__Percentages__

__Percentages__

A value or ratio that may be stated as a fraction of 100 is called a percentage in mathematics. Divide the number by the whole and multiply the result by 100 if we need to get the percentage of a given number. As a result, the percentage denotes a fraction per hundred. The definition of percent is per 100. “%” is the symbol used to represent it.

There are a few methods we can use to determine how much of anything we have left. While making a wild guess is one approach, it’s not the most precise one. Although fractions are a better method, in many cases they are no more accurate than a guess. Fractions are required to make a more accurate assessment.

Percentages are always preferred in math. The main reason for this is that they may be utilized in equations and transformed into decimals. It is necessary to have a measurement in order to determine the proportion of anything. A measurement would be, for instance, ten cookies in a package. 50% would be gone if someone ate five of those cookies. A decimal representation of this % might then be obtained. 5 if someone was looking for a precise count of the remaining cookies.

**Conversion table (Fraction & Percent)**

Fraction |
Percent |
Fraction |
Percent |

Â Â Â Â Â Â Â 1/1 | 100% | 1/11 | 9.09% |

1/2 | 50% | 1/12 | 8.33% |

1/3 | 33.33% | 1/13 | 7.69% |

1/4 | 25% | 1/14 | 7.14% |

1/5 | 20% | 1/15 | 6.66% |

1/6 | 16.66% | 1/16 | 6.25% |

1/7 | 14.28% | 1/17 | 5.88% |

1/8 | 12.50% | 1/18 | 5.55% |

1/9 | 11.11% | 1/19 | 5.26% |

1/10 | 10% | 1/20 | 5% |

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**Solved Examples:**

**What is 14.28% of 560?**

Sol. We know that 14.28% of 560 = 1/7 x 560 = 80.

**What is 37.5% of 720?**

Sol. We know that 12.5% is 1/8. So, 37.5% = (3 x 12.5%) = 3 x 1/8)

Therefore, the required answer is (3/8) x 720 = 270.

**Express 7/8 as a rate percent.**

Sol. 7/8 = (7/8) x 100 = 175/2 = 87.5%

**Calculations: (Important concept to note)**

- % increase of a number

% increase = Total increase/initial value x 100

= Final value – initial value/ initial value x 100

- % decrease of a number

% decrease = Total decrease/ initial value x 100

= Final value â€“ Initial value/ Initial value x 100

- Increase of a number by a given %

Increased number = Number x 100 + rate/100

- Decrease of number by a given %

Decreased number = Number x 100 â€“ rate/100

**Basic concepts of Percentages**

**Concept 1: Change of Base**

When a number A is x% more than another number B

% shortness of B = x/100+ X x 100

When a number A is x% less than another number B

% excess of B = x/100 â€“ X x 100

**Concept 2: Population Change**

Per annum. Then:

If the population of a town (or value of a machine) decreases at R% per annum, then it will just become negative.

**Concept 3: Successive change in percentage**

If a number A is increased successively by X % followed by Y % and then by Z %. The final value of A will be:

In a similar way, decreasing a value by any percentage at any point is equivalent to introducing a negative sign into the formula. This same formula can be applied even for situations with two or more consecutive changes.

**Concept 4: Effect of % change on Expenditure & Consumption**

Let the original rate of an item change (increase/decrease) to a new rate. Since the expenditure on purchasing the item is fixed, a change in the rate will directly affect the quantity available, causing it to decrease when the rate increases and vice versa.

Let the original price = Rs. X per unit, then

**Solved examples of basic concepts of Percentages**

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