Holt CA Course 1 4-6 Solving Equations Containing Fractions AF1.1 Write and solve one-step linear...
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Transcript of Holt CA Course 1 4-6 Solving Equations Containing Fractions AF1.1 Write and solve one-step linear...
Holt CA Course 1
4-6 Solving Equations Containing Fractions
AF1.1 Write and solve one-step linear equations in one variable.Also covered: NS2.1, NS2.2,
NS2.4
California Standards
Holt CA Course 1
4-6 Solving Equations Containing Fractions
The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to get the variable by itself on one side of the equation.
Holt CA Course 1
4-6 Solving Equations Containing Fractions
Solve. Write the answer in simplest form.
Example 1A: Solving Equations by Adding or Subtracting
x – 37
= 57
x – 37
= 57
x – 37
+ 37
= 57
+ 37
x = 87
=1 17
Simplify.
37
Since is subtracted from x, 37
add to both sides.
Holt CA Course 1
4-6 Solving Equations Containing Fractions
Solve. Write the answer in simplest form.
Example 1B: Solving Equations by Adding or Subtracting
512
+ t =38
38
+ t = 512
Find a common denominator.
Subtract.
38
+ t – =5
12–
38
38
t = 1024
– 924
t = 124
Since is added to t, 38
38
subtract from both sides.
Holt CA Course 1
4-6 Solving Equations Containing Fractions
Solve. Write the answer in simplest form.
Example 2A: Solving Equations by Multiplying
38
x = 14
38
x =83
14
83
2
1
=x 23
Multiply by the reciprocal of .38
Then simplify.
38
= 14
x =
To undo multiplying by
Caution!38
, you can divide by 38
or multiply by its reciprocal, 83 .
Holt CA Course 1
4-6 Solving Equations Containing Fractions
Additional Example 2B: Solving Equations by Multiplying
4y = 8989
4y = 14
89
141
2
y = 29
4y = Multiply by the reciprocal of 4.
Then simplify.
Solve. Write the answer in simplest form.
Holt CA Course 1
4-6 Solving Equations Containing FractionsExample 3: Physical Science Application
The amount of copper in brass is of the total weight. If a
sample contains 4 ounces of copper, what is the total
weight of the sample?
34
15
Let w represent the total weight of the sample.34
w = 4 15
34
w 43
= 4 15 4
3
w = 215
43
7
1
w = 285
or 5 35
Write an equation.
Multiply by the reciprocal of 34
·
Write 4 15
as an improperfraction.
Then simplify.
The sample weighs 535
ounces.
Holt CA Course 1
4-6 Solving Equations Containing Fractions
Solve. Write the answer in simplest form.
Check It Out! Example 1
x – 38
= 78
x – 38
= 78
x – 38
+ 38
= 78
+ 38
x = 10 8
= 1 14
Simplify.
Since is subtracted from x, add to both sides.
38
38
Holt CA Course 1
4-6 Solving Equations Containing Fractions
Check It Out! Example 2
3y = 6767
y = 13
67
131
2
y = 27
3y =
3
Multiply by the reciprocal of 3.
Then simplify.
Solve. Write the answer in simplest form.
Holt CA Course 1
4-6 Solving Equations Containing Fractions
The amount of copper in zinc is of the total weight. If a
sample contains 5 ounces of copper, what is the total
weight of the sample?
Check It Out! Example 314
13
Let w represent the total weight of the sample.14
w = 5 13
14
w 41
= 5 13
41
w = 163
41
w = 643
or 21 13
Write an equation.
Multiply by the reciprocal of 14
·
Write 5 13
as an improperfraction.
Multiply.
The sample weighs 2113
ounces.