Understanding Percentage Calculations

Calculating Percentages

Percentage is a measure used to show how much one quantity is of another. In simpler terms, it's the ratio of something out of 100%. For instance, if you have 8 out of 10 pieces of chocolate left in your jar, this can be expressed as 8% (or 8 out of 100) of what was initially there.

Calculating a percentage involves three steps:

1. Identify the part being measured. This could be a fraction of the whole, such as 7 out of 10 people wearing red shirts.
2. Determine the relationship between the part and the total by dividing them with each other. Here, we would divide 7 by 10, resulting in the decimal value 0.7.
3. Convert the result into its corresponding percent form by moving the point two places from right. So, our final answer would be 7%.

For example, let's say you want to find 90% of a certain amount of money. First, determine what you need to multiply that amount by: [ \frac{9}{10} = 0.9 ] Then, multiply the original amount by 0.9: $90%$ of $x = x * 0.9$.

You might also encounter situations where you are given a percentage already, like 12%, and asked to change it back into a decimal. To do this, move the point two spaces to the left in the decimal representation: [ 0.12 ]

Or, think proportionally: If I give you ( \frac{1}{10} ) of my lunch, that means I gave you 10% of it. And since 10% is equal to ( \frac{1}{10} ), 100 times more than 10% will get us ( \frac{1}{10}\cdot{100}=\frac{100}{10}=10 ). Therefore, 100% of any number is simply the number itself.

If you were to calculate 50% of a number (which can also be written as half), you would again look at the the parts involved: [ \frac{\text {part}}{\text {whole}}=\frac{5}{\text{total}}\rightarrow\frac{5}{10}. ] Multiplying both sides of the equation by 10 yields [ 5=50% \text {of } \mathrm{~T}, ] which represents the entire thing in question.