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When we say "Percent" we are really saying "per 100"

One percent ( 1%) means 1 per 100.

1% of this line is shaded green: it is very small isn't it?

50% means 50 per 100
(50% of this box is green)

25% means 25 per 100
(25% of this box is green)

Try it Yourself:

numbers/images/ani-pct.js

Examples:

100% means all.

Example:

100% of 80 is 100 100 × 80 = 80

50% means half.

Example:

50% of 80 is 50 100 × 80 = 40

5% means ⁵/ 100ths.

Example:

5% of 80 is 5 100 × 80 = 4

Using Percent

numbers/images/percentage.js

Use the slider and try some different numbers
(What is 40% of 80? What is 10% of 200? What is 90% of 10?)

Because "Percent" means "per 100" think:

"this should be divided by 100"

And 100% is , or exactly 1
(100% of any number is just the number, unchanged)

A Half can be written...

As a percentage:

As a decimal:

As a fraction:

Read more about this at Decimals, Fractions and Percentages.

Some Worked Examples

Example: Calculate 25% of 80

So 25% of 80 is 20

Example: 15% of 200 apples are bad. How many apples are bad?

Example: if only 10 of the 200 apples are bad, what percent is that?

5% of those apples are bad

Example: A Skateboard is reduced 25% in price.
The old price was $120.
Find the new price.

First, find 25% of $120:

25% of $120 is $30

So the reduction is $30

Take the reduction from the original price

$120 − $30 = $90

The Price of the Skateboard in the sale is $90

Calculation Trick

This little rule can make some calculations easier:

x% of y = y% of x

Example: 8% of 50

8% of 50 is the same as 50% of 8

And 50% of 8 is 4

So 8% of 50 is also 4

The Word

"Percent" comes from the latin Per Centum. The latin word Centum means 100, for example a Century is 100 years.

Percent vs Percentage

My Dictionary says "Percentage" is the "result obtained by multiplying a quantity by a percent". So 10 percent of 50 apples is 5 apples: the 5 apples is the percentage.

But in practice people use both words the same way.

877,878,879, 1301, 1302,880, 1303, 1304, 3501, 3502

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One percent ( 1%) means 1 per 100. 1% of this line is shaded green: it is very small isn't it? 50% means 50 per 100 (50% of this box is green) 25% means 25 per 100 (25% of this box is green) Try it Yourself: numbers/images/ani-pct.js 100% means all.

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Compartir el documento con los compañeros

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Compartir el documento con los compañeros

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✅ Cómo COMPARTIR ARCHIVOS en Google Drive

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Practising Grade 10 maths: 'Percent of a number: VAT, discount and more'

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Fun maths practice! Improve your skills with free problems in 'Percent of a number: VAT, discount and more' and thousands of other practice lessons.

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Comparing Old to New

Change: subtract old value from new value.
Example: You had 5 books, but now have 7. The change is: 7−5 = 2.

Percentage Change: show that change as a percent of the old value ... so divide by the old value and make it a percentage:
So the percentage change from 5 to 7 is: 2/5 = 0.4 = 40%

Percentage Change is all about comparing old to new values. See percentage change, difference and error for other options.

How to Calculate

Here are two ways to calculate a percentage change, use the one you prefer:

Method 1

Step 1: Calculate the change (subtract old value from the new value)

Step 2: Divide that change by the old value (you will get a decimal number)

Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

Note: when the new value is greater then the old value, it is a percentage increase, otherwise it is a decrease.

Method 2

Step 1: Divide the New Value by the Old Value (you will get a decimal number)

Step 2: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

Step 3: Subtract 100% from that

Note: when the result is positive it is a percentage increase, if negative, just remove the minus sign and call it a decrease.

Examples

Example: A pair of socks went from $5 to $6, what is the percentage change?

Answer (Method 1):

Step 1: $5 to $6 is a $1 increase

Step 2: Divide by the old value: $1/$5 = 0.2

Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise.

Answer (Method 2):

Step 1: Divide new value by old value: $6/$5 = 1.2

Step 2: Convert to percentage: 1.2×100 = 120% (i.e. $6 is 120% of $5)

Step 3: Subtract 100%: 120% − 100% = 20%, and that means a 20% rise.

Another Example: There were 160 smarties in the box yesterday, but now there are 116, what is the percentage change?

Answer (Method 1): 160 to 116 is a decrease of 44. Compared to yesterday's value: 44/160 = 0.275 = 27.5% decrease.

Answer (Method 2): Compare today's value with yesterday's value: 116/160 = 0.725 = 72.5%, so the new value is 72.5% of the old value.
Subtract 100% and you get −27.5%, or a 27.5% decrease.

Why Compare to Old Value?

Because you are saying how much a value has changed.

Example: Milk was $2, now it is $3, did it rise $1 compared to $2 or $3 ?

We compare to the original $2 value, so we say the change is $1/$2 = 0.5 which is a 50% increase.

The Formula

You can also put the values into this formula:
(The "|" symbols mean absolute value, so negatives become positive)
Example: There were 200 customers yesterday, and 240 today:

A 20% increase.

Example: But if there were 240 customers yesterday, and 200 today we would get:

A 16.6...% decrease.

How to Reverse a Rise or Fall

Some people think that a percentage increase can be "reversed" by the same percentage decrease. But no!

Example: 10% of 100

A 10% increase from 100 is an increase of 10, which equals 110 ...

... but a 10% reduction from 110 is a reduction of 11 (10% of 110 is 11)

So we ended up at 99 (not the 100 we started with)

What happened?

Because the percentage rise or fall is in relation to the old value:

The 10% increase was applied to 100

But the 10% decrease was applied to 110

How to do it properly

To "reverse" a percentage rise or fall, use the right formula here:

Or use this handy-dandy calculator (just type in a value and click in the other box)

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Change: subtract old value from new value. Example: You had 5 books, but now have 7. The change is: 7−5 = 2. Percentage Change: show that change as a percent of the old value ...

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Practising Grade 10 maths: 'Find the percent: discount and mark-up'

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Fun maths practice! Improve your skills with free problems in 'Find the percent: discount and mark-up' and thousands of other practice lessons.

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Guía del Centro para la exposición oral del trabajo

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Guía del Centro para la exposición oral del trabajo

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IESSR - Guía básica para la realización de exposiciones orales (I)