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2.3b
The Multiplication Principle of Equality
3. Use the multiplication principle to clear
fractions and decimals from equations.
Review: Terms
3x  2  12
Three terms
2
2
x8  x
5
3
Three terms
2 x  3  5  9
Three terms
Review: Terms
1
5 3 1
x
  x
3
12 4 2
Four terms
2
1
y  18  2y  3  y  3
9
3
Four terms
2  32  6 z   4z  1  18
Four terms
Review
1

5 
 5
1
1

7 
7
1
3

12   9
 4 1
3
2

6   4
 3 1
2
Clearing Fractions
Distributive Property
5 8
13


7 7
7
1 5 1 8
5 8
13 


7    7 
7 7
7
1  13 
7   7   7 
 71
 71
 71 
5  8  13
Equivalent equation but no fractions!!!
Multiply EVERY TERM by the LCD, even if the term
does not contain a fraction.
Only works with EQUATIONS!
5 8

6 9
Expression.
Can’t clear the fractions.
Clearing Fractions
2x  1 1
4

6
9
To Solve Linear Equations
1. Clear the fractions.
2. Simplify both sides of the equation as needed.
a. Distribute to clear parentheses.
b. Combine like terms.
3. Use the addition principle so that all variable terms
are on one side of the equation.
4. Use the addition principle so that all constants are
on the other side.
5. Use the multiplication principle to isolate the
variable.
1. Clear fractions.
2. Simplify
3. Move the variable terms.
4. Move the constants.
5. Isolate the variable.
Clearing Fractions
2x  1 1
4

6
9
LCD: 18
Terms: 3
2  1
 2x  1 
184  18
  18 
 61 
 91
3
18  4   32 x  1   21 
72  6x  3  2
 6x  69  2
 69  69
 6x  67
6
6
67
x
6
Goal: Denominators = 1
Take the time to rewrite!
Clearing Fractions
LCD: 12
1
3 5
x   x 2
3
4 6
Terms: 4
1. Clear fractions.
2. Simplify
3. Move the variable terms.
4. Move the constants.
5. Isolate the variable.
4
1  3 3 2 5 

12 x   12   12 x   122
 31 
 41
 61 
4 x  9  10 x  24
 10 x
 10 x
 6x  9  24
9 9
 6x  33
6 6
33
x 
6
11

2
4 x  9  10x  24
 4x
 4x
 9  6x  24
1. Clear fractions.
2. Simplify
3. Move the variable terms.
4. Move the constants.
5. Isolate the variable.
Clearing Fractions
LCD: 10
1
3
2
y  3  
y  5   y
5
10
5
Terms: 3
2
1 3 
2 2
 1
10 y  3  10 y  5  10 y
 5 1
 10 
5
1
1
2  y  3   3 y  5   4 y
2y  6  3y  15  4y
2y  6  15  y
y
y
3y  6  15
6 6
3y  21
3y  21
3
3
y7
Decimals
25
.25 
100
1
.1 
10
55
.055 
1000
Decimals are another way to write
fractions!
Multiplying Powers of 10
2010   200
20100   2000
210  
20
2100   200
.210  
2
.2100   20
.0210   .2
Move decimal point one place.
.02100   2
Move decimal point two places.
Count the number of zeros and
move the decimal that many places.
1. Clear fractions.
2. Simplify
3. Move the variable terms.
4. Move the constants.
5. Isolate the variable.
Clearing Decimals
0.0625  0.27 x  0.304  x 
6 25   27 x  30  4  x 
150  27 x  304  x 
150  27x  120  30x
 30 x
 30 x
150  3x  120
 150
 150
 3x  30
3
3
x  10
LCD: 100
Terms: 3
Clearing Decimals
10
0.5  t  6   10.4  0.41  t 
5  10 t  6   104  4 1  t 
1. Clear fractions.
2. Simplify
3. Move the variable terms.
4. Move the constants.
5. Isolate the variable.
LCD: 10
Terms: 4
5  10t  60  104  4  4t
 10t  65  100  4t
 4t
 4t
 14t  65  100
 65
If the problem starts with decimals,
leave the answer in decimal form.
 65
 14t  35
 14  14
35
5
t
   2.5
14
2
Solve. 0.8 – 4(a – 1) = 0.2 + 3(4 – a)
a)  10
b) 7.4
c) 8.6
d) 20.6
2.3
Solve. 0.8 – 4(a – 1) = 0.2 + 3(4 – a)
a)  10
b) 7.4
c) 8.6
d) 20.6
2.3