involving simple interest (ACMNA211)

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

Review of percentages

Percentages are fractions with a denominator of 100. To convert a percentage to its fraction equivalent, we begin by writing it with a denominator of 100. We can then simplify.

When the number is a whole number we just need to write it as fraction and simplify.

For example:

\(65\% = \dfrac{65}{100} = \dfrac{13}{20}\hspace{30mm}150\% = \dfrac{150}{100} = 1\dfrac{1}{2}\)

We can write these percentages as decimals by writing them as fractions with a denominator of 100 and converting to a decimal. For example:

65% = \(\dfrac{65}{100} = 0.65\hspace{30mm}150\% = \dfrac{150}{100} = 1.5\)

When we are dealing with percentages where the number is not a whole number we need to calculate an 'equivalent fraction'.

For example: 45\(\dfrac{1}{2}\)% = \(\dfrac{45\frac{1}{2}}{100} = \dfrac{91}{200}\)

To write a percentage as a decimal, we divide by 100.

For example: 62.5% = \(\dfrac{62.5}{100}\) = 0.625