## Arithmetic Reasoning Flash Card Set 699929

 Cards 10 Topics Absolute Value, Averages, Defining Exponents, Exponent to a Power, Factorials, Integers, Negative Exponent, Percentages, Probability, Rates

#### Study Guide

###### Absolute Value

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: $$\left|-5\right| = 5$$. In the case of a variable absolute value ($$\left|a\right| = 5$$) the value of a can be either positive or negative (a = -5 or a = 5).

###### Averages

The average (or mean) of a group of terms is the sum of the terms divided by the number of terms. Average = $${a_1 + a_2 + ... + a_n \over n}$$

###### Defining Exponents

An exponent (cbe) consists of coefficient (c) and a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).

###### Exponent to a Power

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: (x2)3 = x(2x3) = x6

###### Factorials

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

###### Integers

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

###### Negative Exponent

A negative exponent indicates the number of times that the base is divided by itself. To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal: $$b^{-e} = { 1 \over b^e }$$. For example, $$3^{-2} = {1 \over 3^2} = {1 \over 9}$$

###### Percentages

Percentages are ratios of an amount compared to 100. The percent change of an old to new value is equal to 100% x $${ new - old \over old }$$.

###### Probability

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.

###### Rates

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