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Mathematical Reasoning

The Mathematical Reasoning module measures your ability to work with numbers, solve algebra problems, understand geometry, and interpret data. Roughly half of the questions focus on quantitative problem solving, such as fractions, percents, and ratios, while the other half emphasize algebraic reasoning with expressions, equations, and graphs. You are allowed an on-screen calculator for most of the test, but you still need a firm grasp of the underlying concepts. This chapter reviews the essential math skills, from basic operations to interpreting charts, so you can reason through both routine and multi-step problems.

Number Sense and Operations

Number sense is the foundation of the math test. You must add, subtract, multiply, and divide whole numbers, fractions, decimals, and integers, including negative numbers. Understanding place value and the order of operations ensures you compute in the correct sequence. Comfort with these basics lets you handle more complex problems with confidence.

Follow the order of operations

Work through parentheses, exponents, multiplication and division, then addition and subtraction, in that order.

Operate with fractions

Find common denominators to add or subtract fractions, and simplify results to lowest terms.

Handle negative numbers

Adding a negative moves left on the number line, and subtracting a negative is the same as adding a positive.

Convert between forms

Fractions, decimals, and percents represent the same values and can be converted from one to another.

Ratios, Proportions, and Percents

Ratios compare quantities, proportions set two ratios equal, and percents express parts per hundred. These concepts appear constantly in real-life problems such as discounts, tax, tips, and scaling recipes. Setting up a proportion or finding a unit rate lets you solve for unknown values efficiently. Percent problems often ask you to find a part, a whole, or a percentage of change.

Set up proportions

Write two equal ratios and cross-multiply to solve for an unknown quantity.

Find the unit rate

Divide to find the cost or amount per single unit, then scale up to any quantity.

Calculate percents

Convert a percent to a decimal and multiply to find a percentage of a number.

Compute percent change

Divide the amount of increase or decrease by the original value, then multiply by 100.

Algebra and Equations

Algebra uses letters to represent unknown numbers. You will evaluate expressions, solve linear equations and inequalities, and translate word problems into algebraic form. Solving an equation means isolating the variable by performing the same operation on both sides. These skills let you model real situations and find unknown values systematically.

Isolate the variable

Use inverse operations on both sides of an equation to get the variable by itself.

Use the distributive property

Multiply a factor outside parentheses by each term inside, as in 4(2x + 3) = 8x + 12.

Solve inequalities carefully

Treat inequalities like equations, but reverse the sign when multiplying or dividing by a negative number.

Translate words to symbols

Turn phrases like 'a fixed fee plus a rate per item' into expressions such as 30 + 0.10t.

Check your solution

Substitute your answer back into the original equation to confirm it makes the statement true.

Geometry and Measurement

Geometry on the GED covers perimeter, area, volume, and properties of shapes and angles. You should know formulas for the area of rectangles, triangles, and circles, and how to find the circumference of a circle. Angle rules, such as the fact that a triangle's angles sum to 180 degrees, come up frequently. Careful use of formulas and units produces correct measurements.

Know key area formulas

Rectangle area is length times width, and triangle area is one-half base times height.

Work with circles

Circumference equals 2 times pi times the radius, and area equals pi times the radius squared.

Apply angle rules

The angles of a triangle add to 180 degrees, and complementary angles add to 90 degrees.

Track your units

Express area in square units and volume in cubic units to keep measurements meaningful.

Data, Statistics, and Probability

Many questions ask you to read and interpret data shown in tables, bar graphs, line graphs, and pie charts. You should be able to calculate the mean, median, mode, and range of a data set and understand simple probability. Probability compares favorable outcomes to total possible outcomes. Interpreting data accurately is a practical skill used in everyday decision making.

Calculate the mean

Add all values in a set and divide by the number of values to find the average.

Find the median

Order the values and identify the middle one; with an even count, average the two middle values.

Compute probability

Divide the number of favorable outcomes by the total number of possible outcomes.

Read graphs carefully

Check titles, labels, and scales before drawing conclusions from a chart or graph.

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Last updated: July 2026