To add or subtract terms with exponents, both the base and the exponent must be the same. If the base and the exponent are the same, add or subtract the coefficients and retain the base and exponent. For example, 3x² + 2x² = 5x² and 3x² - 2x² = x² but x² + x⁴ and x⁴ - x² cannot be combined.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

Many of the arithmetic reasoning problems on the ASVAB will be in the form of word problems that will test not only the concepts in this study guide but those in Math Knowledge as well. Practice these word problems to get comfortable with translating the text into math equations and then solving those equations.

Probability is the numerical likelihood that a specific outcome will occur. Probability = \({ \text{outcomes of interest} \over \text{possible outcomes}}\). To find the probability that two events will occur, find the probability of each and multiply them together.

A rate is a ratio that compares two related quantities. Common rates are speed = \({distance \over time}\), flow = \({amount \over time}\), and defect = \({errors \over units}\).