Skill: Calculate discounts, markups, taxes, and tips

A percentage change has three parts:

• Original amount: the starting price or bill
• Percentage amount: the discount, markup, tax, or tip
• Final total: the amount after adding or subtracting

Convert the percent to a decimal before calculating:

• Discount: multiply by $1-r$
• Markup, tax, or tip: multiply by $1+r$

Here, $r$ is the decimal form of the percentage.

Example: A backpack costs 40$. The sales tax is$7%$. What is the total cost?

1. Convert $7\%$ to a decimal:

$$7\% = 0.07$$

2. Find the tax amount by multiplying the original price by the tax rate:

$$40(0.07)=2.80$$

The sales tax is 2.80$.

3. Add the tax to the original price:

$$40+2.80=42.80$$

So, the total cost is:

$$\boxed{\$42.80}$$

You can also find the total in one step by using the increase multiplier:

$$40(1+0.07)=40(1.07)=42.80$$

For a discount, subtract the percentage amount instead. For example, a $20\%$ discount uses the multiplier $1-0.20=0.80$. Markups and tips use addition, just like sales tax.