1-3 Purpose Multiply real numbers. Divide real numbers.

Positive + , + + , - or - , + Negative - , - Positive Factors Product This is true for division also.

Multiplication Division (3)(10) = 30 (-12)(-2) = 24 Multiplying & Dividing signed numbers Multiplication Division Same Signs answer is + (3)(10) = 30 (-12)(-2) = 24 Different Signs answer is - (-9)(2) = -18 (7)(-4) = -28

Find the value of each expression. Example 1 Find the value of each expression. A. The product of two numbers with different signs is negative. –5 B. The quotient of two numbers with the same sign is positive. 12

Example 1C: Multiplying and Dividing Signed Numbers Find the value of the expression. First substitute for x. The quotient of two numbers with different signs is negative.

You can use multiplicative inverses when dividing fractions! Reciprocal: Two #’s when multiplied together give you 1. EX: 4(1/4) = 4/4 = 1 Multiplicative Inverse: A number and it’s reciprocal. EX: 4 is the mult. inv. of 1/4 You can use multiplicative inverses when dividing fractions!

Flip the 2nd term and multiply! Multiplicative inverses 1 10 10 ÷ 5 = 2 10 ∙ = = 2 5 5 Dividing by 5 is the same as multiplying by the reciprocal of 5, .

Flip the 2nd # and multiply!! Example 2A: Dividing by Fractions Divide. Example 2 Dividing by Fractions Flip the 2nd # and multiply!! To divide by , multiply by . Multiply the numerators and multiply the denominators. and have the same sign, so the quotient is positive.

Flip the 2nd # and multiply!! You Try! Divide. Flip the 2nd # and multiply!! Write as an improper fraction. To divide by , multiply by . and have the same signs, so the quotient is positive.

(1/2)0 = 0 0(-17) = 0 a(0) = 0 0(a) = 0 Properties of zero Number Example Algebra Example Multiplication by zero (1/2)0 = 0 0(-17) = 0 a(0) = 0 0(a) = 0 Zero Divided by a number Division by zero or or or or Undefined Undefined

Example 3: Multiplying and Dividing with Zero Multiply or divide. A. 15 Zero is divided by a nonzero number. The quotient of zero and any nonzero number is 0. B. –22  0 undefined A number is divided by zero. C. –8.45(0) Division by zero is undefined. A number is multiplied by zero. The product of an number and 0 is 0.

You Try! Divide: 3b. 0 ÷ 0 Any number divided by 0 is undefined. 3c. (–12.350)(0) The product of any number and 0 is 0. (–12.350)(0) = 0

Example 4: Recreation Application The speed of a hot-air balloon is 3 mi/h. It travels in a straight line for 1 hour before landing. How many miles away from the liftoff site does the balloon land? 1 3 4 Find the distance traveled at a rate of 3 mi/h for 1 hour. To find distance, multiply rate by time. 3 4 1 rate times time 3 4 1 3  1 3

Example 4: Recreation Application 3 4 • 1 = 15 Write and as improper fractions. 3 4 1 15(4) 4(3) = 60 12 Multiply the numerators and multiply the denominators. 3 4 and have the same sign, so the quotient is positive. 1 = 5 The hot-air balloon lands 5 miles from the liftoff site.

Exit Task Find the value of each expression. 1. 35 –7 –5 2. 2x for x = –6 – 12 Multiply or divide if possible. undefined 3. –3 ÷ 1 3 4 (0) 4. –2 1 3 – 12 7 5. –  0 3 4