Whole x Rate = Part. One triangle that solves commission, tax, interest and percentage problems on the NY exam.
Whole × Rate = Part · Part ÷ Rate = Whole · Part ÷ Whole = Rate
How to solve it, step by step
- Identify which of the three values you have and which is missing.
- Draw a T: the whole on the bottom left, the rate on the bottom right, the part on top.
- Cover the value you are solving for. If the two remaining sit side by side, multiply. If one sits above the other, divide.
- Convert every percentage to a decimal before calculating.
Worked examples
A home sells for $400,000 with a $24,000 commission. Rate = Part ÷ Whole = $24,000 ÷ $400,000 = 6%.
Solving for the whole: a 6% commission produced $9,000. Sale price = $9,000 ÷ 0.06 = $150,000.
What the NY exam actually asks
Most NY percentage questions are the same problem wearing different clothes. Identify which of the three values you are missing, and the T tells you whether to multiply or divide.
Try one yourself
A property sold and the broker received $19,500, which represented 6.5% of the sale price. What was the sale price?
Show the answer
$300,000. You have the part and the rate, so divide: $19,500 ÷ 0.065 = $300,000.
Common mistakes
- Guessing whether to multiply or divide. Draw the T and cover the unknown.
- Mislabelling which figure is the whole. The whole is the number the percentage is taken of.
- Leaving the rate as a whole number instead of a decimal.
Questions students ask
Does the T-method work on interest and tax questions too?
Yes. Any question of the form “X is what percent of Y” fits the same triangle.
What counts as the whole?
The figure the percentage is taken of — usually the sale price, loan amount, or assessed value.
Related formulas
- The real estate commission formula
- The capitalization rate formula
- All 12 formulas — NY Real Estate Math Cheat Sheet
- Real Estate Math Calculator
Practise this. The free 10-question math quiz drills these formulas, and the free timed practice exam puts them under exam conditions.
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