1. 1-3 Multiplying and Dividing Real Numbers Warm Up Lesson Presentation
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm Up Multiply or divide. 1. 6(7) 42 3. 42 7 ÷ 6 2. 4. 4
42 7 ÷ 6 2. 4. 4
5. Write as a mixed number. 6.
Write as an improper fraction.

3. Objectives
Multiply real numbers.
Divide real numbers.

4. Vocabulary
reciprocal
multiplicative inverse

5. Factors Product 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
15 Positive
3(–5) One negative
– Negative
–3(–5) Both negative
Positive
This is true for division also.

6. Multiplying and Dividing Signed Numbers
WORDS
Multiplying and Dividing Numbers with the Same Sign
If two numbers have the same sign, their product or quotient is positive.
NUMBERS
4  5 = 20
–15 ÷ (–3) = 5

7. Multiplying and Dividing Signed Numbers
WORDS
Multiplying and Dividing Numbers with Different Signs
If two numbers have different signs, their product or quotient is negative.
NUMBERS
6(–3) = –18
–18 ÷ 2 = –9

8. Example 1: Multiplying and Dividing Signed 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

9. 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.

10. Check It Out! Example 1a and 1b
Find the value of each expression.
1a. 35  (–5)
The quotient of two numbers
with different signs is negative. –7
1b. –11(–4)
The product of two numbers
with the same sign is positive. 44

11. Check It Out! Example 1c
Find the value of each expression.
1c. –6x for x = 7
–6x = –6(7)
First substitute 7 for x.
The product of two numbers with different signs is negative.
= –42

12. 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.

13. Multiplicative inverses1 10
10 ÷ 5 = 2
10 ∙ = = 2 5 5
Dividing by 5 is the same as multiplying by the
reciprocal of 5, .

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

15. Example 2A: Dividing by 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.

16. Example 2B: Dividing by Fractions
Divide.
Write as an improper fraction.
To divide by , multiply by
and have different signs, so the quotient is negative.

17. Check It Out! Example 2a
Divide.
Write as an improper fraction.
To divide by , multiply by
and have the same signs, so the quotient is positive.

18. Check It Out! Example 2b
Divide.
Write the reciprocal of
To divide by , multiply by
and have different signs, so the quotient is negative.

19. 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.

20. 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.

21. Properties of Zero Multiplication by Zero The product of any number
and 0 is 0.
WORDS 1 3
· 0 = 0
0(–17) = 0
NUMBERS
ALGEBRA
a · 0 = 0
0 · a = 0

22. Properties of Zero Zero Divided by a Number The quotient of 0 and any
nonzero number is 0.
WORDS 6
= 0
0 ÷ 2 3
= 0
NUMBERS a
= 0
ALGEBRA
0 ÷ a = 0

23. Properties of Zero Division by Zero WORDS Division by 0 is undefined.–5
12 ÷ 0
NUMBERS
Undefined a
ALGEBRA
a ÷ 0
Undefined

24. Example 3: Multiplying and Dividing with Zero
Multiply or divide. 15 A.
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 an number and 0 is 0.

25. Check It Out! Example 3a
Divide:
Turn into an improper
fraction.
Multiply by the reciprocal.
Any number multiplied by
0 equals 0.

26. Check It Out! Example 3b and 3c
Divide:
3b. 0 ÷ 0
Any number divided by 0 is
undefined.
0 ÷ 0 = undefined
3c. (–12.350)(0)
The product of any number and 0 is 0.
(–12.350)(0) = 0

27. 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

28. Example 4: Recreation Application3 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.

29. Check It Out! Example 4
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. How many miles away from the liftoff site will the balloon land?
5.25(1.5)
Speed times time equals distance.
= mi
Distance traveled.

30. Lesson Quiz
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 6.
A cyclist traveled on a straight road for 1 hours at a speed of 12 mi/h. How many miles did the cyclist travel? 1 4
15 miles