# KS3. Number. 15. Equivalent Fractions, Decimals & Percentages

Two of the easiest ways to compare fractions are:

• By converting them to fractions with a common denominator;
• By converting them to decimals

Let’s use both of these methods to compare:

• 2/5 and 3/7
• 2/9 and 3/15

Exercise

Let’s try exercise 10H on page 154 of the textbook

Equivalent Fractions, Percentages and Decimals

We have now learned enough that we should be able to compare numbers whether they are written as fractions, as decimals, or as percentages. These three are just different ways of writing the same thing (The s<=>d button on your calculator can be helpful here). A percentage is simply a fraction over 100, so 33% = 33/100.

If we want to turn a fraction into a percentage, we can either convert it to an equivalent fraction whose denominator is 100, or we can treat it as a division to convert it to a decimal and then read off the first two digits after the decimal place, which tell us the “hundredths”. Let’s try this.

Changing percentages into fractions (or decimals) is easier, because we just write the percentage as a fraction over 100 and then either simplify it or just write the answer as a decimal.

Example

Let’s try some of these with the teacher doing some and students coming up to the board to do some:

Exercise

Let’s try exercise 13A from pages 204 and 205 of our textbook (without using a calculator unless the questions asks for one):