Download Algebra: Solving Equations 6-5 (pages 258-261)

Algebra: Solving Equations
6-5 (pages 258-261)
P4  Create visual representations of
equation-solving processes that
model the use of inverse
operations.
Addition and multiplication of fractions have the
same properties as addition and multiplication of
whole numbers. Two numbers whose product is 1
are multiplicative inverses, or reciprocals.
Multiplicative Inverse
Property
For all fractions
, where a, b ≠
a b
 1
0,
b a
Multiplicative Property of If
Equality
a = b, then ac = bc
Example 1
2
3
Find the multiplicative inverse of
3
2
2
The multiplicative inverse of
3
is ?? .
2 3
 1
3 2
(reciprocal)
2
3
2
3
Multiply by
to get the product 1
3
2
Example 1b
If there is a mixed number, rename as an improper fraction,
then…
2
4
5
2
Rename the mixed number, 4
5
5
22
22
5
22 5
 1
5 22
as an improper fraction.
Find the multiplicative inverse of
22
5
Multiply 5 by 22to get the product 1.
Example 2
Solve
Write the problem.
You can undo dividing by 7 by multiplying each
side of the equation by 7.
Simplify.
The solution is q = 42.
3
Solve
x  6
4
Example 3
3
x  6
4
4 3
4
 x  6 
3 4
3
6
4
x  ( ) 
1
3
24
x
 8
3
Write the problem.
Multiply each side of the equation by the
reciprocal of
3 , 4.
4 3
Multiply.
Simplify.
The solution is x = -8.
You try…
Find the multiplicative inverse of each number.
A.
B. 6 1

4

Solve
p
 11. Check your solution.
6
Homework

Periods 1,7,8


Page 260-261 #1, 3-14, 38-51
Period 5
 Page 260-261 #30-36, 38-51