Succeed with maths – Part 1
Succeed with maths – Part 1

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Succeed with maths – Part 1

1.3 Writing a fraction as a percentage

Using the same idea that multiplication by 100 per cent means multiplication by 1, you can also convert fractions into percentages.

So if you want to convert three divided by 25 to a percentage, it can be shown as follows:

three divided by 25 multiplication 100 percent equals open three divided by 25 multiplication 100 close percent equation left hand side equals right hand side open three divided by 21 times five multiplication 100 super four divided by one close percent equation left hand side equals right hand side open three multiplication four divided by one multiplication one close percent equals 12 percent

As an alternative, you can turn the fraction into a decimal (by dividing the numerator by the denominator) and then move the decimal point two places to the right (because you are multiplying by 100). This is shown in the example below, where seven divided by 20 is converted to a percentage.

seven divided by 20 equals zero .35 equals 35 percent

As with a lot of maths, there are other alternative ways to convert a fraction into a percentage. You can also multiply the fraction by 100 divided by 100, as shown in this example:

equation sequence two divided by five equals two multiplication 100 super 20 divided by five sub one multiplication 100 equals 40 divided by 100 equals 40 percent

For this last example, note that the fraction can be expanded by multiplication so that the denominator is turned into 100. For some fractions, this gives you another alternative for the conversion. For this last example, it looks like this:

equation sequence two divided by five equals two divided by five multiplication 20 divided by 20 equals 40 divided by 100 equals 40 percent

You’ve covered a few ideas here, so here’s a quick summary as a reminder before you have a go yourself:

  • Percentage to fraction – write the percentage value as a fraction out of 100, and simplify.
  • Percentage to a decimal – divide the percentage value by 100.
  • Decimal to percentage – multiply the decimal by 100 per cent.
  • Fraction to percentage – multiply the fraction by 100 per cent, and simplify as necessary.

You may be wondering why any of this matters! It is not just some interesting maths; being able to carry out these conversions can help you when it comes to working with percentages in problems.

Bear all these ‘rules’ in mind as you work through this week.

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