Download 3.8 Solving Equations Containing Fractions

3-8 Solving Equations Containing Fractions
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
3-8 Solving Equations Containing Fractions
Warm Up
Solve.
1. x – 16 = 8
x = 24
2. 7a = 35
a=5
3. x = 11
x = 132
4. y + 21 = 31
y = 10
12
3-8 Solving Equations Containing Fractions
Learn to solve one-step equations that
contain fractions.
3-8 Solving Equations Containing Fractions
Gold classified as 24 karat is pure
gold, while gold classified as 18
karat is only 3 pure.
4
The remaining 1 of 18-karat gold is
4
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.
3-8 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.
3-8 Solving Equations Containing Fractions
Example 1: Solving Equations by Adding or
Subtracting
A. Solve. Write the answer in simplest form.
x – 3= 5
7
7
x– 3 =5
7
7
x – 3 + 3= 5+ 3
7
7 7 7
1
x = 8 =1
7
7
Use the Addition Property of
Equality.
Add.
3-8 Solving Equations Containing Fractions
Example 1: Solving Equations by Adding or
Subtracting
B. Solve. Write the answer in simplest form.
4
-1
+r=
9
2
4 + r = -1
9
2
Use the Subtraction Property
4 + r – 4 = -1 – 4
of Equality.
2
9
9
9
r = -9 – 8
Find a common denominator.
18 18
17
r = – 18
Helpful Hint
Subtract.
You can also isolate the variable r by adding the
4 , – 4 , to both sides.
opposite of
9
9
3-8 Solving Equations Containing Fractions
Check It Out
C. Solve. Write the answer in simplest form.
3
7
x – 8= 8
x– 3 =7
8
8
x – 3 + 3= 7+ 3
8
8 8 8
1
x = 10 = 1
4
8
Use the Addition Property of
Equality.
Simplify.
3-8 Solving Equations Containing Fractions
Check It Out
D. Solve. Write the answer in simplest form.
3
– 2
+
t
=
14
7
3 + t =– 2
7
14
3
3
3
+ t–
=– 2 –
14
14
14
7
4 – 3
t=–
14
14
7
t =–
14
1
t =–
2
Use the Subtraction Property
of Equality.
Find a common denominator.
Subtract.
Simplify.
3-8 Solving Equations Containing Fractions
3-8 Solving Equations Containing Fractions
Day #2
3-8 Solving Equations Containing Fractions
Problem of the Day
Write 15 positive integers less than
1,000 with digits that, when added
together, total 4.
4, 13, 22, 31, 40, 103, 112, 121,
130, 202, 211, 220, 310, 400
3-8 Solving Equations Containing Fractions
Example 2: Solving Equations by Multiplying
A. Solve. Write the answer in simplest terms.
3x
1
=
8
4
3 =1
x
3.
8
4
Multiply
by
the
reciprocal
of
8
3x . 8= 1 . 8 2
Then simplify.
8
3 41 3
x =2
3
Caution!
To undo multiplying by 3 , you can divide by 3
8
or multiply by its reciprocal, 8 .
3
8
3-8 Solving Equations Containing Fractions
Example 2: Solving Equations by Multiplying
B. Solve. Write the answer in simplest terms.
4x = 8
9
4x = 8
9
2
.
1
=8 .1
4x
4 9 41
x= 2
9
Multiply by the reciprocal of 4.
Then simplify.
3-8 Solving Equations Containing Fractions
Check It Out
C. Solve. Write the answer in simplest terms.
3x
1
=
4
2
3 =1
x
4
2
3x . 4= 1 . 4 2
4
3 21 3
x =2
3
Multiply by the reciprocal of 3 .
4
Then simplify.
3-8 Solving Equations Containing Fractions
Check It Out
D. Solve. Write the answer in simplest terms.
3x = 6
7
3x = 6
7
2
.
1
=6 .1
3x
3 7 31
x= 2
7
Multiply by the reciprocal of 3.
Then simplify.
3-8 Solving Equations Containing Fractions
End Day #2
3-8 Solving Equations Containing Fractions
Day #3
3-8 Solving Equations Containing Fractions
Example 3: Physical Science Application
The amount of copper in brass is 3 of the total weight.
4
If a sample contains 4 1 ounces of copper, what is the
5
total weight of the sample?
Let w represent the total weight of the sample.
3w = 41
5
4
Write an equation.
3 w ·4
= 41· 4
4
3
5 3
7
w = 21 · 4
5
31
Multiply by the reciprocal of 3 ·
1
Write 4 as an improper
5
fraction.
w = 28 or 5 3
5
5
Then simplify.
The sample weighs 5 3 ounces.
5
4
3-8 Solving Equations Containing Fractions
Check It Out
The amount of copper in zinc is 1
4 of the total weight. If
a sample contains 5 1 ounces of copper, what is the
3
total weight of the sample?
Let w represent the total weight of the sample.
1w = 51
3
4
Write an equation.
1 w ·4
= 51· 4
4
1
3 1
Multiply by the reciprocal of 1 ·
1
Write 5 as an improper
3
w = 16 · 4
3
fraction.
1
w = 64 or 21 1
3
3
Then simplify.
The sample weighs 21 1 ounces.
3
4
3-8 Solving Equations Containing Fractions
Lesson Quizzes
3-8 Solving Equations Containing Fractions
Lesson Quiz
Solve. Write each answer in simplest form.
1. x – 3 = 5
8
8
2. y + 7 = 19
16 32
3. x4 = 3
7
4. 3 x = 1 1
3
4
1
5
32
12 or 1 5
7
7
16 or 1 7
9
9
5. During the week, Marissa ate some apples from a
basket. She left 20 apples. This was five-eights the
number of apples she had bought earlier in the week. How
many apples did she buy? 32