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Percentages:

A percentage is a mathematical expression, written as a number, followed by the % sign, which expresses a part of a whole in terms of hundredths. The number may be written as a decimal number, with the number (between 0 and 100) shown as hundredths.

In other words:	10% may be written as	0.10
	20%	0.20
	25%	0.25
	40%	0.40
	50%	0.50
	75%	0.75
	100%	1.00
	150%	1.50

and so on.

Percentages are often for example used to express the size of a group within a larger group, as in 40% of the class are girls and 60% are boys. If we know the class has 30 students, how do we calculate how many girls there are? We multiply the number of all the students in the class by the percentage, expressed as decimal number:

30 x 0.40 = 12

Therefore there are 12 girls in the class and similarly:

30 x 0.60 = 18

There are 18 boys in class.

Percentages must always add up to 100, since 100% is the total. Quite often, however, there may be a certain percentage, which is not included or described, as in for example 42% of voters in Canada have voted for the Conservatives, 34% for the Liberals, 16% for the NDP and 4% for the Green Party. (By the way, the above percentages do not correspond to the actual records and are made up for illustration purposes only), In the above figures,

0.42 + 0.34 + 0.16 + 0.04 = 0.96

That does not mean that there is something mathematically wrong with the Canadian voters, but that 4% of Canadians voted for other parties and/or independents.

Probably our most frequent use of percentage is with taxes, most often the sales tax and with discounts, as all sales involve discounting the regular prices.

Let’s assume that the sales tax is 5%. Then for a product, priced at $50.00, we will calculate the amount of tax by multiplying:

50.00 x 0.05 = 2.50

The amount of tax will be $2.50 and the total due will be:

50.00 + 2.50 = 52.50

What we can also do is to shorten this calculation. Since the price of the product is $50.00, which corresponds to 100% and we know that we will have to add the sales tax, which is 5%, then a simpler and faster of performing the calculation is to multiply:

50.00 x 1.05 = 52.50

The multiplier 1.05 corresponds to the value of the product (100%) and the tax (5%) and since:

100 + 5 = 105

and expressed as a decimal number, 105% equals 1.05, multiplying the price by 1.05 will provide us with the answer of how much the product will cost with the tax added on.

Similarly, if a product, priced at $80.00 is subject to a 10% discount, the amount of discount will be:

80.00 x 0.10 = 8.00

The product will be discounted by $8.00 and therefore the sale price will be:

80.00 - 8.00 = 72.00

In the same way, we cam perform our calculation faster. Since the product is subject to a 10% discount, its final price will be:

100 - 10 = 90

or 90% of its price before the sale. We can therefore multiply:

80.00 x 0.90 = 72.00

to get the same result faster.

Examples:

1)	60% of 120 =	11)	$45.00 purse subject to 5% tax will cost:
2)	80% of 500 =	12)	$350.00 desk subject to 6% tax will cost:
3)	40% of 400 =	13)	$500.00 watch subject to 4% tax will cost:
4)	50% of 120 =	14)	$30,000 car subject to 5% tax will cost:
5)	10% of 800 =	15)	$80.00 hockey stick subject to 6% tax:
6)	75% of 520 =	16)	$120.00 CD player discounted by 8%:
7)	25% of 200 =	17)	$450.00 camera discounted by 20%:
8)	30% of 150 =	18)	$25.00 soccer ball discounted by 15%:
9)	90% of 900 =	19)	$680.00 coat discounted by 30%:
10)	42% of 500 =	20)	$3,200 plasma TV discounted by 18%:

Answers:

1)	72	11)	47.25
2)	400	12)	371.00
3)	160	13)	520.00
4)	60	14)	31,500.00
5)	80	15)	84.80
6)	390	16)	110.40
7)	50	17)	360.00
8)	45	18)	21.25
9)	810	19)	476.00
10)	210	20)	2,624.00

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