Download 3 - Math 2 (7th)

PRE-ALGEBRA
Lesson 7-3 Warm-Up
PRE-ALGEBRA
Two-Step Equations with Fractions
and Decimals (7-3)
How do you solve
equations that involve
fractions?
To solve equations involving fractions: 1. clear the equation of
fractions first or undo fractions as you normally would using
properties of equality.
How do you clear
fractions from both
sides of an equation?
To clear fractions from both sides of an equation, multiply all of the terms
by a common denominator (preferably the Lowest Common
Denominator, or LCD)
Example: Solve
3x
x
+
= 17
2
5
Method 1: Use reciprocals (Division Property of Equality).
3x
x
+
2
5 = 17
3
1
x
1x
1
x
+
x
=
17
Rewrite
as
or
2
5
5
5
5 x.
3
1
15
2
x
+
x
=
17
A
common
denominator
of
and
2
5 is 10.
10
10
17
10 x = 17
10 ( 17 x) = 10(17)
17 10
17
x = 10
Combine like terms.
Multiply each side by the reciprocal
of 17 , which is 10 .
10
17 PRE-ALGEBRA
Two-Step Equations with Fractions
and Decimals (7-3)
Method 2: Multiply by the LCD to clear fractions.
3x x
+ 5
2
3x
= 17
x
10( 2 + 5 ) = 10(17)
3x
x
10( 2 ) + 10( 5 ) = 10(17)
15x + 2x = 170
17x = 170
17x
170
=
17
17
x = 10
Multiply each side by 10, a common
multiple of 2 and 5.
Use the Distributive Property.
Multiply.
Combine like terms.
Divide each side by 17.
Simplify.
PRE-ALGEBRA
Two-Step Equations With Fractions and Decimals
LESSON 7-3
Additional Examples
Solve 3 p – 7 = 11.
4
3
p – 7 = 11
4
3
p – 7 + 7 = 11 + 7
4
3
p = 18
4
4 3
4
•
p
=
• 18
3 4
3
1p =
4 • 18 6
31
p = 24
Add 7 to each side.
Simplify.
4
3
Multiply each side by 3 , the reciprocal of 4 .
Divide common factors.
Simplify.
PRE-ALGEBRA
Two-Step Equations With Fractions and Decimals
LESSON 7-3
Additional Examples
(continued)
Check:
3
p – 7 = 11
4
3
(24) – 7
4
11
Replace p with 24.
3 • 24 6
–7
4 1
11
Divide common factors.
18 – 7
11
Simplify.
11 = 11
PRE-ALGEBRA
Two-Step Equations With Fractions and Decimals
LESSON 7-3
Additional Examples
Solve 1 y + 3 = 2 .
2
3
1
2
y
+
3
=
2
3
1
2
6 2y+3 = 6 3
1
2
6•2y+6•3=6 3
3y + 18 = 4
3y + 18 – 18 = 4 – 18
3y = –14
3y
–14
=
3
3
2
y = –4 3
Multiply each side by 6, the LCM of 2 and 3.
Use the Distributive Property.
Simplify.
Subtract 18 from each side.
Simplify.
Divide each side by 3.
Simplify.
PRE-ALGEBRA
Two-Step Equations with Fractions
and Decimals (7-3)
How do you clear solve To solve equations involving decimals, it might be easier to clear the
equations that involve equation decimals first.
decimal?
How do you clear
To clear decimals from both sides of an equation, multiply all of the terms by
decimals?
by the power of 10 that would move the decimal with the greatest number of
decimal places to the end to make a whole number.
Example: Solve 0.6a + 18.65 = 22.85.
100(0.6a + 18.65) = 100(22.85)
100(0.6a) + 100(18.65) = 100(22.85)
60a + 1865 = 2285
60a + 1865 = 2285
- 1865 - 1865
60a
= 420
60a
420
=
60
60
a = 7
The greatest number of decimal
places is two places, so multiply each
side by 102 or 100.
Use the Distributive Property.
Simplify.
Subtract 1865 from each side.
Simplify.
Divide each side by 60.
Simplify.
PRE-ALGEBRA
Two-Step Equations With Fractions and Decimals
LESSON 7-3
Additional Examples
Suppose your cell phone plan is $30 per month plus
$.05 per minute. Your bill is $36.75. Use the equation
30 + 0.05x = 36.75 to find the number of minutes on your bill.
30 + 0.05x = 36.75
100(30) + 100(0.05x) = 100(36.75) The greatest number of decimal places is
two places, so multiply each side by 102 or 100
3000 – 3000 + 5x = 3675 – 3000 Simplify and subtract 3000 from each side.
5x = 675
5x
5
=
675
5
x = 135
Simplify.
Divide each side by 0.05.
Simplify.
There are 135 minutes on your bill.
PRE-ALGEBRA
Two-Step Equations With Fractions and Decimals
LESSON 7-3
Lesson Quiz
Solve each equation.
1.
1
d + 13 = 20
6
42
4. 0.07x + 0.03 = 0.38
5
2.
3
(s – 8) = 9
5
23
3. 5 +
2c
= 14
4
18
5. 0.015w – 1.85 = 1.615
231
PRE-ALGEBRA