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Operations of Rational Numbers Notes Rational number: a number that can be written as a ratio; whole number, fractions, repeating or terminating decimals Adding Subtracting Multiplying Dividing Signed Numbers *Think of the sign as a direction on a number line + = right - = left pos + pos = pos pos + neg = depends on larger neg + neg = neg neg + pos = number Fractions *Get like denominators and rename the fractions *Re-write the subtraction problem as addition of the opposite number ex: -1.2 – 3.8 = -1.2 + (-3.8) -2 – (-5) = -2 + 5 “double negative” pos – neg = pos + pos = pos neg – pos = neg + neg = neg pos – pos = pos + neg = depends on larger neg – neg = neg + pos = number *If the signs are the same, the product is positive *If the signs are different, the product is negative *(-1) times a number equals the opposite of that number pos x pos = pos pos x neg = neg neg x neg = pos neg x pos = neg *Same as multiplying since division is the same as multiplying by the reciprocal pos pos = pos = neg pos neg neg neg = pos = neg neg pos *Get like denominators and rename the fractions Decimals *Line up the decimals *Mixed numbers are okay *Line up the decimals *Mixed numbers are okay, but you may have to borrow from a whole number *Cross simplify then multiply across the numerators and denominators *convert to improper fractions first *Multiply by the reciprocal; “switch and flip” = switch the sign from division to multiplication and then flip the second fraction *convert to improper fractions first *Don’t line up the decimals, count the number of decimal places “held” after finished multiplying *Convert the divisor (the number you’re dividing by) into a whole number by moving the same number of decimal places in each number (equivalent to multiplying both numbers by a power of ten) € € Absolute value = = the distance from zero; always positive because it is a distance; complete the operations inside the absolute € and then make the final result € value signs positive €