## Arithmetic Reasoning Flash Card Set 467451

 Cards 10 Topics Defining Exponents, Defining Radicals, Factors & Multiples, Prime Number, Probability, Proportions, Rational Numbers, Ratios, Scientific Notation, Simplifying Fractions

#### Study Guide

###### 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).

Radicals (or roots) are the opposite operation of applying exponents. With exponents, you're multiplying a base by itself some number of times while with roots you're dividing the base by itself some number of times. A radical term looks like $$\sqrt[d]{r}$$ and consists of a radicand (r) and a degree (d). The degree is the number of times the radicand is divided by itself. If no degree is specified, the degree defaults to 2 (a square root).

###### Factors & Multiples

A factor is a positive integer that divides evenly into a given number. The factors of 8 are 1, 2, 4, and 8. A multiple is a number that is the product of that number and an integer. The multiples of 8 are 0, 8, 16, 24, ...

###### Prime Number

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

###### 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.

###### Proportions

A proportion is a statement that two ratios are equal: a:b = c:d, $${a \over b} = {c \over d}$$. To solve proportions with a variable term, cross-multiply: $${a \over 8} = {3 \over 6}$$, 6a = 24, a = 4.

###### Rational Numbers

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form $${a \over b}$$ where a is the numerator and b is the denominator. An improper fraction ($${5 \over 3}$$) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number ($$1 {2 \over 3}$$) which has a whole number part and a fractional part.

###### Ratios

Ratios relate one quantity to another and are presented using a colon or as a fraction. For example, 2:3 or $${2 \over 3}$$ would be the ratio of red to green marbles if a jar contained two red marbles for every three green marbles.

###### Scientific Notation

Scientific notation is a method of writing very small or very large numbers. The first part will be a number between one and ten (typically a decimal) and the second part will be a power of 10. For example, 98,760 in scientific notation is 9.876 x 104 with the 4 indicating the number of places the decimal point was moved to the left. A power of 10 with a negative exponent indicates that the decimal point was moved to the right. For example, 0.0123 in scientific notation is 1.23 x 10-2.

###### Simplifying Fractions

Fractions are generally presented with the numerator and denominator as small as is possible meaning there is no number, except one, that can be divided evenly into both the numerator and the denominator. To reduce a fraction to lowest terms, divide the numerator and denominator by their greatest common factor (GCF).