24.1 Basic Formulas and Functions
Real estate math is mostly about being consistent with a few core skills: working with fractions, converting between decimals and percentages,
multiplying percentages, and calculating area. If you can do these quickly and accurately, you’ll be in great shape for commissions, pricing,
legal descriptions, finance, investments, taxes, and closings.
Adding Fractions
Same denominator:
Formula: a/c + b/c = (a + b)/c
Different denominators:
Formula: a/c + b/d = (ad + bc) / (cd)
Quick tip: When denominators are different, you’re finding a common denominator by multiplying them (c × d),
then adjusting each numerator to match.
Multiplying Fractions
Formula: (a/c) × (b/d) = (ab) / (cd)
Multiply across the top for the numerator, and across the bottom for the denominator. Reduce the fraction if possible.
Converting Decimals and Percentages
Decimal → Percent
Formula: (decimal) × 100 = percent
Percent → Decimal
Formula: percent ÷ 100 = decimal
Reality check: 72.1% becomes 0.721 (move the decimal two places left).
0.294 becomes 29.4% (move the decimal two places right).
Converting Fractions and Percentages
Fraction → Percent
- Step 1: divide numerator by denominator to get a decimal
- Step 2: multiply the decimal by 100 to get a percent
Percent → Fraction (and reduce)
Formula: X% = X/100 (then reduce)
Reducing means dividing the numerator and denominator by the same number (try 2, 3, 5, or 7 first).
Multiplying Percentages (“Percent of” Problems)
- Convert the percent to a decimal (divide by 100)
- Multiply the whole amount by the decimal to get the part
Formula: whole × (percent ÷ 100) = part
Calculating Area
Many area formulas are based on base and height. Height is measured perpendicular to the base.
For irregular shapes, break the shape into smaller shapes (rectangles, triangles, trapezoids), find each area, and add them together.
Square / Rectangle: a = b × h
Triangle: a = (b × h) / 2
Trapezoid: a = h(b1 + b2) / 2
In this chapter, area is often expressed in square feet (SF).
Practice Problems + Answer Key
This chapter includes practice problems (Problems 1–8 for the basics). The answer key is on page 427.
Use the answer key to check your work after you attempt each problem—don’t peek first.
Math Toolkit
Choose the best answer for each question, then select Check Answers.
To convert a decimal to a percent, you should:
Multiply by 100 Decimal → percent means “out of 100,” so you multiply by 100 (move the decimal two places right).
What is the area formula for a triangle?
a = (b × h) / 2 A triangle is half of a rectangle with the same base and height.
Great job! You have the key points of this topic down.
