Ratio Math Help

Ratio Math Help Online

The Mathematical Definition of Ratio : A method of comparing two quantities measured in similar units by considering the quotient of the two quantities.

In other words ratio is a way of comparing the amounts of two or three or more things as long as the measurements are in the same units.

So for example the ratio of £2 to 50p is written like this 200:50

If your question says to simplify this answer, then you would write 200:50=4:1

NOTE : Ratios are simplified similarly to fractions

How did we get 4:1? we cancelled the numbers 200:50 down into its simplest form in the same way we do with fractions. So, the number 50 goes into 200 four times. 50 goes into 50 once, therefore 200:50=4:1

There are many ways to cancel the number 200:50 down, as many numbers go into these two numbers. Lets have a look at it another way


=100:25 (since 2 goes into 200 and 50)

=20:5 (as 5 goes into 100 and 25)

=4:1 (only 5 goes into 20 and 5)

You see! This is a more long winded approach but the final answer is still the same.

The next example is more typical of the type of ratio asked by most people. Its also the most likely question asked in an exam.

A Ratio Question

John and Paul have won a prize worth $60. John receives the prize money in the ratio of 2 and Paul in the ratio of 3. How much money do each person get?


Now they share the prize in the ratio of 2:3 so altogether thats 5 bits.

Or rather John receives 2/5 of the money and Paul receives 3/5 of the money.

1/5 of $60= $12

Then John receives 2×12=$24

And Paul receives 3×12=$36

Another Question - Only harder

Emma and Josh recieve £20 pocket money in the ratio of 4 to 6. How much do they each receive?


Now they share the pocket money in the ratio of 4:6 so altogether that's 10 bits.

We can either cancel down the 4:6 into its lowest term, or you can complete this by doing it in the same way as the above example.

Lets do the canceling down example. 4:6 cancels down to 2:3, therefore that's 5 parts.

So, Emma receives 2/5 out of £20 and Josh gets 3/5 of £20.

1/5 of £20= £4

Then Emma receives 2×4=£8

and Josh gets 3×4=£12

That's it! How is this example harder than the above one? Well, we canceled the ratio down a little bit into its simplest form.

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