Introduction to Rate | Cambridge IGCSE Mathematics

Rate in Mathematics

[Please watch the video attached at the end of this blog for a visual explanation of the rate]

You will obviously have heard the word “rate” before, especially used when measuring one thing against the other. Rate of decay and rate of inflation are phrases that are familiar to you, especially if you are a Science student or Commerce student respectively. 


With this word being used so much currently, it is only apt that you learn the importance of rate in the context of Mathematics. Read on to find out!


What is Rate?

Rate is defined as a measure, quantity, or frequency, that is usually measured against another quantity or measure. Rate is a special ratio which we use to compare two different units.


Ex 1:

If a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. 


Be mindful that ratios and rates are NOT the same thing!

As we learnt in the lesson Ratios and Proportions, ratios are the comparison or simplified form of two quantities that are the same type  


For example, if there were 5 sweets in total and 3 were given to Sally while 2 were given to Nina, the ratio between Sally and Nina would be 3:2.


In the above example, we can see that we are talking about the same type of quantities, i.e. number of sweets.


However, when considering rates, we are talking about two different things.  But in Example 1, we are talking about the 12 ounce can and the price of the can. So there’s two different things like cents and ounces, which are two different units.


Therefore, ratio is basically when it is between the same type of units and rate is a special type of ratio which is between two different types of units. 


Example 2:


A machine fills containers at a rate of 134 containers in 2 minutes. How long would it take to fill 1000 containers at the same rate?

We are looking at a rate of 134 containers being filled in 2 minutes. We are to find out how long it would take to fill 1000 containers at the same rate. 


In order to do this, we must first find out the current rate of the machine. If it fills 134 containers in 2 minutes, this means the rate would be 2/134. This tells us how many minutes it takes to fill one container, meaning how many minutes per container, 


Hence, if we find out how many minutes per container it takes, and we know that there are 1000 containers, if you multiply this value by 1000, we can identify how many minutes it takes for 1000 containers.

2/134 * 1000

Once the calculator is done, you can see that it takes 14.9 minutes for the machine to fill 1000 containers at the current rate of the machine.


What should you do next?

Always remember that rates and ratios are two different lessons. You can watch this video on Ratios and Proportions to revise ratios before starting rates! Hence, pay close attention to whether the question is focused on ratios or rates, and change your answers accordingly.


Past paper questions tend to be tricky, and this is where practice comes in handy. Some questions can be found here as well, and you can time your answers to see if you can stick to the time limit given.


If you are struggling with IGCSE revision or Mathematics in particular, you can reach out to us at Tutopiya to join revision sessions or find yourself the right tutor for you.


Watch the video below for a visual explanation of the lesson “Rate”. Make sure to attempt the quiz once you’re done!

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