Maths: Percentages

Understanding Maths Series:

[Percent (%) = per  cent = in relation to (one) hundred]

The following are a series of calculations on how to reach (the sum of)

You should understand the relation of all figures in the equation. The MAIN VARIABLE will determine whether you use the multiply/divide by 0.xx% or 1.xx%. Generally, if the main variable is to increase, then we use 1.xx% but, if the main variable decreases then we should use 0.xx% . Therefore, identifying the main variable is imperative and find out whether we need to extract a larger or smaller figure from it.

Look out for this in the examples below:

  • How do I find a percentage of a number?

Q. What is 12% of  48?

The figure we are looking for is a smaller portion of 48, therefore 12% is represented as the decimal 0.12

x= ∑ 48 x 0.12

x= 5.76

In Q.1 the main variable is 48 . The extracted figure was smaller than the base, which is also the main variable. We multiplied it by .12

  • How do I find out the result of x percent increase?

Q. I have £48 and it increases by 12%

In this calculation, the base figure (48) increases by 12% which means that x = 112% of the base.

112% is represented here by the decimal 1.12  (it is merely 112 represented as a rational number ÷100)

x= ∑ 48 x 1.12

x= 53.76

In Q.2 the main variable was still 48, this time the figure was to INCREASE so we multiply it by 1.12

NB. the base is not increasing by 112% but is increasing only by 12%. To increase by 112% the calculation is more than 2 x base, the figure to multiply by would be 2.12

  • How do I find out the result of x percent decrease?

Q. I have £48 and it decreases by 12%

In this calculation, the base figure (48) decreases by 12% which means that x= 88% of the base.

88% is represented here by the decimal 0.88  (it is merely 88 represented as a rational number ÷100)

x= ∑ 48 x 0.88

x= 42.24

Alternatively, if we use the 0.12 (12%) we will arrive at the sum 5.76 which you can subtract from the base, like so:

48 x 0.12 = 5.76 (this is 12% of the base)

48 – 5.76 = 42.24 (if you subtract the 12% from the base you arrive at the sum)

In Q.3 main variable is 48 yet again. The extracted figure was smaller than the base, which is also the main variable. We multiplied it by .88

  • Percentages as a proportionate figure

Q. 48 is 12% of x, how do I find ‘x’?

The result is 12% of x so we convert 12% into it’s decimal format: 0.12

x (multiplied by) 0.12 = 48

:. (therefore) 48 ÷ 0.12 = x

x = 400

Q.4 the main variable is ‘x’. The formula is actually x (multiplied by) y% = z. The figure represented by ‘x‘ is larger than the base figure(48), therefore to find 12% of x we would use the sum: ‘x’ multiplied by 0.12 but that is not the question.

What we are doing is finding a smaller figure from x, the main variable.

We know 12% of is 48 so we divide 48 by 12% of it’s parent (x) using 0.12

‘x’ X 12% = 48 —-> ‘x’ X 0.12 = 48 —-> We now rearrange the formula:

x’ X 0.12 ÷ 0.12 = 48 ÷ 0.12 —-> x’ X 0.12 ÷ 0.12 = 48 ÷ 0.12 —->x’ = 48 ÷ 0.12

oh, alternatively! (48 ÷ 12) X 100 🙂 but that’s too easy!

  • Representative percentage increases

Q. I had £x and it increased by 12% to £48, what is x?

I’m trying to find out what I used to have, so this becomes the main figure.  The result is 112% of ‘x’

x (multiplied by) 1.12 = 48

:. 48 ÷ 1.12 = 42.86

Q.5 main variable = x. The formula is actually x (multiplied by) y% = z.

‘x’ increased in size therefore we use the figure: 1.12

x’ X 12% = 48 —-> ‘x’ X 1.12 = 48 —-> We now rearrange the formula:

x’ X 1.12 ÷ 1.12 = 48 ÷ 1.12 —-> x’ X 1.12 ÷ 1.12 = 48 ÷ 1.12 —->x’ = 48 ÷ 1.12

  • Representative percentage decreases

Q. I had £x and it decreased by 12% to £48, what is x?

I’m trying to find out what I used to have, so this (x) becomes the main figure.  The result decreased (by 12% which is equal to 88% value of ‘x‘) so x is obviously larger than 48.

We know that 48 is 88% (100 – 12) of ‘x’

x (multiplied by) 0.88 = 48

:. 48 ÷ 0.88 = 54.54 (r)

Q.6 the main variable is again x. This is because, like in question 4, the formula is actually x (multiplied by) y% = z. In this case we have x (multiplied by) 88% = 48 because we are trying to find 88% of ‘x‘ Once again, we are searching for a smaller figure of x

Here is another example:

I have $48 to spend on CD’s. The shop has a discount of 20% on selected items, what is the highest pre-discount priced item I can purchase?

:. the formula is:  x X y% = 48

If we multiply x by 1.2 it will = a mark the price upwards. This is not correct becausex’ is greater than 48.

If we multiply x by o.2 it will = a 20% reflection of the price not a 20% reduction. This is not correct.

:. we need to represent x with a 20% decrease in value, this is done by multiplying by 0.8 (See Q.3)

:. x X 0.8 = 48 —-> We now rearrange the formula:

x’ X 0.8 ÷ 0.8 = 48 ÷ 0.8 —-> x’ X 0.8 ÷ 0.8 = 48 ÷ 0.8 —-> x = 48 ÷ 0.8

x = 60

  • Percentage increase differences

This is very simple.

Q. I have 48 apples, yesterday I had 40, what is the % increase?

the difference between the two figures is 48-40 = 8

8 ÷ previous amount —-> 8 ÷ 40 = 20

the increase is 20%

  • Percentage decrease differences

Q. I have 48 apples, yesterday I had 60, what is the % increase?

the difference between the two figures is 48-60 = 12

12 ÷ previous amount —-> 8 ÷ 60 = 20

the decrease is 20%

Hope that all makes sense!

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s