1. Multiplying and Dividing Real Numbers
Section 1-6

2. Goals Goal Rubric To Find products and quotients of real numbers.
Level 1 – Know the goals.
Level 2 – Fully understand the goals.
Level 3 – Use the goals to solve simple problems.
Level 4 – Use the goals to solve more advanced problems.
Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary
Multiplicative Inverse
Reciprocal

4. Multiplying Real Numbers
When you multiply two numbers, the signs of the
numbers you are multiplying determine whether
the product is positive or negative.
Factors
Product
3(5) Both positive
Positive
3(–5) One negative
– Negative
–3(–5) Both negative
Positive
This is true for division also.

5. Rules for Multiplying and Dividing

6. Example: Multiplying and Dividing Real Numbers
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

7. Example: Multiplying and Dividing Real Numbers
Find the value of each expression. C.
Multiply.
The quotient of two numbers
with different signs is negative.

8. Your Turn: Find the value of each expression. a. 35  (–5) –7
The quotient of two numbers
with different signs is negative. –7
b. –11(–4)
The product of two numbers
with the same sign is positive. 44
c. –6(7)
The product of two numbers with different signs is negative.
–42

9. Reciprocals Two numbers are reciprocals if their product is 1.
A number and its reciprocal are called multiplicative inverses. To divide by a number, you can multiply by its multiplicative inverse.
Dividing by a nonzero number is the same as Multiplying by the reciprocal of the number.

10. Reciprocals Multiplicative inverses 1 10 10 ÷ 5 = 2 10 ∙ = = 2 5 5
10 ∙ = = 2 5 5
Dividing by 5 is the same as multiplying by the
reciprocal of 5, .

11. You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1.
Helpful Hint

12. Example: Dividing with Fractions
Example 2 Dividing by Fractions
Divide.
To divide by , multiply by
Multiply the numerators and multiply the denominators.
and have the same sign,
so the quotient is positive.

13. Example: Dividing with Fractions
Divide.
Write as an improper fraction.
To divide by , multiply by
and have different signs, so the quotient is negative.

14. Your Turn: Divide. Write as an improper fraction.
To divide by , multiply by
and –9 have the same signs, so the quotient is positive.

15. Your Turn: Divide. To divide by , multiply by .
Multiply the numerators and multiply the denominators.
and have different signs, so the quotient is negative.

16. To divide by multiply by .
Check It Out! Example 2c
Divide.
Write as an improper fraction.
To divide by multiply by .
The signs are different, so the
quotient is negative.

17. Zero
No number can be multiplied by 0 to give a product of 1, so 0 has no reciprocal.
Because 0 has no reciprocal, division by 0 is not possible. We say that division by zero is undefined.
The number 0 has special properties for multiplication and division.

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

20. Your Turn: Multiply or divide. a. b. 0 ÷ 0 undefined c. (–12.350)(0)
Zero is divided by a nonzero number.
The quotient of zero and any nonzero
number is 0.
b ÷ 0
A number is divided by zero.
undefined
A number divided by 0 is undefined.
c. (–12.350)(0)
A number is multiplied by zero.
The product of any number and 0 is 0.

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

22. Example: Continued 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.

23. Your Turn:
What if…? On another hot-air balloon trip, the wind speed is 5.25 mi/h. The trip is planned for 1.5 hours. The balloon travels in a straight line parallel to the ground. How many miles away from the liftoff site will the balloon land?
5.25(1.5)
Rate times time equals distance.
= mi
Distance traveled.

24. Joke Time What’s a fish with no eyes? A fsh.
What do you call a nun that walks in her sleep?
A roamin’ Catholic.
Why did the cookie go to the doctor?
Because he was feeling crummy.

25. Assignment
1.6 Exercises Pg. 49 – 51: #8 – 74 even.