Solving Equations with Rational Number Solutions

Solving equations with rational number solutions requires a review of the specific skills procedures which have alread been covered.

Equation procedures: Identify the operation, or in the case of more than one operation, identify the operation farthest from the variable Use the opposite operation on both sides of the equal sign Use the number you need to move/remove which goes with the operation you selected in the first step. Be sure to do both sides of the = sign Simplify

Positive and Negative Numbers (remember, these rules only apply one operation at a time - be sure you are following the order of operations) Addition If the sign of the numbers are the same - add If the signs are different Find the absolute value of each term Subtract the smallest absolute value from the largest - this is the absolute value of the answer Use the sign of the number which gave the largest absolute value Subtraction To subtract , change the subtraction sign to addition Change the sign of the number after the subtraction sign to its opposite Continue as if adding (see the rules for adding Multiplication and Division If the signs are the same the answer is positive If the signs are different the answer is negative

a/b (b not 0) Rational Number (Fraction) Operations Addition Find a common denominator for the fractions Calculate the equivalent fraction forms Add the numerators Add the whole numbers (if any) Simplify Subtraction Find a common denominator Calculate the equivalent fraction forms If you can subtract numerators without borrowing then do so If you need to borrow, borrow 1 from the whole number and change it to an equivalent form with the common denominator Add the numerators, and continue with subtraction Subtract the whole numbers (if any) Simplify Multiplication (Standard algorithem) Change the numbers to fraction form Multiply the numerators Multiply the demonimators Simplify Division (Standard algorithem) Change the numbers to fraction form Change the ÷ sign to x Change the number after the division sign (÷) to its reciprocal Multiply the numerators Multiply the denominators Simplify