Lesson video

Hello, my name is Mr Clasper and today we are going to going to be looking at repeated percentage increase and decrease.

Before we begin it might be useful for you to look at other lessons on repeated percentage increase and repeated percentage decrease as this lesson will be combining the two.

If you have already watched those then you shouldn't have a problem.

Let's have a look at our first example.

Increase 600 by 10%, then decrease by 20%.

An increase of 10% would give us 110% and this is equivalent to 1.

1.

A decrease of 20% would be equivalent to 80% and this is equivalent to 0.

8.

Therefore the calculation I'm going to carry out would be 600 multiplied by 1.

1 multiplied by 0.

8 and this would give me a final answer of 528.

Let's try another example decrease 300 by 5%, then increase by 15%.

So, a decrease of 5% would be representative of 95% and this is equivalent to 0.

95.

If we increase by 15% this is equivalent to 115% which is equivalent to 1.

15.

So my calculation would be 300, my original amount multiplied by 0.

95, so this is a decrease of 5% then multiplied by 1.

15 which is our increase of 15%, and this would give us a final answer of 327.

75.

Here is a question for you to try, pause the video to complete your task and click resume once you've finished.

And, here are your solutions, so if we take a look at the first question.

We multiply it by 1.

1, this is because this represents the total percentage of 110%, which will be achieved when we increase by 10%.

For the second problem we have multiplied by 0.

9, this is because we have decreased by 10% this time.

So, decreasing by 10% will be equivalent to finding 90% of something and 90% as a decimal will be 0.

9.

Let's have a look at this example.

A farm has 200 cows.

The number of cows increases by 5% every year.

How many cows will be on the farm in 4 years? This is an increase so that means my new percentage would be 105% which is equivalent to 1.

05.

So, my calculation could be 200 multiplied by 1.

05 and this would give me approximately 243 as my solution.

However, there is a more efficient way to carry out this calculation.

Instead of carrying out this calculation we could calculate 200 multiplied by 1.

05 to the power of 4 as this would be equivalent to our original calculation.

Therefore, giving us the same answer in a more efficient way.

Let's try this example.

A woodland has 500 trees.

The number of trees decreases by 5% every year.

How many trees will be in the woodland in 3 years? Well, if we decrease by 5% that will leave us with 95%, and as a decimal this is equivalent to 0.

95.

So, the calculation I could carry out would be 500 multiplied by 0.

95 as we have the 5% decrease 3 times.

This gives us an answer of approximately 429.

However, there is a more efficient calculation we could use, we could calculate 500 multiplied by 0.

95 to the power of 3 as this is equivalent to multiplying by 0.

95 three times.

Here are some questions for you to try, pause the video to complete your task and click resume once you've finished.

And, here are our two solutions so, if we take a look at question two, as we decreased by 6% this would leave us with 94% which means that we would need to use the decimal 0.

94.

Our calculation is 7000 multiplied by 0.

94 to the power of 4, as we are decreasing by 6% four times.

This leaves us with our answer of 5465 to the nearest pound.

And, if we take a look at question 3, this time we've increased in value.

An increase of 1.

8% would represent 101.

8% and as a decimal that would be 1.

018.

So, if we calculate 230000 multiplied by 1.

018 to the power of 7 we get our final answer of 260593.

Here is another question for you to try.

Pause the video to complete your task and click resume once you've finished.

And, here is the solution.

So, for this question we're told that a horse increases in weight first of all, and then the horse decreases in weight after this.

So, the increase of 12% would be our multiplication of 1.

12, which represents our 112% and then a decrease of 5% would leave 95%, which is where our multiplication of 0.

95 came from.

Your final answer was 744.

8 kilogrammes.

Let's take a look at this example, after one year, a company's profits decrease by 8%.

The next year profits increase by 17%.

Find the total percentage profit after 2 years.

Well, the first year there was a decrease of 8% which is equivalent to 92% and this is equivalent to 0.

92.

In the second year profits increased by 17% which represents 117% in total, this is equivalent to 1.

17.

If we calculate 0.

92 multiplied by 1.

17 we get 1.

0764 as a percentage this is equivalent to 107.

64%, that means there was an increase or a profit of 7.

64%.

Here is your last question, pause the video to complete your task and click resume once you've finished.

And, here is the solution to our final problem.

So, for this question we multiply 0.

85 by 1.

3.

This represent 85% leftover when we lose 15% followed by 130% represented by our increase of 30%.

So, when we multiply these two together we get a decimal of 1.

105, if we turn this into a percentage this would represent the percentage 110.

5%, which means we've increased in total by 10.

5%.

And, that brings us nicely to the end of our lesson.

I hope you're feeling more confident using repeated percentage change to calculate increases and decreases.

Why not have a go at the exit quiz, just to boost your confidence further.

I'll hopefully see you soon.