# Helpful Facts

 If you subtract the remainder from the dividend, the resulting # is divisible by the divisor. ex. r=1, Dividend (N) = 31, Divisor (D)= 3 N - r = # divisible by D 31 - 1 = 30 (divisible by 3) If you add the difference b/w the divisor and the remainder to the dividend, the resulting # will be divisible by the divisor. ex. r=1, Dividend (N) = 31, Divisor (D)= 3 D-r = # (dif b/w Divisor & remainder) 3-1 = 2 Dif + Dividend = # divisible by divisor 2 + 31 = 33 (divisible by divisor 3) When a smaller integer is divided by a greater integer, the quotient is 0 and the remainder is the dividend. ex. 8 ÷ 17 = 0 r8 When working with complex fractions, always start with the innermost fraction first. If a # has exactly three factors... it must be the square of a prime # ex. 9 = 32Factors of 9: 9, 3, 1 All positive integers other than 1 have an even # of factors, unless the # is a perfect square. ex: Factors of 12: 1, 2, 3, 4, 6, 12 (6 factors) ex: Factors of 15: 1, 3, 5, 15(4 factors) ex: Factors of 16: 1, 2, 4, 8, 16(5 factors) 16 = perfect square of 4 Sometimes the fastest way to solve a ratio problem is to set up a proportion. Ex: 3 = 9 4 _x X = 12(Multiplier was 3) Remember to solve for any quantity on a ratio problem, you must have the multiplier or at least one amount. If you are given one ratio and a certain # is added/subtracted to the ratio, the new ratio can't be determined unless the original amount is given. All ratios can be expressed with a multiplier: Ex: 3/5 = 3x/5x or 3:5 = 3x:5x Percents: When increasing a value by a certain % and then decreasing it by the same %, the end result will always be less than the orig. value. Ex: 10 + 20% = 12, 12 - 20% = 9.6 Setting an exponent to Zero is an easy way to create a number (1) that divides evenly into any integer. If wording "percent greater" is used, what do you need to do? Add the starting # to the new # (starting # * # was increased by). Ex: LY = \$12mil, TY = 150 percent greaterThen TY = ? (1.5 * 12) --> (18) + 12 = 30 If wording is "percent of _____", the #/wording which comes after the "of" or "per" goes where? Under the fraction line Remember if you have a variable with no coefficient, i.e. coefficient = 1, remember you can turn into a fraction if needed to combine terms. i.e. 1C = 5/5 C AuthorJanineG14 ID81595 Card SetHelpful Facts DescriptionHelpful Math Facts Updated2011-06-30T06:54:13Z Show Answers