TEAS math formulas and conversions: the cheat sheet

Fractions, decimals and percents

Most TEAS math rests on moving smoothly between the three forms of the same number.

To compare or order numbers in mixed forms, convert them all to decimals first. To add or subtract fractions, find a common denominator; to multiply, multiply straight across; to divide, multiply by the reciprocal of the second fraction. Practice the order of operations (parentheses, exponents, multiplication and division left to right, addition and subtraction left to right) until it is automatic, because the calculator follows your keystrokes, not the rules.

Percent problems

Every percent question is a version of one sentence: part = percent × whole. Decide which of the three is missing.

• Find the part: 15% of 240 = 0.15 × 240 = 36.
• Find the percent: 18 is what percent of 72? 18 ÷ 72 = 0.25 = 25%.
• Find the whole: 42 is 35% of what? 42 ÷ 0.35 = 120.

Percent change = (new − original) ÷ original × 100. A price that rises from $40 to $46 changed by 6 ÷ 40 = 15%. Divide by the original value, not the new one; that is the most common trap. For a discount followed by tax, apply each step to the running total: $80 with 25% off is $60, and 5% tax on $60 makes $63.

Ratios, proportions and rates

Set a proportion up with matching units in matching positions, then cross-multiply.

Example. A recipe uses 3 cups of flour for 24 cookies. How much flour for 40 cookies? 3/24 = x/40, so 24x = 120 and x = 5 cups.

A rate is a ratio with different units (miles per hour, dollars per pound). Distance = rate × time. A unit rate puts 1 in the denominator: $7.50 for 3 pounds is $2.50 per pound. When a question asks which deal is better, compare unit rates.

Equations, inequalities and word problems

Solve a one-variable equation by undoing operations in reverse order, doing the same thing to both sides: 4x − 7 = 21 → 4x = 28 → x = 7. Inequalities work the same way with one extra rule: multiplying or dividing both sides by a negative number flips the sign (−2x > 10 becomes x < −5).

For word problems, translate phrase by phrase: "is" means =, "of" usually means ×, "more than" means +, "less than" reverses order (5 less than a number is n − 5). Estimate first so you can catch an answer that is off by a factor of ten. When a question says "about" or "approximately", round early and pick the closest option.

Geometry formulas

Watch the units: perimeter is in units, area in square units, volume in cubic units. If a circle question gives the diameter, halve it before using πr². Use π ≈ 3.14 unless the question says otherwise.

Statistics and data

• Mean: add the values, divide by how many there are.
• Median: the middle value once the list is in order; with an even count, the mean of the two middle values.
• Mode: the value that appears most often (there can be more than one, or none).
• Range: largest minus smallest.

An outlier pulls the mean toward it but barely moves the median, which is why median is the better summary of skewed data such as incomes or hospital stays. On graphs, read the axis labels and units before the bars. When two variables rise together the correlation is positive; when one rises as the other falls it is negative. The independent variable is the one that is changed or chosen; the dependent variable is the one measured.

Unit conversions to know by heart

Within the metric system, each prefix step is a factor of 10: kilo (1,000), hecto, deka, base unit, deci, centi (1/100), milli (1/1,000). Convert with a chain of fractions so units cancel: 3.5 ft × 12 in/ft × 2.54 cm/in = 106.68 cm. If the units in your setup do not cancel to the units asked for, the setup is wrong. Try the TEAS math practice set to drill these with full steps.