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...

All positive integers other than 1 have an even # of factors, unless the # is a perfect square.

Sometimes the fastest way to solve a ratio problem is to set up a proportion.
Ex:
3 = 9
4 _x

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?

If wording is "percent of _____", the #/wording which comes after the "of" or "per" goes where?

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