Warm-up Check homework Odds w/book Evens with a neighbor “We cannot hold a torch to light another’s path without brightening our own.” – Ben Sweetland Check homework Odds w/book Evens with a neighbor Sections 2.1 – 2.4 No more than 5 minutes! Warm-up

2.5 Multiplication of Integers Properties of Multiplication a * b = b * a The order of 2 numbers being multiplied does not matter. 1 * a = a The product of one & a number is that number. 0 * a = 0 The product of zero & a number is zero.

The product of a number and -1 is the opposite of that number. -1 * a = -a The product of a number and -1 is the opposite of that number. a * -b = -ab The product of a and –b is the opposite of ab. Multiplying 2 numbers with different signs is ALWAYS a negative answer. -a * - b = ab The product of –a and –b is ab. Multiplying 2 numbers with the same sign is ALWAYS a positive answer.

examples -3 * -2 * -4 = -4 * x * -12 = (-x)3 = (-x)2 = (-2)4 = -24 =

Sect. 7 – Division of Real # The integer rules for division are the same as for multiplication. Same signs = positive answer -20/-4 = 5 Different signs = negative answer -20/4 = -5

Division can be written as multiplication. Reciprocals – numbers when multiplied together equal 1 (excluding 1 * 1) Reciprocal of a/b is b/a Reciprocal of 4 is ¼ Division w/reciprocals To divide “a” by “b”, you can multiply by the reciprocal of “b” and get the same answer. 20/4 is the same as 20 * 1/4

Write the division as multiplication & solve 3/5 divided by 2 = 3/5 * ½ = 3/10 3x divided by 1/3 = 3x * 3 = 9x -x / (-6) = -x * (-1/6) = x/6

Simplifying a quotient Change to multiplication (32x – 8)/4 = (32x – 8) ¼ = ¼(32x) – ¼(8) = 8x – 2 (32x – 8)/4 = (another easy way) 32x/4 – 8/4 = 8x - 2

Try these 6/7 divided by 3 = 6/21 4x divided by 3 = 4x/3 (12x + 28)/4 = 3x + 7

Questions? Mid-chp quiz tomorrow Need to see some of you