2. 1-3 Multiplying and Dividing Real Numbers Warm Up Lesson Presentation
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz

3. 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.

4. Objectives
Multiply real numbers.
Divide real numbers.

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. 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

9. 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

10. 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.

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

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

13. 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.

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

15. 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.

16. 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.

17. 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

18. 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

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

20. 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

21. Homework Due Friday, September 18th Page 23: 1-12; 21-46
Reminder: Homework Quiz tomorrow and turn in assignment sheets!