Classification of Numbers Properties of Real Numbers Order of Operations R1 Real Numbers

The numbers 3, 4, 5, and 6 are called elements. S = { 3, 4, 5, 6 } When we want to treat a collection of similar but distinct objects as a whole, we use the idea of a set.

We do not list an element more than once, because the elements of a set are distinct. If a set has no elements, it is called the empty set or null set. The order in which you list elements in a set is not relevant.

Natural Numbers – N 1, 2, 3, 4, 5, 6, 7, … Whole Numbers – W 0, 1, 2, 3, 4, 5, 6, … Integers – I …, – 2, – 1, 0, 1, 2, … Classification of Real Numbers

Rational Numbers Any number that can be written in the form of a fraction. Irrational Numbers Any number that neither terminates nor repeats.

Truncation Drop all the digits that follow the specified final digit in the decimal. Rounding Identify the specified final digit in the decimal. If the next digit is 5 or more, add 1 to the final digit. Otherwise leave the number as it appears. Approximations

Truncating: Rounding: Approximate to 3 decimal places by both truncating and rounding.

Convert Natural Numbers, Whole Numbers, and Integers into fractional form

Convert each mixed number into fractional form Multiply the whole number by the denominator and add the numerator all over the denominator

Convert terminating decimals into fractional form The number of places you move the decimal point is equal to the number of zeros in the denominator.

Convert repeating decimals into fractional form Repeating decimals are over 9 Nonrepeating decimals are over 0 Work from right to left in the denominator Subtract the nonrepeating digits from the entire decimal for the numerator

1.Perform all operations within grouping symbols from innermost outward. 2.Perform all operations with exponents from left to right. 3.Perform all multiplication and division from left to right. 4.Perform all addition and subtraction from left to right. Order of Operations

1.Find the LCD 2.Multiply numerator by factor of LCD 3.Add the numerators together 4.Keep the denominator the same 5.Simplify the expression Adding and Subtracting Rational Numbers

1.Inverse Property for division 2.Reduce fractions with common factors 3.Multiply the numerators together 4.Multiply the denominators together 5.Simplify the expression Multiplying and Dividing Rational Numbers

R2 Algebra Review Graphing Inequalities Absolute Value Evaluating Expressions

A real number that corresponds to a particular point on the number line is called a coordinate. The origin corresponds to the real number zero. The correspondence between points on a line and the real numbers is called a coordinate system. Real Number Line

Graph the following inequalities on the number line. Graphing Inequalities

Distance from zero on the number line. The absolute value of a real number a is denoted by the symbol |a|. Absolute Value

The distance between two points P and Q is denoted by d(P,Q) = |b – a|. Let P, Q, and R be points on the number line with coordinates –7, 4, and –3. 1. Find the distance between P and Q. 2. Find the distance between Q and R..

Write an equivalent expression without using absolute value bars.

1.Substitute each value for the variable using a grouping symbol 2. Follow all order of operations 3. Simplify your answer Evaluating Expressions

Evaluate each expression, if x = 4, y = –2, and z = 3