Markup and commission, and percent error

Markup, commission and percent error are all percents in real jobs. Each one is a part, a whole and a percent in disguise.

Markup: from cost to selling price

A shop buys goods at one price, called the cost, and sells them for more. The extra is the markup, usually given as a percent of the cost.

For example, a shop buys a toy for $20 and marks it up by 50%. 50% of $20 is $10, so the selling price is $30. In one step: $20 × 1.5 = $30.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

Cost: $20Price: $30
A 50% markup adds half the cost: $20 becomes $30.
5%100%1002000percentamount
5% commission on $2,000 of sales is $100.
percentamount0%090%45100%50
A guess of 45 is 90% of the true 50, so the error is 10%.

Finding the percent markup

If the cost and selling price are known, find the markup and divide by the cost. A game costs the shop $40 and sells for $50. The markup is $10, and 10 ÷ 40 = 25%.

Always divide by the cost, the starting amount. This is the same rule as percent change.

Commission: pay as a percent of sales

Many salespeople earn commission: a percent of what they sell. An agent who earns 3% commission on a $200,000 house earns $6,000.

Some jobs pay a base wage plus commission. A worker earning $400 a week plus 5% of $2,000 in sales gets $400 + $100 = $500 that week.

Find a commission

Type the commission rate and the sales. The calculator shows each step.

Percent error: how far off was the guess?

Percent error measures how far an estimate or measurement is from the true value. Find the difference, then divide by the true value.

For example, Sam guessed 45 marbles and there were 50. The error is 5, and 5 ÷ 50 = 10%. Percent error is always written as a positive number.

One idea behind all three

Markup, commission and percent error look different, but each one compares an amount with a starting value. Markup compares with the cost, commission with the sales and error with the true value.

So the questions are always part, whole and percent. Spot the whole, and the rest of the method is the same as any percent of a number question.

Where these show up in real jobs

Shop owners set prices with markups. Estate agents and car sellers earn commission. Scientists and engineers report percent error to show how accurate a measurement is.

Ask your child which jobs they think use each idea. It turns a page of sums into a picture of how money and measurement work.

Quiz: markup, commission and error

Find selling prices, commissions and percent errors. Type numbers only.

Where this fits: percentages step by step

  1. What is a percent
  2. Percent to fraction
  3. Fraction to percent
  4. Percent to decimal
  5. Decimal to percent
  6. Comparing fractions, decimals and percents
  7. Benchmark percents
  8. Percent mental math
  9. Over 100% and under 1%
  10. Percent of a number
  11. Finding the percent
  12. Finding the whole
  13. Percent change
  14. Percent increase and decrease
  15. Discounts and sale price
  16. Sales tax
  17. Tips
  18. Simple interest
  19. Markup, commission and percent error (this page)
  20. Percent word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “A shop buys a ball for $10 and adds 40%. What is 40% of $10?” ($4.)
  2. “So what does the ball sell for?” ($14.)
  3. “A salesperson gets 10% of a $300 sale. How much?” ($30.)
  4. “You guessed 18 sweets, but there were 20. How far off?” (2.)
  5. “As a percent of 20?” (10%.)

More worked examples

Example 1: markup

Cost $60, markup 25%: 25% of $60 is $15. Price $75.

Example 2: percent markup

Cost $80, price $100: markup $20. 20 ÷ 80 = 25%.

Example 3: commission

4% commission on $5,000: $200.

Example 4: percent error

Measured 9.5 cm, true length 10 cm: error 0.5. 0.5 ÷ 10 = 5%.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. Cost $40, 50% markup. Price?
  2. Cost $25, 20% markup. Price?
  3. Cost $50, price $60. Percent markup?
  4. 5% commission on $800
  5. 10% commission on $1,500
  6. $300 a week plus 2% of $5,000
  7. Guess 90, true 100. Percent error?
  8. Guess 26, true 25. Percent error?
  9. Measured 48 cm, true 50 cm. Percent error?
  10. Stretch: cost $80, 25% markup, then 20% off. Final price?
Show the answers
  1. $60
  2. $30
  3. 20%
  4. $40
  5. $150
  6. $400
  7. 10%
  8. 4%
  9. 4%
  10. $80

Common mistakes

Dividing by the selling priceFinds markup as $10 ÷ $50.Fix: divide by the cost: $10 ÷ $40 = 25%.
Dividing by the guessFinds error as 5 ÷ 45.Fix: divide by the true value: 5 ÷ 50 = 10%.
A negative percent errorWrites −10%.Fix: percent error is the size of the difference, so it is positive.

How to teach it at home

Shop owner

Play shop: buy items at a cost and set a 50% markup.

Guess and check

Guess how many beans are in a jar, count them and find the percent error.

Commission game

Pay 10% commission for helping sell old toys.

By grade

More for each grade: Grade 7 math and the CBSE class 7 maths guide.

Worksheets and practice

Percent word problems worksheet, page 1

Percent word problems worksheet: printable PDF with an answer key. · Make a fresh test

Percent practice · percent calculator · fraction, decimal and percent converter · percentage quiz · percent levels · percent games · percentages for kids

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Questions parents ask

What is a markup?

The amount added to the cost to get the selling price, usually a percent of the cost.

How do you calculate commission?

Multiply the sales by the commission rate as a decimal. 5% of $2,000 is $100.

How do you calculate percent error?

Find the difference between the estimate and the true value, divide by the true value, and write it as a percent.

Is percent error ever negative?

No. It uses the size of the difference, so it is always positive.

What grade learns markup and commission?

Grade 7 under Common Core 7.RP.A.3. In India, class 7 and 8.