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1-3 Multiplying and Dividing Real Numbers
Warm UpWarm Up
Lesson PresentationLesson Presentation
California Standards
PreviewPreview
1-3 Multiplying and Dividing Real Numbers
Warm UpMultiply or divide.
1. 6(7)
3. 42 ÷ 7
4.2.
6. Write as an improper fraction.
42 6
4
5. Write as a mixed number.
1-3 Multiplying and Dividing Real Numbers
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
California Standards
1-3 Multiplying and Dividing Real Numbers
reciprocalmultiplicative inverse
Vocabulary
1-3 Multiplying and Dividing Real Numbers
When you multiply or divide two numbers, the signs of the numbers determine whether the result is positive or negative.
Numbers Product/Quotient
Both positive
One negative
Both negative
Positive
Negative
Positive
1-3 Multiplying and Dividing Real Numbers
1-3 Multiplying and Dividing Real Numbers
Find the value of each expression.
–5The product of two numbers with different signs is negative.
Additional Example 1: Multiplying and Dividing Signed Numbers
A.
12 The quotient of two numbers with the same sign is positive.
B.
1-3 Multiplying and Dividing Real Numbers
The quotient of two numbers with different signs is negative.
Multiply.
C.
Find the value of each expression.
Additional Example 1: Multiplying and Dividing Signed Numbers
1-3 Multiplying and Dividing Real Numbers
Find the value of each expression.
–7 The quotient of two numbers with different signs is negative.
Check It Out! Example 1
1a. 35 (–5)
44 The product of two numbers with the same sign is positive.
1b. –11(–4)
1c. –6(7)
–42 The product of two numbers with
different signs is negative.
1-3 Multiplying and Dividing Real Numbers
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.
1-3 Multiplying and Dividing Real Numbers
Example 2 Dividing by FractionsAdditional Example 2A: Dividing with Fractions
Divide.
To divide by , multiply by .
Multiply the numerators and multiply the denominators.
and have the same sign, so the quotient is positive.
1-3 Multiplying and Dividing Real Numbers
Additional Example 2B: Dividing with Fractions
Divide.
Write as an improper fraction.
To divide by , multiply by .
and have different signs,
so the quotient is negative.
1-3 Multiplying and Dividing Real Numbers
You can write the reciprocal of a number by switching the numerator and denominator. A number written without a denominator has a denominator of 1.
Helpful Hint
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 2a
Divide.
Write as an improper fraction.
To divide by , multiply by .
and –9 have the same signs,
so the quotient is positive.
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 2b
Divide.
To divide by , multiply by .
Multiply the numerators and multiply the denominators.
and have different signs,
so the quotient is negative.
1-3 Multiplying and Dividing Real Numbers
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.
1-3 Multiplying and Dividing Real Numbers
The number 0 has special properties for multiplication and division.
1-3 Multiplying and Dividing Real Numbers
1-3 Multiplying and Dividing Real Numbers
Additional Example 3: Multiplying and Dividing with Zero
Multiply or divide if possible.
A. 15
0
B. –22 0
undefined
C. –8.45(0)
0
Zero is divided by a nonzero number.
The quotient of zero and any nonzero number is 0.
A number is divided by zero.Division by zero is undefined.
A number is multiplied by zero.
The product of any number and 0 is 0.
0
1-3 Multiplying and Dividing Real Numbers
Check It Out! Example 3
Multiply or divide.
3a.
0
Zero is divided by a nonzero number.
The quotient of zero and any nonzero number is 0.
3b. 0 ÷ 0
undefined A number divided by 0 is undefined.
3c. (–12.350)(0)
0 The product of any number and 0 is 0.
A number is divided by zero.
A number is multiplied by zero.
1-3 Multiplying and Dividing Real Numbers
rate
334
times
time
113
Additional Example 4: Recreation Application
Find the distance traveled at a rate of 3 mi/h for 1 hour.To find distance, multiply rate by time.
34
13
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?
13
34
1-3 Multiplying and Dividing Real Numbers
Additional Example 4 Continued
3 34 • 1 1
3 = 15 4 • 4
3Write and as improper fractions.3
43 1 13
15(4) 4(3)
= 6012
= 5
Multiply the numerators and multiply the denominators.
3 34 and have the same sign, so
the quotient is positive.1 1
3
The hot-air balloon lands 5 miles from the liftoff site.
1-3 Multiplying and Dividing Real Numbers
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?
Check It Out! Example 4
5.25(1.5) Rate times time equals distance.
= 7.875 mi Distance traveled.
1-3 Multiplying and Dividing Real Numbers
Find the value of each expression.
1. 35–7
–5 2. 2(–6) –12
Lesson Quiz
Multiply or divide if possible.
3. –3 ÷ 1 34
(0)4. –213 5. – 03
4– 12
70
undefined
15 miles
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?
14