Could you please explain why, when increasing something, you put a 1 in front of it?
For example, if something is increased by 5%, why do you multiply by 1.05?
What exactly does that 1 mean or represent?
Thank you.
if I have 100 dollars
and increase that by 5%
I then have
100*1 + 100*0.05
which is
100 (1.05)
The 1 represents 100% of something. It's the whole.
If you need to find the new price of something that has increased by 5%, you want to know what 5% is plus the original price.
For instance, if the original price was $20 and it's increased by 5%, then you need to multiply by 1.05 to find the new price.
20 * 1.05 = 21
( distributive property :)
When you want to increase something by a certain percentage, you multiply it by a number slightly greater than 1. This may seem a bit counterintuitive, so let me explain why it works this way.
To understand this, let's take an example where you want to increase a base value by 5%. If you were to simply add 5% to the base value, you would get a result that is less than intended because you're not accounting for the compounded effect of the increase.
To correctly calculate the increase, you need to consider not just the total increase, but also the base value itself. So instead of adding 5%, you multiply the base value by (1 + 5%). The 1 in front represents the original base value. When you add the 5% (which is 0.05 in decimal form) to the 1, you're effectively increasing the base value by 5%.
In this example, multiplying by 1.05 gives you the desired result of a 5% increase because the base value is preserved, and the additional percentage is accounted for.
So, in general, when you want to increase something by a certain percentage, you multiply the base value by (1 + the percentage in decimal form). That 1 in the equation represents the original value, and the increased percentage is added to it.
I hope this explanation clears up any confusion!