How Percentages Work in Shopping: Discounts and Sale Prices

Percentages run shopping, and a child who can work out a discount in seconds never pays a label price blind. A percentage is a part out of 100, so a 25 percent discount takes 25 dollars off every 100 dollars of price.

I have taught Grade 6 math for over thirty years, and I teach percentages the shopping way: sale prices first, deals second, and traps last.

What Is a Percentage, Really?

A percentage is a part out of 100, so 25 percent means 25 parts from every 100 parts of a whole. The sign % stands for ‘per hundred,’ and it turns any part into a number you can compare. That is why shops, tests, and surveys all speak in percentages.

Think of a test with 100 marks. A score of 75 percent means 75 marks from 100. A score of 75 percent on a 40 mark test still means 75 parts from every 100, which works out to 30 marks. The percent stays the same, even when the whole changes.

That is why shops love percentages. One label, like 30 percent off, works on every price in the shop. Learn the percent habit once, and it works on shoes, shirts, and snacks alike.

How Do You Work Out a Sale Price?

To work out a sale price, find the discount amount first, then take it off the full price. For a 20 percent discount on 50 dollars, the discount is 10 dollars, so the sale price is 40 dollars. Find the percent, take it off, and the price left is what you pay.

Try a jacket priced at 80 dollars with 25 percent off. Find 25 percent of 80, which is 20 dollars. Take 20 off 80, and the sale price is 60 dollars. Two steps, and the label stops scaring you.

Some children try a shortcut and it works: pay 75 percent instead. Find 75 percent of 80, which is 60 dollars, and you land on the same sale price. Both paths are right, so pick the one your child trusts.

How Do You Compare Two Deals?

Compare two deals by working out the final price for each one, not by comparing the discount labels alone. A 50 percent discount on a dear item can still cost more than a 10 percent discount on a cheap item. Work out both final prices, then pick the lower one.

Try two pairs of trainers. Pair A costs 100 dollars with 40 percent off, so the final price is 60 dollars. Pair B costs 70 dollars with 10 percent off, so the final price is 63 dollars. Pair A wins, even though its full price looks dearer.

Labels lie by shouting. A huge percent on a dear item can still lose to a small percent on a cheap item. Final prices tell the truth, so always work them out.

What About Tax on Top of a Discount?

Tax comes after the discount, so you pay tax on the sale price, not on the full price. First take the discount off, then work out the tax on the smaller amount and add it on. That order matters, because tax on the full price would cost you more.

Try a game priced at 50 dollars with 20 percent off and 10 percent tax. The discount takes 10 dollars off, so the sale price is 40 dollars. Tax on 40 dollars is 4 dollars, so the total is 44 dollars. Tax on the full 50 would have pushed the total higher.

Shops in some places show tax at the till, not on the shelf. Always ask whether the shelf price holds tax or not. A surprise at the till is no surprise once you know the order: discount first, tax second.

How Do Shops Fake a Discount?

Shops fake discounts by raising the price first, then cutting it back to the old price and calling the cut a sale. Check the price history and compare the same item in other shops. If the final price is not lower, the sale is only a label.

Watch for the old price trick. A shop raises a shirt from 30 dollars to 60 dollars, then cuts it to 30 dollars and shouts 50 percent off. The buyer pays the same 30 dollars as before, and the sale is only a label.

Price history apps and a quick check in two other shops expose the trick fast. If the same shirt costs 30 dollars everywhere, no shop is giving you a deal. Real discounts show a final price below the usual price.

Mistakes I See Every Year

Mistake one: a child takes the percent off the wrong base, like 20 percent of the sale price instead of the full price. Fix it by asking: percent of what? The answer names the base.

Mistake two: a child adds the discount and the tax in the wrong order. Fix it with the order rule: discount first, tax second, every time.

Mistake three: a child trusts a big percent without working out the final price. Fix it by covering the label and comparing only final prices.

One habit fixes most of these: after every discount sum, read the answer back as a sentence. “Sixty dollars, after 25 percent off 80 dollars” either sounds right or it does not, and a child hears the error before I do.

Try It Yourself: 3 Quick Questions

Cover the answers, let your child try, then check together.

1. A toy costs 80 dollars with 25 percent off. What is the sale price? Answer: 60 dollars. 25 percent of 80 is 20, and 80 minus 20 is 60.
2. Deal A: 60 dollars with 50 percent off. Deal B: 40 dollars with 20 percent off. Which deal is cheaper? Answer: Deal A. Deal A costs 30 dollars, and Deal B costs 32 dollars.
3. A book costs 40 dollars with 10 percent off, then 10 percent tax on the sale price. What is the total? Answer: 39 dollars and 60 cents. Discount takes 4 dollars off, so the sale price is 36 dollars. Tax on 36 dollars is 3 dollars and 60 cents, so the total is 39 dollars and 60 cents.

If your child handled those three questions, she can walk into any sale and work out the real price. Try it on the next shopping trip, and let her check every label before you pay.

For more topics at this level, browse our Grade 6 math worksheets page.