1. SEC. 1-6: Multiplying & dividing real numbers

2. Sign Rules:
An ODD amount of negative signs will cause your product or quotient to be NEGATIVE.
An EVEN amount of negative signs will produce POSITIVE products & quotients.
i.e.
-2 ∙ 9 = a NEGATIVE product = ____
-3 ∙ -4 ∙ 2 = a POSITIVE product = ____
7 ∙ 8 = a ____________ product = ____
-10 ÷ -5 = a POSITIVE quotient = _____
-28 ÷ 4 = a _________ quotient = _____

3. Be careful of “exponents”. Follow the Order of Operations. i. e
** Be careful of “exponents”. Follow the Order of Operations!! i.e. -34 means – (3)4 NOT (-3)(-3)(-3)(-3) Because you work with the exponent first and THEN multiply the result by a “-1” So -34 = - 81

4. Multiplicative Inverse: (reciprocal)
Any number multiplied by its multiplicative inverse is one. (flip the fraction & KEEP the sign.)
i.e.
-5  - 1/5 because -5 ∙ -1/5 = 1
2/3  3/2 because 2/3 ∙ 3/2 = 1
-4/7  -7/4 because -4/7 ∙ -7/4 = 1

5. We need the reciprocal when dividing fractions because we really NEVER divide fractions, instead we multiply by the reciprocal. i.e. -1 ÷ Would be written as: -1 ∙ Then multiply STRAIGHT ACROSS (reduce ANY numerator with ANY denominator if possible.) Final answer is: -5/12

6. Here’s another: -8 ÷ -4 3 12 -8 ∙ -12 3 4
Here’s another: -8 ÷ ∙ **We can do some reduction here… Final answer: 8

7. Substitution:
Basically, “plug & chug”…substitute the values given for a variable and then use order of operations to reduce the expression.
Look at the example on p. 41 of your book.