Helpful Facts

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Author:
JanineG14
ID:
81595
Filename:
Helpful Facts
Updated:
2011-06-30 02:54:13
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Math Facts
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Helpful Math Facts
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  1. 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)
  2. 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)
  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
  4. When working with complex fractions, always start with the innermost fraction first.
  5. If a # has exactly three factors...
    it must be the square of a prime #

    • ex. 9 = 32
    • Factors of 9: 9, 3, 1
  6. 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
  7. 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)
  8. Remember to solve for any quantity on a ratio problem, you must have the multiplier or at least one amount.
  9. 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.
  10. All ratios can be expressed with a multiplier:

    Ex: 3/5 = 3x/5x or 3:5 = 3x:5x
  11. 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
  12. Setting an exponent to Zero is an easy way to create a number (1) that divides evenly into any integer.
  13. 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 greater
    • Then TY = ? (1.5 * 12) --> (18) + 12 = 30
  14. If wording is "percent of _____", the #/wording which comes after the "of" or "per" goes where?
    Under the fraction line
  15. 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

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