Lesson 2-6 and 2-7 Multiplying and Dividing Rational Numbers Objective Students will be able to: 1. multiply rational numbers 2. divide rational numbers.
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Lesson 2-6 and 2-7 Multiplying and Dividing
Rational Numbers
ObjectiveStudents will be able to:1.multiply rational numbers2.divide rational numbers
Multiplying Rules
1) If the numbers have the same signs then the product is positive.
(-7) • (-4) = 282) If the numbers have
different signs then the product is negative.
(-7) • 4 = -28
Examples
1) (3x)(-8y)
20 4
5
2) Write both numbers as a fraction.
Cross-cancel if possible.
20
1
4
5
80
5= -16
Multiplying fractions:
top # • top #
Bottom # • bottom#
-24xy
When multiplying two negative numbers, the
product is negative.1. True2. False
Answer NowAnswer Now
When multiplying a negative number and a positive number,
use the sign of the larger number.1. True2. False
Answer NowAnswer Now
2
5
5
8
3)
10
40=
1
4=
Multiply: (-3)(4)(-2)(-3)1. 722. -723. 364. -36
Answer NowAnswer Now
an easy way to determine the sign of the answer
3 negative signs -> Odd -> answer is negative-480
When you have an odd number of negatives, the answer is negative.
When you have an even number of negatives, the answer is positive.
4) (-2)(-8)(3)(-10)Do you have an even or odd number of
negative signs?
Last one!
5) 1
2
6 5 2
5
2
Positive or negative answer?Positive - even # of negative signs (4)
Write all numbers as fractions and multiply.
=12
1
2
6
1
5
1
2
5
2
1
12010
Dividing Rules (same as multiplication)
1) If the numbers have the same signs then the quotient is positive.
-32 ÷ (-8 )= 42) If the numbers have different
signs then the quotient is negative.
81 ÷ (-9) = -9
When dividing two negative numbers, the quotient is
positive.1. True2. False
Answer NowAnswer Now
When dividing a negative number and a positive number, use the
sign of the larger number.1. True2. False
Answer NowAnswer Now
The reciprocal of is
where a and b 0.
a
b
b
a
The reciprocal of a number is called its multiplicative inverse.
A number multiplied by its reciprocal/multiplicative inverse is
ALWAYS equal to 1.
Example #1
7
2.
2
7The reciprocal of is
2
7
7
2 1
11
Example #2
The reciprocal of -3 is
1
3.
1
11
3
1
1
3
Basically, you are flipping the fraction!
We will use the multiplicative inverses
for dividing fractions.
Which statement is false about reciprocals?
1. Reciprocals are also called additive inverses
2. A number and its reciprocal have same signs
3. If you flip a number, you get the reciprocal
4. The product of a number and its reciprocal is 1Answer NowAnswer Now
When dividing fractions, change division to multiplying by the reciprocal.
Examples
1) 3
4
5
8
3
4
8
5
6
5
24
20
2) 1
5
3
10
1
5
10
3
10
15
2
3
What is the quotient of-21 ÷ -3?
1. 182. -183. 74. -7
Answer NowAnswer Now
1. .
2. .
3. .
4. .
1 10?
5 3
Answer NowAnswer Now
2
3
2
33
503
50
Homework:
OLesson 2-6 p. 109, 110 # 18-
45 every 3rd
OLesson 2-7 p. 115 # 15 -42
every 3rd
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