Decrease 40 by 45% Percent of Its Value. What Is the Result When the Number Is Reduced (Discounted) by a Percentage?

Decrease 40 by 45% percent of value. What is the result when the number is reduced by a percentage of 45? Calculate the amount of the decrease

How to decrease the number 40
by 45% of its value?
Value of Percentage Decrease. New Value

  • A percentage value is nothing but a fraction with a denominator of 100:
  • 45% = 45/100 = 45 ÷ 100 = 0.45
  • ...
  • To decrease a positive number, subtract from it the 'Value of Percentage Decrease'.
  • To decrease a negative number, don't subtract from it, but add to it the 'Value of Percentage Decrease'.
  • ...

Value of Percentage Decrease =

Percentage of the Decrease % × The original value =

45% × 40


New Value =

The original value - Value of Percentage Decrease =

40 - (45% × 40)


1. Calculate the End Value
decreased by a percentage of its Initial Value

End Value =

40 - Value of Percentage Decrease =

40 - (45% × 40) =

40 - 45% × 40 =
(40 is a common factor)

(1 - 45%) × 40 =

(100% - 45%) × 40 =

55% × 40 =

55 ÷ 100 × 40 =

55 × 40 ÷ 100 =

2,200 ÷ 100 =

22

2. Calculate the absolute difference between the End Value and the Original Value

The Absolute Difference =

End Value - The original value =

22 - 40 =

- 18


3. Value of Percentage Decrease

It can be calculated in two ways.


The first method:

Value of Percentage Decrease =

Percentage of the Decrease % × The original value =

45% × 40


The second method:

Value of Percentage Decrease =

The original value - New Value


Value of Percentage Decrease =

18

The end value: 40 decreased by 45% percent = 22
The Absolute Difference = - 18
Value of Percentage Decrease = 18

The symbols used: % percent, ÷ division, × multiplication, = the equal sign, / the fraction bar, ≈ approximately the same. Writing numbers: comma ',' - as a thousands separator, point '.' as a decimal mark.

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Decrease numbers by percentages of their values and calculate the absolute percentage change (difference). Examples

How to calculate the new value of a number by decreasing it by percentage of its value and the absolute percentage change (difference)

  • Percentage decreased number = Initial value - Absolute percentage change (difference)
  • Absolute percentage change (difference) = Percentage decrease % × Initial value
  • Percentage decreased number = Initial value - Percentage decrease % × Initial value = (1 - Percentage decrease %) × Initial value
  • In conclusion:

    Percentage decreased number = (1 - Percentage decrease %) × Initial value

    Initial value = Percentage decreased number / (1 - Percentage decrease %)

    Absolute percentage change (difference) = Percentage decrease % × Initial value = New value - Initial value

Four examples of calculations below.

  • Examples on how to decrease a number by percentage of its value and how to calculate the absolute percentage change.

Example 1:

  • If Percentage decrease % = 20%, (1 - Percentage decrease %) = 1 - 20% = 100/100 - 20/100 = 80/100 = 0.8 =>
  • Percentage decreased number = 0.8 × Initial value, and Initial value = Percentage decreased number / 0.8; Absolute percentage change (difference) = New value - Initial value;

Example 2:

  • If Percentage decrease % = 5%, (1 - Percentage decrease %) = 1 - 5% = 100/100 - 5/100 = 95/100 = 0.95 =>
  • Percentage decreased number = 0.95 × Initial value, and Initial value = Percentage decreased number / 0.95; Absolute percentage change (difference) = New value - Initial value;

Example 3:

  • If Percentage decrease % = 120%, (1 - Percentage decrease %) = 1 - 120% = 100/100 - 120/100 = -20/100 = -0.2 =>
  • Percentage decreased number = -0.2 × Initial value, and Initial value = Percentage decreased number / -0.2; Absolute percentage change (difference) = New value - Initial value;

Example 4:

  • If Percentage decrease % = -30%, (1 - Percentage decrease %) = 1 - (-30%) = 1 + 30% = 100/100 + 30/100 = 130/100 = 1.3 =>
  • Percentage decreased number = 1.3 × Initial value, and Initial value = Percentage decreased number / 1.3; this is in fact a percentage increase of the initial number; Absolute percentage change (difference) = New value - Initial value.