Transcript Solving equations with Mixed Numbers

Solving Equations Containing
4-12
Fractions
Warm Up
Problem of the Day
Lesson Presentation
Course 2
4-12 Solving Equations Containing Fractions
Warm Up
Solve.
1. x – 16 = 8 x = 24
2. 7a = 35
a=5
3. x = 11
x = 132
12
4. y + 21 = 31 y = 10
Course 2
4-12 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
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 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.
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.
Course 2
4-12 Solving Equations Containing Fractions
Additional Example 1A: Solving Equations by Adding
or Subtracting
Solve. Write the answer in simplest form.
3
5
A. x – 7 = 7
x– 3 =5
7
7
x – 3 + 3= 5+ 3
7
7 7 7
1
x = 8 =1
7
7
Course 2
Add to isolate x.
Simplify.
4-12 Solving Equations Containing Fractions
Additional Example 1B: Solving Equations by Adding
or Subtracting
Solve. Write the answer in simplest form.
B. 3 + y = 1
4
8
3 +y = 1
4
3 + y– 3
4
4
y
y
8
= 1–
8
= 1 –
8
=– 5
8
3
4
6
8
Subtract to isolate y.
Find a common denominator.
Subtract.
Helpful Hint
You can also isolate the variable y by adding the opposite
of 3 , – 3 , to both sides.
4
Course 2
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4-12 Solving Equations Containing Fractions
Additional Example 1C: Solving Equations by Adding
or Subtracting
Solve. Write the answer in simplest form.
5
3
C. 12 + t = – 8
5 + t =– 3
8
12
3 – 5
5
5
–
+ t–
=
12
8
12
12
9 – 10
24 24
19
t =–
24
t =–
Course 2
Subtract to isolate t.
Find a common denominator.
Subtract.
4-12 Solving Equations Containing Fractions
Try This: Example 1A
Solve. Write the answer in simplest form.
3
7
A. x – 8 = 8
x– 3 =7
8
8
x – 3 + 3= 7+ 3
8
8 8 8
1
x = 10 = 1
4
8
Course 2
Add to isolate x.
Simplify.
4-12 Solving Equations Containing Fractions
Try This: Example 1B
Solve. Write the answer in simplest form.
B. 3 + y = 1
8
4
3 +y = 1
8
4
3 + y– 3 = 1 –
4
8
8
y = 2–
8
y = –1
8
Course 2
3
8
3
8
Subtract to isolate y.
Find a common denominator.
Subtract.
4-12 Solving Equations Containing Fractions
Try This: Example 1C
Solve. Write the answer in simplest form.
3
2
C. 14 + t = – 7
3 + t =– 2
7
14
2 – 3
3
3
–
+ t–
=
14
7
14
14
4 – 3
t=–
14
14
7
t =–
14
1
t =–
2
Course 2
Subtract to isolate t.
Find a common denominator.
Subtract.
Simplify.
4-12 Solving Equations Containing Fractions
Additional Example 2A: Solving Equations by
Multiplying
Solve. Write the answer in simplest terms.
3
1
x
=
A. 8
4
3
1
x =
8
4
3x . 8= 1 . 8 2
8
3 41 3
x =2
3
Multiply by the reciprocal of 3 .
8
Then simplify.
Remember!
To undo multiplying by 3 , you can divide by 3 or multiply
8
8
8
by its reciprocal, .
3
Course 2
4-12 Solving Equations Containing Fractions
Additional Example 2B: Solving Equations by
Multiplying
Solve. Write the answer in simplest terms.
B. 4x = 8
9
4x = 8
9
2
.
1
=8 .1
4x
4 9 41
x= 2
9
Course 2
Multiply by the reciprocal of 4.
Then simplify.
4-12 Solving Equations Containing Fractions
Try This: Example 2A
Solve. Write the answer in simplest terms.
3
1
x
=
A. 4
2
3
1
x =
4
2
3x . 4= 1 . 4 2
4
3 21 3
x =2
3
Course 2
Multiply by the reciprocal of 3 .
4
Then simplify.
4-12 Solving Equations Containing Fractions
Try This: Example 2B
Solve. Write the answer in simplest terms.
B. 3x = 6
7
3x = 6
7
2
.
1
=6 .1
3x
3 7 31
x= 2
7
Course 2
Multiply by the reciprocal of 3.
Then simplify.
4-12 Solving Equations Containing Fractions
Additional 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
Course 2
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4-12 Solving Equations Containing Fractions
Try This: Example 3
1
The amount of copper in zinc is 4 of the total weight. If
a sample contains 5 1 ounces of zinc, what is the total
3
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
Course 2
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4-12 Solving
Containing
Insert Equations
Lesson Title
Here Fractions
Lesson Quiz
Solve. Write each answer in simplest form.
1. x – 3 = 5
8
1
8
2. y + 7 = 19 5
16 32 32
3. x = 3 12 or 1 5
4
7
7
7
4. 3 x = 1 1 16 or 1 7
9
3 9
4
5. Over the course of a week, Marissa ate some
apples from a basket on the table. She left 20 apples
in the basket. This was five-eights the number of
apples her mother had picked earlier in the week.
How many apples did her mother pick? 32
Course 2