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# Percentage [Portion], Rate and Base

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## John Michael Gatchalian

on 21 March 2014

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#### Transcript of Percentage [Portion], Rate and Base

Percentage [Portion], Rate and Base
Formula
Percentage = Rate x Base or P= R x B ( Formula 4-1 )

Rate = Percentage/ Base or R = P/B ( Formula 4-2 )

Base = Percentage/ Rate or B= P/R ( Fomula 4-3 )

Finding the Percentage (Portion)
Example. What is 30 percent of 250 ?
Solution : Since the Problem says' percent of 250, "the base is 250. The rate is 30%. From the formula:

Percentage = Rate x Base = 30% x 250 = 0.35 x 250 =75
Thus, 75 is 30% of 250.

Percent increase
is used to illustrate how much a quantity of an amount has increase over it's original value.

Percent Decrease
is used to illustrate how much a quantity or an amount has decreased from its original value.
A. Percentage of Increase and Decrease
Formula :
Percentage of Increase = Base + (Base x Rate)
Percentage of Decrease = Base - (Base x Rate)

The variables have the following characteristics, which will be useful to identify them.
Percentage

(or portion) is the variable in the percentage formula that represents a part of the base.

The
Base
is the number represents 100%, or the total value of something, or the whole thing. The base is usually preceded by the word of in the given statement because it is being multiplied by the rate.

The
Rate
defines what part the percentage is of the base. If the rate is less than 100%, the percentage is less than the value of the base.
Percent Increase and Percent Decrease
Example 1. 285 increase by 30%?
Solution :
Given: Rate = 36% = 0.36 Base = 285
Percentage of Decrease = Base + (Base x Rate)
= 285 + (285 x 0.36)
= 285 + 102.6
= 387.6

B. Rate of Increase and Decrease
Formula:
Rate = Larger Amount - Smaller Amount
-----------------------------------------
Base
Example: find the part less than 272 is 85?
Solution:
Larger Amount = 272 Smaller Amount = 85
Base = 272

= 272 - 85 187 11
----------- = ----- = ---
272 272 16
C. Base of Increase
and Decrease

Formula:
Base of Increase = Percentage/1+Rate
Base of Decrease = Percentage/1-Rate

Example: 2/7 Greater what amount is 54?

Percentage = 54 Rate = 2/7

= 54 54 54
-------- = ------------ = ----- = 54 (7/9) = 42
1+2/7 7/7 + 2/7 9/7
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