Understanding Percentage Calculations

Study Notes

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:

Identify the part being measured. This could be a fraction of the whole, such as 7 out of 10 people wearing red shirts.
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.
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.

Description

Learn how to calculate percentages by identifying the part being measured, determining the relationship between the part and the total, and converting the result into its corresponding percent form. Practice converting between decimals and percentages to solidify your understanding.