Math 110 Intermediate Algebra

VARIABLES, EXPRESSIONS, AND EQUATIONS An expression containing a variable is evaluated by __________

An expression containing a variable is evaluated by substituting a given number for the variable.

FRACTIONS Multiplication

Multiply numerators and multiply denominators.

FRACTIONS Division

Multiply the first fraction by the reciprocal of the second fraction.

ORDER OF OPERATIONS

Simplify within parentheses, brackets, or absolute value bars or above and below fraction bars first, in the following order. i. Apply all exponents. ii. Perform any multiplications or divisions from left to right. iii. Perform any additions or subtractions from left to right.

REAL NUMBERS AND THE NUMBER LINE ,The absolute value of x, denoted |x|, is the distance (a positive number) between __________ on the number line.

The absolute value of x, denoted |x|, is the distance (a positive number) between x and 0 on the number line.

REAL NUMBERS AND THE NUMBER LINE, The additive inverse of x is___________

The additive inverse of x is -x.

OPERATIONS ON REAL NUMBERS, Adding Real Numbers, with different signs

To add two numbers with different signs, subtract their absolute values. The sum has the sign of the number with the larger absolute value.

OPERATIONS ON REAL NUMBERS Adding Real Numbers, with the same sign, with different signs

To add two numbers with the same sign, add their absolute values. The sum has the same sign as each of the numbers being added.

VARIABLES, EXPRESSIONS, AND EQUATIONS Values for a variable that make an equation __________ are _______________ of the equation

Values for a variable that make an equation true are solutions of the equation

REAL NUMBERS AND THE NUMBER LINE, a is less than b if a is to the _________of b on the number line.

a is less than b if a is to the left of b on the number line.

Subtracting Real Numbers

i. Change the subtraction symbol to the addition symbol. ii. Change the sign of the number being subtracted. iii. Add using the rules for adding real numbers

FRACTIONS Addition and Subtraction To add or subtract fractions with the same denominator,

i. To add or subtract fractions with the same denominator, add or subtract the numerators and keep the same denominator.

FRACTIONS Addition and Subtraction ii. To add or subtract fractions with different denominators,

ii. To add or subtract fractions with different denominators, find the LCD and write each fraction with this LCD. Then add or subtract the numerators and keep the same denominator.