Warm Up Solve. 1. x – 16 = 8 2. 7a = 35 3. 4. y + 21 = 31 x 12 = 11 Course 2 4-12 Solving Equations Containing Fractions
Warm Up Solve. 1. x – 16 = 8 2. 7a = 35 3. 4. y + 21 = 31 x 12 = 11 Course 2 4-12 Solving Equations Containing Fractions.
Dec 13, 2015
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Warm UpSolve.
1. x – 16 = 8
2. 7a = 35
3.
4. y + 21 = 31
x12
= 11
Course 2
4-12 Solving Equations Containing Fractions
Learn to solve one-step equations that contain fractions.
Course 2
4-12 Solving Equations Containing Fractions
Gold classified as 24 karat is pure gold, while gold classified as 18 karat is only pure. 3
4
14
The remaining of 18-karat gold is
made up of one or more different metals, such as silver, copper, or zinc. The color of gold varies, depending on the type and amount of each metal added to the pure gold.
Course 2
4-12 Solving Equations Containing Fractions
Course 2
4-12 Solving Equations Containing Fractions
Equations can help you determine the amounts of metals in different kinds of gold. The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to isolate the variable on one side of the equation.
Solve. Write the answer in simplest form.
Additional Example 1A: Solving Equations by Adding or Subtracting
A. x – 37
= 57
x – 37
= 57
x – 37
+ 37
= 57
+ 37
Add to isolate x.
x = 87
=1 17
Simplify.
Course 2
4-12 Solving Equations Containing Fractions
Solve. Write the answer in simplest form.
Additional Example 1B: Solving Equations by Adding or Subtracting
B. 34
+ y = 18
34
+ y = 18
34
+ y– 34
= 18
– 34
Subtract to isolate y.
y = 18
– 68
y = – 58
Find a common denominator.
Subtract.
You can also isolate the variable y by adding the opposite of
Helpful Hint
34 , – 3
4, to both sides.
Course 2
4-12 Solving Equations Containing Fractions
Solve. Write the answer in simplest form.
Additional Example 1C: Solving Equations by Adding or Subtracting
C. 512
+ t = – 38
512
+ t = – 38
=t –9
24– 10
24
t = – 1924
Subtract to isolate t.
Find a common denominator.
Subtract.
Course 2
4-12 Solving Equations Containing Fractions
512
+ t – = – 38
–5
125
12
Solve. Write the answer in simplest form.
Try This: Example 1A
A. x – 38
= 78
x – 38
= 78
x – 38
+ 38
= 78
+ 38
Add to isolate x.
x = 10 8
= 1 14
Simplify.
Course 2
4-12 Solving Equations Containing Fractions
Solve. Write the answer in simplest form.
Try This: Example 1B
B. 38
+ y = 14
38
+ y = 14
38
14
38
+ y– = – 38
Subtract to isolate y.
28
y = – 38
y = – 18
Find a common denominator.
Subtract.
Course 2
4-12 Solving Equations Containing Fractions
Solve. Write the answer in simplest form.
Try This: Example 1C
C. 314
+ t = – 27
314
+ t = – 27
Subtract to isolate t.
Find a common denominator.
Subtract.
Course 2
4-12 Solving Equations Containing Fractions
314
+ t – = – 27
–3
143
14
t = – – 314
414
t = – 714
Simplify.t = – 1 2
Solve. Write the answer in simplest terms.
Additional Example 2A: Solving Equations by Multiplying
A. 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
Remember!38 , you can divide by 3
8or multiply
by its reciprocal, 83
.
Course 2
4-12 Solving Equations Containing Fractions
Additional Example 2B: Solving Equations by Multiplying
B. 4x = 89
89
x =. 14
89
. 141
2
x = 29
4x =
4
Multiply by the reciprocal of 4.
Then simplify.
Solve. Write the answer in simplest terms.
Course 2
4-12 Solving Equations Containing Fractions
Solve. Write the answer in simplest terms.
Try This: Example 2A
A. 34
x = 12
34
x =. 43
12
. 43
2
1
=x 23
Multiply by the reciprocal of .34
Then simplify.
34
= 12
x =
Course 2
4-12 Solving Equations Containing Fractions
Try This: Example 2B
B. 3x = 67
67
x =. 13
67
. 131
2
x = 27
3x =
3
Multiply by the reciprocal of 3.
Then simplify.
Solve. Write the answer in simplest terms.
Course 2
4-12 Solving Equations Containing Fractions
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?
Additional Example 3: Physical Science Application
34
15
Let w represent the total weight of the sample.
34
w = 4 15
34
w · 43
= 4 15
· 43
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.
Course 2
4-12 Solving Equations Containing Fractions
The amount of copper in zinc is of the total weight. If
a sample contains 5 ounces of zinc, what is the total
weight of the sample?
Try This: 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.
Then simplify.
The sample weighs 2113
ounces.
Course 2
4-12 Solving Equations Containing Fractions
Assignment
• Page 246 – 247– # 21 – 44, 48 - 55
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