Transcript Ch 2.7 Dividing Real Numbers

Algebra 1
Ch 2.7 – Dividing Real Numbers
Objective

Students will divide real numbers
Reciprocals
The inverse property of multiplication states:
“for every real number other than zero there exists a
number called its reciprocal. The product of a
number and its reciprocal is 1”
Example:

The reciprocal of 3 is
1
3
Recall that the number 3 can be expressed as a fraction of
3
1
Therefore, the reciprocal of
3
1
is
1
3
Proof:


Recall the rule for multiplying fractions is to multiply
the numerator (top number) and multiply the
denominator (bottom number), then simplify
In this instance the following is true:
3
1
1
●
3
=
3
3
= 1
Therefore, the product of a number and its reciprocal is 1
Division Rule
Now that we know what a reciprocal is we can look at
the division rule:
 The division rule states:
“to divide a number a by a nonzero number b, multiply a
by the reciprocal of b

This rule can be expressed as follows:
Algebraically:
Example:
ab  a
1
b
1  3  1 
1
3
 
1
3
Comments


The reason that we are reviewing this concept
now is because…later in this course we will
study solving equations, linear equations and
quadratic equations. At that point you will be
asked to transform equations…
If you do not know how to handle dividing real
numbers and how to figure out their
sign…you will not be able to transform the
equations….
Sign of a Quotient

The rules for the sign of a quotient are the
same as multiplying



If the signs are the same the answer is positive
If the signs are different the answer is negative
Let’s see what that looks like
Example # 1
18  3 = 6
In this instance both numbers are positive so your answer will
be positive
18  3 = 6
Example #2
- 20  - 5 = 4
In this instance both numbers are negative so your answer will
be positive
- 20  - 5 = 4
Example #3
- 10  2 = - 5
In this instance the numbers have different signs. The 10 is
negative and the 2 is positive – your answer will be negative
- 10  2 = - 5
Example # 4
20  - 4 = - 5
In this instance the numbers have different signs. The 20 is
positive and the 4 is negative – your answer will be negative
20  - 4 = - 5
Finding the Quotient of a
Number
You can use the rule that you just learned to find
the quotient of a number
Example:

7
1
2
 7
2
1

14
 14
1
Recall that the number 7 can be expressed as
7
1
Then multiply the numerators and the denominators and simplify to
get your answer
In this case both numbers are positive so your answer will be
positive
Example #5
16
2
9
The problem can be simplified by re-writing the
expression as follows:
16
2
 16 
2
9
 16 
9
2

144
2
  72
9
In this instance the answer is negative because the
numerator is positive and the denominator is negative
Comments



On the next couple of slides are some practice
problems…The answers are on the last slide…
Do the practice and then check your answers…If
you do not get the same answer you must
question what you did…go back and problem
solve to find the error…
If you cannot find the error bring your work to me
and I will help…
Your Turn

Find the quotient
1.
 51  (  17 )
2.
64  (  8 )
3.
2 I
F
 90  G J
H3 K
4.
5.
3I
F
 87  G
 J
H5 K
26

1
2
Your Turn

6.
Simplify the Expression
42 y 
1
7
7.
d
9.
3r  7
11
6
4
10.
15 x  10
2
y
8.
w hen r = 17
42 t
 14 z

6
7t
w hen x = - 3 and y =
2
3
Your Turn Solutions
1.
2.
3.
3
7.
24
8
135
d
8.
147 t
42 z
4.
145
5.
52
9.
10.
6.
294 y
4
435
2
2
Summary



A key tool in making learning effective is being
able to summarize what you learned in a lesson in
your own words…
In this lesson we talked about reciprocals and
dividing real numbers… Therefore, in your own
words summarize this lesson…be sure to include
key concepts that the lesson covered as well as
any points that are still not clear to you…
I will give you credit for doing this lesson…please
see the next slide…
Credit


I will add 25 points as an assignment grade for you working on
this lesson…
To receive the full 25 points you must do the following:




Have your name, date and period as well a lesson number
as a heading.
Do each of the your turn problems showing all work
Have a 1 paragraph summary of the lesson in your own
words
Please be advised – I will not give any credit for work
submitted:



Without a complete heading
Without showing work for the your turn problems
Without a summary in your own words…