(1 + 5%) × 1,500 = ? Percentage increase change: increment the number 1,500 by 5% (percent) of its value and Calculate the actual change (the absolute difference)
Increase the number 1,500 by 5% of its value
A brief introduction. Definitions and formulas
Percent, p%
'Percent (%)' means 'out of one hundred':
5% = 5 'out of one hundred',
p% is read p 'percent',
p% = p/100 = p ÷ 100
5% = 5/100 = 5 ÷ 100 = 0.05
100% = 100/100 = 100 ÷ 100 = 1
How to increase the number 1,500 by 5% of its value?
The value of the percentage increase = 5% × 1,500
The new value = 1,500 + The value of the percentage increase
Detailed calculations and the calculation proof
1. Calculate the new value of the number... ... increased by percentage of its initial value
The new value =
1,500 + The value of the percentage increase =
1,500 + (5% × 1,500) =
1,500 + 5% × 1,500 =
(1 + 5%) × 1,500 =
(100% + 5%) × 1,500 =
105% × 1,500 =
105 ÷ 100 × 1,500 =
105 × 1,500 ÷ 100 =
157,500 ÷ 100 =
1,575
2. Calculate the actual change (the absolute difference)... ... between the new value and the initial one
The actual change =
The new value - 1,500 =
1,575 - 1,500 =
75
Proof of calculation
We will prove below that the calculations are correct:
Calculate the value of the percentage increase and see if we get as a result the actual change (the absolute difference) between the new value and the initial one.
For positive numbers, the actual change = The value of the percentage increase
Calculate the value of the percentage increase:
The value of the percentage increase =
5% × 1,500 =
5 ÷ 100 × 1,500 =
5 × 1,500 ÷ 100 =
7,500 ÷ 100 =
75
The value of the percentage increase = The actual change =>
The calculations are correct.
The answer:
1,500 increased by 5% of the value = 1,575 The actual change: 1,575 - 1,500 = 75
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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Increase numbers by percentage of their value, calculate the percentage increased values
Increase numbers by percentage of their initial value and calculate the absolute percentage change (difference). Examples
How to calculate the new value of a number when increasing it by percentage of its initial value and how to calculate the absolute percentage change (difference)?
New value = Initial value + Absolute percentage change (difference)
Number increased by value percentage = 1.20 × Initial value, and Initial value = Number increased by value percentage / 1.20; Absolute percentage change = New value - Initial value;
Number increased by value percentage = 1.05 × Initial value, and Initial value = Number increased by value percentage / 1.05; Absolute percentage change = New value - Initial value;
Number increased by value percentage = 2.24 × Initial value, and Initial value = Number increased by value percentage / 2.24; Absolute percentage change = New value - Initial value;
Number increased by value percentage = 0.92 × Initial value, and Initial value = Number increased by value percentage / 0.92; in this case we have in fact a decreasing of the value of the number; Absolute percentage change = New value - Initial value.