The formula to back out sales tax from a purchase is written as total price / 1 + sales tax rate = cost without sales tax, according to the financial section of the Houston Chronicle. To determine the cost of the item without sales tax, one would divide the final price by 1 plus the sales tax rate.
The NBC News Answer Desk explains how to back out the sales tax from a purchase as a step-by-step process. Assuming that an item costs $10,000 at the register and that the state sales tax rate is 8 percent, one would lay out the information as a formula: item + tax (8 percent) = $10,000. Then one would convert the percentage tax into a decimal form and add 1, which is 1.08. Thirdly, one would solve for item by dividing both sides of the equation by the tax that was expressed as 1.08 in the previous step. One would start with the formula "item + 1.08 = $10,000" and divide the terms. Thus, (item +1.08)/1.08 = 10000/1.08, which is 9259.25, is the cost of the item without the sales tax. The only tricky part is converting the percentage tax into a decimal form in the second step. If the state sales tax is 8 percent, then one would express the percentage in the formula as 0.08 and add 1. Therefore, (1 + sales tax rate) = (1 + 0.08), which equals 1.08.