Transcript Ch. 7.4 Equations with Fractions and Decimals

Ch. 7.4 Equations with
Fractions and Decimals
To solve an equation with fractions:
• Find the least common denominator (LCD)
of all fraction terms on both sides of the
equation.
• Multiply each term on both sides of the
equation by the LCD. This should remove
all fractions from the equation.
• Solve the resulting equation using the
methods from earlier sections.
Solve:
• LCD = 20, so multiply
both sides by 20.
3 x 45

4 20
 3x 
 45 
20    20  
 4 
 20 
5  3x   1 45 
15 x  45
15 x 45

15 15
x3
3 x 13
Solve:  
4 6 12
• LCD = 12, so
multiply each
term by 12
3
 x
 13 
12    12    12  
4
6
 12 
3  3  2  x   113
9  2 x  13
9  2 x  9  13  9
2x  4
x2
Solve: 2 x  4  x
9
6
 2x 
 x
18    18  4   18  
 9 
6
4 x  72  3 x
4 x  72  4 x  3 x  4 x
72   x
72  x
Solving Linear Equations
Tip: Equations containing fractions and decimal numbers can lead
to messy computations. To avoid such messy computations, be
sure to follow these tips.
• When clearing an equation containing fractions, be sure to
multiply every term on each side of the equation by the LCD.
• When clearing an equation containing decimals, be sure to
multiply every term on each side of the equation by an
appropriate power of 10. Choose the smallest exponent on 10
needed to eliminate the decimals.
Solving an Equation with Fractions
5 m – 10 =
8
8
8
5 m
8
3 m + 1 m
4
2
5 m – 10
8
=
8
3 m + 1 m
4
2
– 8 10
=
8
3 m
4
+
5m – 80 = 6m + 4m
Now use the four steps to solve this
equivalent equation.
8
Multiply by LCD: 8.
1 m
2
Distribute.
Multiply.
5m – 80 = 6m + 4m
Step 1
5m – 80 = 10m
Step 2
5m – 80 – 5m = 10m – 5m
Step 3
– 80 = 5m
– 80 = 5m
5
5
– 16 = m
Combine terms.
Subtract 5m.
Combine terms.
Divide by 5.
Step 4
Check by substituting –16 for m in the original equation.
5 m – 10 =
8
5 (–16) – 10 =
8
3 m + 1 m
4
2
3 (–16) + 1 (–16)
4
2
–10 – 10 = –12 – 8
–20 = –20
The solution to the equation is –16.
?
Let m = –16.
?
Multiply.
True
Solving an Equation with Decimals
0.2v – 0.03 ( 11 + v ) = – 0.06 ( 31 )
20v – 3 ( 11 + v ) = – 6 ( 31 )
Multiply by 100.
Step 1 20v – 3 ( 11) – 3 ( v ) = – 186
Distribute.
20v – 33 – 3v = – 186
Multiply.
17v – 33 = – 186
Step 2
Step 3
Combine terms.
17v – 33 + 33 = – 186 + 33
Add 33.
17v = – 153
Combine terms.
17v
– 153
=
17
17
Divide by 17.
v = –9
Check to confirm that
– 9 is the solution.