Arithmetic Reasoning Flash Card Set 412433

Cards 10
Topics Adding & Subtracting Fractions, Defining Exponents, Exponent to a Power, Factors & Multiples, Least Common Multiple, Prime Number, Rational Numbers, Simplifying Radicals

Study Guide

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.

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

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, ...

Least Common Multiple

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

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.

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.

Simplifying Radicals

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