Cards | 10 |

Topics | Absolute Value, Adding & Subtracting Fractions, Commutative Property, Defining Radicals, Exponent to a Power, Rational Numbers, Scientific Notation, Sequence, Simplifying Fractions, Simplifying Radicals |

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).

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.

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.

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**).

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: (x^{2})^{3} = x^{(2x3)} = x^{6}

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.

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 10^{4} 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}.

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.

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).

The radicand of a simplified radical has no perfect square factors. A **perfect square** is the product of a number multiplied by itself (squared). To simplify a radical, factor out the perfect squares by recognizing that \(\sqrt{a^2} = a\). For example, \(\sqrt{64} = \sqrt{16 \times 4} = \sqrt{4^2 \times 2^2} = 4 \times 2 = 8\).