Converting between ratios, fractions and percentages

You can now write about this using fractions, by thinking about the whole and its parts.

The bar model is split into 7 parts, which make the whole, so 7 is the denominator.

There are 4 green parts. As a fraction, it’s \(\frac {4} {7}\).

There are 3 blue parts. As a fraction, it’s \(\frac {3} {7}\).

Now, let's find out how to convert a fraction to a ratio.

Here is a bowl containing apples and oranges.

You can see that\(\frac {3} {5}\) of the items in the basket are oranges.

Putting what you know into a bar model can help you convert the information into a ratio.

If \(\frac {3} {5}\) are oranges, then \(\frac {2} {5}\) must be apples.

How to convert between fractions and percentages

When converting fractions to percentages it's important to remember that per cent means ‘parts out of 100’.

So your fraction must have a denominator of 100 before you can complete the conversion.

Here are two fractions with a denominator of 100 and their equivalent percentages:

• \(\frac {25} {100}\) = 25%
• \(\frac {33} {100}\) =30%

Notice how when the denominator is 100, the numerator becomes the percentage.

Let's look at a fraction where the denominator is not 100.

Here, a square has been split into 10 equal-sized rectangles. It is split into tenths. \(\frac {7} {10}\) of the square is shaded.

By using your knowledge of tenths and hundredths, you can say that 7 tenths is the same as 70 hundredths.

You can say that \(\frac {7} {10}\) is equivalent to \(\frac {70} {100}\).

As the denominator is now 100 you can use this to say that 70% of the square is shaded.

Tenths are easier to convert into percentages, but what about the fraction \(\frac {2} {5}\)?

To convert it, first you need to find an equivalent fraction with a denominator of 100.

\(\frac {2} {5}\) is equivalent to \(\frac {40} {100}\), which is 40%.

You can convert percentages to fractions very simply.

Remember - per cent means ‘parts out of 100’.

Place the percentage figure as the numerator and use 100 as the denominator.

75% is equivalent to \(\frac {75} {100}\).

Then you just simply the fraction.

You can divide by 25 to find the equivalent fraction is \(\frac {3} {4}\).

75% = \(\frac {3} {4}\).

As fractions:

\(\frac {3} {5}\) are blue

\(\frac {2} {5}\) are pink