Mathguru – Help – To find the percentage based on given conditions.

8.1 Recalling ratios and percentages > No. 3

To find the percentage based on given conditions.

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Explanation:

Percentage

In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in Latin). It is often denoted using the percent sign, "%", or the abbreviation "pct". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. (Our solved example in mathguru.com uses this concept)

Percentages are used to express how large/small one quantity is, relative to another quantity. The first quantity usually represents a part of, or a change in, the second quantity, which should be greater than zero. For example, an increase of $ 0.15 on a price of $ 2.50 is an increase by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage, this is therefore a 6% increase.

Calculations

The fundamental concept to remember when performing calculations with percentages is that the percent symbol can be treated as being equivalent to the pure number constant $1 / 100 = 0.01$ , for example 35% of 300 can be written as (35/100) × 300 = 105. (Our solved example in mathguru.com uses this concept)

To find the percentage that a single unit represents out of a whole of N units, divide 100% by N. For instance, if you have 1250 apples, and you want to find out what percentage of these 1250 apples a single apple represents, 100%/1250 = (100/1250)% provides the answer of 0.08%. So, if you give away one apple, you have given away 0.08% of the apples you had. Then, if instead you give away 100 apples, you have given away 100 × 0.08% = 8% of your 1250 apples.

To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:

(50/100) × (40/100) = 0.50 × 0.40 = 0.20 = 20/100 = 20%.

It is not correct to divide by 100 and use the percent sign at the same time. (E.g. 25% = 25/100 = 0.25, not 25% / 100, which actually is (25/100) / 100 = 0.0025.)

http://en.wikipedia.org/wiki/Percentage

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.