Key takeaway: A commission is pay that a salesperson earns as a percent of the total value of the goods or services they sell.
Grade 77.RP.A.3Ratios, Rates and Percents
Definition of Commission
A commission is a payment based on how much someone sells. Real estate agents, car salespeople and many store employees earn one, sometimes on top of a base salary.
The pay is found by multiplying the total sales by a percent rate. If sales double, the pay doubles too. That makes it a proportional relationship: the rate is the constant that connects sales to earnings, and a slow month means a smaller paycheck. Some employers raise the rate once a seller passes a target, but the same multiplication applies to each portion.
Formula and notation
Change the rate to a decimal and multiply by the sales:
\[\text{commission} = \text{rate} \times \text{total sales}\]
With a base salary, \(\text{total pay} = \text{base salary} + \text{commission}\). To work backward, \(\text{total sales} = \frac{\text{pay}}{\text{rate}}\).
Key facts
- The rate is a percent of sales, so 3.5% is written 0.035 in the formula.
- If a salary is also paid, add it to the sales earnings to get total pay.
- Earnings are proportional to sales, so doubling the sales doubles the pay.
- Working backward, sales equal the pay divided by the rate.
Commission example
Imani sells solar panels and earns 3.5% of everything she sells. In March she closes sales worth \$12,400. How much does she earn from these sales?
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Write 3.5% as a decimal: \(3.5\% = 0.035\).
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Multiply by the sales: \(0.035 \times 12400 = 434\).
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Check: 1% of 12,400 is 124, and \(3.5 \times 124 = 434\).
Imani’s commission for March is \$434.
Common mistake
Watch out
Imani turns 3.5% into 0.35 and finds \(0.35 \times 12400 = 4340\), so she expects \$4,340.
Why it is wrong
Moving the decimal point only one place gives 35%, not 3.5%. Dividing 3.5 by 100 moves it two places: 0.035. The correct amount is \$434, one tenth of her figure. A quick estimate warns of the slip: 3.5% is far less than 10%, and 10% of 12,400 is only 1,240, so a result of 4,340 cannot be right.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Ratios, Rates and Percents