Key takeaway: Sales tax is a percent of an item’s price that a state or city adds at checkout, so the total you pay equals the price plus the tax.
Grade 77.RP.A.3Ratios, Rates and Percents
Definition of Sales Tax
Sales tax is money collected by a state, county or city when you buy goods. The seller adds it to the price and sends it to the government, which uses it for roads, schools and public services.
The tax is a percent of the price before tax, so a higher price means more tax. Rates differ from place to place: one town might charge 6.5% while the next charges 8%. Some items, such as groceries or clothing, are exempt in certain states.
Formula and notation
With the tax rate \(r\) as a decimal:
\[\text{tax} = r \times \text{price}, \qquad \text{total} = \text{price} + \text{tax}\]
One step: \(\text{total} = \text{price} \times (1 + r)\). For a 6.5% rate, multiply the price by \(1.065\).
Key facts
- The rate is applied to the price before tax, never to a total that already includes tax.
- Round the tax to the nearest cent, because money has two decimal places.
- A receipt lists the price, the tax and the total as three separate lines.
- Multiplying by 1 plus the rate gives the total in a single step.
Sales Tax example
Dara buys a soccer ball for \$46.00 in a town with a 6.5% sales tax. How much tax does she pay, and what is the total?
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Write the rate as a decimal: \(6.5\% = 0.065\).
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Tax: \(0.065 \times 46 = 2.99\).
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Total: \(46.00 + 2.99 = 48.99\).
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Check: \(46 \times 1.065 = 48.99\).
Dara pays \$2.99 in tax, so the total is \$48.99.
Common mistake
Watch out
Dara multiplies \(46 \times 0.065 = 2.99\) and says the soccer ball costs \$2.99 at the register.
Why it is wrong
That product is only the tax. The register total also includes the \$46.00 price, so Dara must add: \(46.00 + 2.99 = 48.99\). Estimating helps: 6.5% is a bit more than 5%, which is a bit more than a twentieth of the price, so the tax should be a few dollars, not the whole bill.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Ratios, Rates and Percents