Math Rules

What is the first rule for positive and negative numbers

Numbers or expressions w/o a sign are always Positive

2nd rule positive and negative

Numbers w/ the same sign add them up & prefix them w/ the same sign as the individual numbers

3rd rule positive and negative

Summing up a group of #'s w/ mixed signs:

• Add positive #'s; add negative #'s

• Subtract smaller sum from larger sum

• Prefix answer w/ sign of larger sum

4th rule positive and negative

Two negative signs make positive; a positive & negative make a negative

5th rule positive and negative

Multiplying & dividing two #'s w/ the same sign, answer always positive

6th positive and negative

Multiplying & dividing #'s w/ different signs, the answer always negative

7th positive and negative

More than two #'s being multiplied or divided, follow rule 5 & 6.

1st rule fractions

Fraction–another way of division / means "divide top expression by bottom expression”

2nd rule fractions

Cannot divide any # by 0, means mistake was made.

3rd rule fractions

Can turn any expression into fraction. Expression = numerator; putting 1 for denominator

4th rule fractions

To multiply fractions, multiply numerators together & denominators together

5th fraction

Multiplying both numerator & denominator of a fraction by the same # doesn't change its value

6th fraction

To divide a fraction, invert & multiply; Invert the fraction you're dividing (divisor) then multiply.

7th fraction

To add or subtract fractions, they must have same (common) denominator. Find least common denominator, multiply both numerator & denominator to make equal.

1st rule decimals

The positions of the numbers after the decimal point tell you what denominator (10, 100, 1000, etc.) you are working with.

2nd rule decimals

Decimals w/ continuous decimals can get rounded off a #.

3rd rule fraction

Percents are simply fractions of 100 (two-place decimals)

1st rule exponents roots

Exponent tells how many times a number or expression is to be multiplied by itself.

2nd rule exponents roots

Roots → Square roots opposite of exponent of 2, cube roots opposite of exponent of 3.

3rd exponents roots

The square root of a number is the value that when multiplied by itself, equals that number. Take the square root of everything shown under the roof of the radical

1st rule order of computation

When expression is enclosed in parentheses, treat whats inside like a single #. Do any operations on the expression before working on the outside. Work from inside out.

2nd rule order of computation

No parentheses? Do all multiplication & division before adding & subtracting.

3rd rule order of computation

Exponents & square roots are treated as single #, square #'s or take square root before adding, subtracting, multiplying, or dividing. My Dear Aunt Sally = Roughly Evict My Dear Aunt Sally, Roots & exponents first.

Summation

Sigma sign; add what comes next; each X is called x_i and the values of i run from 1 to N

1st rule Equations

Adding or subtracting the same number from each side of an equation is acceptable; the two sides will be equivalent

2nd rule equations

If you add or subtract a number from one side of an equation, you must do the same to the other side to balance the equation, if both sides are to remain equal.

3rd rule equation

If you multiply or divide one side of an equation by some #, you must do the same to the other side by the same #.