Multiplying and Dividing Integers What will the sign be?
Multiplication You can think of multiplication as repeated addition 3 x 2 = 2 + 2 + 2 = 6 3 x (–2) = (–2) + (–2) + (–2) = –6
Random Examples 4 x 5 = 20 -4 x 5 = -20 4 x -5 = -20 -4 x -5 = 20 What do we notice about the signs? Is there anything you can conclude?
Rules MULTIPLYING INTEGERS If the signs are: Your answer will be: the same positive different negative
Examples 3 x 12 =36 4 x -12 -1 x 7 = - 48 4(-3) -3(-5) = -7 13(-2) = - 12 = 15 = - 26
Division Multiplication and division are inverse operations. They “undo” each other. You can use this fact to discover the rules for division of integers.
Examples 4 • (–2) = –8 –8 ÷ (–2) = 4 –4 • (–2) = 8 8 ÷ (–2) = –4 Course 2 Examples 4 • (–2) = –8 –8 ÷ (–2) = 4 Same signs Positive –4 • (–2) = 8 8 ÷ (–2) = –4 Different signs Negative The rule for division is like the rule for multiplication!
Rules DIVIDING INTEGERS If the signs are: Your answer will be: the same positive different negative
Examples 15 ÷ 5 32 ÷ -4 -12 ÷ 3 -4 ÷ -2 27 ÷-3 -125 ÷ -5 =3 = - 8 = -4 =2 = - 9 = 25