## Arithmetic Reasoning Flash Card Set 86443

 Cards 10 Topics Adding & Subtracting Fractions, Defining Exponents, Exponent to a Power, PEMDAS, Percentages, Rates, Rational Numbers, Simplifying Radicals

#### Study Guide

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.

###### 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

###### PEMDAS

Arithmetic operations must be performed in the following specific order:

1. Parentheses
2. Exponents
3. Multiplication and Division (from L to R)
4. Addition and Subtraction (from L to R)

The acronym PEMDAS can help remind you of the order.

###### Percentages

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

###### Rates

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

###### 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.

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