 Equivalent fractions to 10ths, 100ths and 1000ths | KS2 Maths

## What you need to know

Things to remember:

• We can think of the fractions as their place values.
• If there are 0s on the ends of the numbers in the fraction, we can divide by 10.

What is $\dfrac{30}{100}$ as an equivalent fraction in tenths?

Well, let’s think about it. We are told that there are “30 hundredths”, but we know that 10 hundredths make 1 tenth, so how many tenths do we have here?

$$30\div10=3$$

$$30\text{ Hundredths }= 3\text{ Tenths }$$

Or, if we were to write these both as fractions:

$$\frac{30}{100}=\frac{3}{10}$$

Notice how this is the same as just taking a 0 off the top and bottom, which is just dividing both by 10.

$$\frac{30}{100}=\frac{30\div10}{100\div10}=\frac{3}{10}$$

And whenever we have 0s on the top and bottom we can do this.

$$\frac{50}{100}=\frac{50\div10}{100\div10}=\frac{5}{10}$$

$$\frac{80}{100}=\frac{80\div10}{100\div10}=\frac{8}{10}$$

$$\frac{140}{100}=\frac{140\div10}{100\div10}=\frac{14}{10}$$

We don’t just have to do this with tenths and hundredths, we can do this for bigger numbers like thousandths too!

$$\frac{250}{1000}=\frac{250\div10}{1000\div10}=\frac{25}{100}$$

$$\frac{600}{1000}=\frac{600\div10}{1000\div10}=\frac{60}{100}$$

But did we have to stop there? We can divide by 10 again for $\frac{60}{100}$

$$\frac{60}{100}=\frac{60\div10}{100\div10}=\frac{6}{10}$$

$$\frac{600}{100}=\frac{6}{10}$$

So, as long as we have 0s at the ends of the numbers in the fraction, we can divide by 10!

## Example Questions

$$\frac{90}{100}=\frac{90\div10}{100\div10}=\frac{9}{10}$$

$$\frac{600}{1000}=\frac{600\div10}{1000\div10}=\frac{60}{100}$$

$$\frac{60}{100}=\frac{60\div10}{100\div10}=\frac{6}{10}$$

$$\frac{600}{1000}=\frac{6}{10}$$

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