Understanding Percentages: Calculations and Tricks

What symbol is often used to represent percentages?

If you have $80 and it represents 40% of your total income, what is your total income?

When calculating a 25% tip on a $60 bill, how much do you need to tip?

What is the result of multiplying $90 by 12.5%?

If someone leaves a 30% tip on a $40 bill, what is the total amount paid?

When calculating percentages, what does 'the base' represent?

What is another strategy mentioned for solving percentage problems besides imagining bases increasing or decreasing?

If a car's price decreases by 15%, what percentage of the original price remains?

When a product's price increases from $20 to $25, what is the percentage increase?

Percentage is a term used to express how much of something belongs to another thing. It's often represented by using the symbol "%" after a number. For example, if you have $50 and want to know what percentage it makes up of your total income, you could divide $50 by the total amount of money ($100) to find out that it represents 50% of your total income. To calculate this, you would need to multiply the two numbers together: [50\times \frac{1}{100} = 0.5] So, half of your total income comes from $50.

To do more complicated calculations with percentages, like figuring out how much to tip someone based on their service, you can use formulas. For instance, if you get a bill for $75 and leave a 20% tip, which means giving them $15 for good service, then $75 minus $15 equals $60, which is what you paid for dinner. This kind of calculation involves dividing $75 by 80 (since there are 100 cents in a dollar).

When solving percentage problems, it helps to know some tricks. One trick is to imagine that the whole quantity, called the base, increases or decreases by certain amounts multiple times. Another idea is to think about parts of things being equivalent to other parts, such as when a person has the same size feet as her mother does. In these situations, you might see numbers like 5%, 10%, 25%, 50%, etc., because each one represents a part of something equal in size to its own piece plus one more similar bit of information. Also remember that every time you go through a process where all the pieces stay the same except for one, only the new piece matters.

Learn about using percentages to express proportions and perform calculations like finding tips or discounts. Discover tricks to simplify percentage problems, such as imagining changes in the base quantity or comparing parts to find equivalents.