Arithmetic Reasoning Flash Card Set 506024

Cards 10
Topics Absolute Value, Adding & Subtracting Fractions, Adding & Subtracting Radicals, Averages, Commutative Property, Defining Exponents, Exponent to a Power, Integers, Rational Numbers, Sequence

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).

Adding & Subtracting Fractions

Fractions must share a common denominator in order to be added or subtracted. The common denominator is the least common multiple of all the denominators.

Adding & Subtracting Radicals

To add or subtract radicals, the degree and radicand must be the same. For example, \(2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}\) but \(2\sqrt{2} + 2\sqrt{3}\) cannot be added because they have different radicands.

Averages

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

Commutative Property

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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

Integers

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

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.

Sequence

A sequence is a group of ordered numbers. An arithmetic sequence is a sequence in which each successive number is equal to the number before it plus some constant number.