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Basic Math & Number Sense

Study Guide

Basic math skills are the foundation of the GED Mathematical Reasoning test. You need to be comfortable working with whole numbers, fractions, decimals, and percents, as well as understanding the order of operations (PEMDAS).

1Order of Operations (PEMDAS)

When an expression has multiple operations, follow this order: Parentheses first, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right). Remember: Please Excuse My Dear Aunt Sally.

Examples:

•3 + 4 × 2 = 3 + 8 = 11 (multiply before adding)
•(3 + 4) × 2 = 7 × 2 = 14 (parentheses first)
•2 + 3² × 4 = 2 + 9 × 4 = 2 + 36 = 38
2Working with Fractions

To add or subtract fractions, find a common denominator. To multiply fractions, multiply numerators and denominators. To divide fractions, multiply by the reciprocal of the second fraction.

Examples:

•1/3 + 1/4 = 4/12 + 3/12 = 7/12
•2/5 × 3/7 = 6/35
•3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 1/8
3Decimals and Percents

To convert a percent to a decimal, divide by 100 (move the decimal point two places left). To convert a decimal to a percent, multiply by 100. To find a percent of a number, convert to decimal and multiply.

Examples:

•25% = 0.25
•0.6 = 60%
•15% of 200 = 0.15 × 200 = 30
•What percent is 8 of 40? → 8/40 = 0.20 = 20%
4Absolute Value

The absolute value of a number is its distance from zero on the number line. It is always positive or zero. Written as |x|.

Examples:

•|5| = 5
•|-3| = 3
•|0| = 0
•|-7| + |3| = 7 + 3 = 10
Key Formulas to Remember
1Percent of a number: (percent/100) × number
2Percent change: (new - old) / old × 100%
3Simple interest: I = P × r × t
Test-Taking Tips
Always follow PEMDAS — many GED questions test whether you know the correct order.
When working with fractions on the GED, you can use the calculator. But practice by hand to build confidence.
Percent problems often appear as word problems on the GED. Identify what you're solving for: the part, the whole, or the percent.