The math on the ParaPro is school math: the kind you’d help a fifth to eighth grader with. If it’s been years, that’s normal; most of it comes back with a little practice. This page walks through the main topics on ParaPathways, the ETS test that replaced the ParaPro in 2026, with a worked example for each.

On the real Mathematics subtest (5759) you get 60 minutes for 36 questions and an on-screen four-function calculator. It adds, subtracts, multiplies and divides, but it won’t simplify fractions or apply the order of operations for you, so the skills below still matter.

Fractions

Adding and subtracting: find a common denominator first.

Example: 3 ¹⁄₃ − 1 ⁵⁄₆ - Change to improper fractions: 3 ¹⁄₃ = ¹⁰⁄₃ and 1 ⁵⁄₆ = ¹¹⁄₆. - Common denominator 6: ¹⁰⁄₃ = ²⁰⁄₆. - Subtract: ²⁰⁄₆ − ¹¹⁄₆ = ⁹⁄₆ = 1 ³⁄₆ = 1 ¹⁄₂.

Multiplying: multiply tops and bottoms, then simplify. ²⁄₃ × ³⁄₈ = ⁶⁄₂₄ = ¹⁄₄.

Dividing: flip the second fraction and multiply. ³⁄₄ ÷ ¹⁄₈ = ³⁄₄ × ⁸⁄₁ = ²⁴⁄₄ = 6.

The most common student mistake, and a favorite wrong answer, is adding straight across: ¹⁄₂ + ¹⁄₃ is ⁵⁄₆, not ²⁄₅.

Percents

“Percent” means “out of 100.” To find a percent of a number, change the percent to a decimal and multiply.

Example: a 15% tip on a \(24 bill is 0.15 × 24 = **\)3.60**.

Percent change = change ÷ original amount.

Example: class size grows from 20 to 25 students. The change is 5, and 5 ÷ 20 = 0.25, so it’s a 25% increase. Divide by the starting number, not the new one.

Order of operations

Work in this order: Parentheses, Exponents, Multiplication and Division from left to right, then Addition and Subtraction from left to right. Many students remember it as PEMDAS.

Example: 12 ÷ (5 − 2) + 4 × 3 - Parentheses: 5 − 2 = 3, so 12 ÷ 3 + 4 × 3 - Multiply and divide left to right: 4 + 12 - Add: 16

An exponent tells you how many times to multiply a number by itself: 3² = 3 × 3 = 9, not 3 × 2. So 2 + 3² × 2 = 2 + 9 × 2 = 2 + 18 = 20.

One-variable equations

Undo what was done to the variable, in reverse order, doing the same thing to both sides.

Example: 3x + 8 = 29 - Subtract 8 from both sides: 3x = 21 - Divide both sides by 3: x = 7 - Check: 3 × 7 + 8 = 29. ✓

Writing the equation is often the real question. Example: museum tickets cost \(4 each, parking is \)6, and the class spent $38 in all. If t is the number of tickets, then 4t + 6 = 38, so 4t = 32 and t = 8 tickets.

Perimeter, area and volume

Example: a 9 ft by 5 ft rug has a perimeter of 9 + 5 + 9 + 5 = 28 ft and an area of 9 × 5 = 45 square feet.

A triangle’s area is half of base × height: a triangle with base 10 cm and height 6 cm has area (10 × 6) ÷ 2 = 30 square cm.

A box 4 in long, 3 in wide and 2 in tall has a volume of 4 × 3 × 2 = 24 cubic inches.

Unit conversions

You’ll convert within one system (customary to customary, metric to metric), not between them.

To go to a smaller unit, multiply; to go to a larger unit, divide.

Examples: 54 inches ÷ 12 = 4.5 feet. 2.5 km × 1,000 = 2,500 m. 3 gallons = 12 quarts = 24 pints = 48 cups.

Mean, median, mode and range

Take the data set 4, 8, 6, 8, 9.

With an even number of values, the median is the mean of the two middle values. Always sort first: the middle of an unsorted list is a classic wrong answer.

Practice these topics

For more, take the ParaPro math practice test, or start the free Math: Numbers and Operations sample section on the home page. Our full practice test adds Geometry, Measurement and Data, then the reading and writing sections; a 7-day free trial unlocks them all, then it is $29 a month. For scoring and format, see the ParaPathways test guide.