Cards | 10 |

Topics | Commutative Property, Defining Exponents, Defining Radicals, Least Common Multiple, Proportions, Rational Numbers, Ratios, Scientific Notation, Simplifying Radicals |

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.

An exponent (cb^{e}) 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 (b^{1} = b) and a base with an exponent of 0 equals 1 ( (b^{0} = 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**).

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

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.

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 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 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}.

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, \(\sqrt{64} = \sqrt{16 \times 4} = \sqrt{4^2 \times 2^2} = 4 \times 2 = 8\).