PRE-ALGEBRA

PRE-ALGEBRA

Lesson 7-3 Warm-Up

PRE-ALGEBRA

How do you solve equations that involve fractions?

How do you clear fractions from both sides of an equation?

To solve equations involving fractions: 1. clear the equation of fractions first or undo fractions as you normally would using properties of equality.

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 + = 173x2

x5

Method 1: Use reciprocals (Division Property of Equality).

+ = 173x2

x5

x + x = 17 Rewrite as or x. 32

15

x + x = 17 A common denominator of and is 10. 1510

210

32

15

x = 17 Combine like terms. 1710

( x) = (17) Multiply each side by the reciprocal of , which is .

1710

1017

1017 17

101017 x = 10

x5

1x5

15

Two-Step Equations with Fractions

and Decimals (7-3)

PRE-ALGEBRA

15x + 2x = 170 Multiply.

17x = 170 Combine like terms.

x = 10 Simplify.

Method 2: Multiply by the LCD to clear fractions.

+ = 173x2

x5

10( + ) = 10(17) Multiply each side by 10, a commonmultiple of 2 and 5.

3x2

x5

10( ) + 10( ) = 10(17) Use the Distributive Property.3x2

x5

= Divide each side by 17.17x17

17017

Two-Step Equations with Fractions

and Decimals (7-3)

PRE-ALGEBRA

Solve p – 7 = 11.

p – 7 = 1134

Add 7 to each side.p – 7 + 7 = 11 + 734

Simplify.p = 1834

p =34

43 •

43 • 18 Multiply each side by , the reciprocal of .

34

43

1p =4 • 18

3 1

6Divide common factors.

p = 24 Simplify.

34

Two-Step Equations With Fractions and DecimalsLESSON 7-3

Additional Examples

PRE-ALGEBRA

(continued)

Simplify.18 – 7 11

11 = 11

Check: p – 7 = 1134

(24) – 7 11 Replace p with 24.34

– 7 11 Divide common factors.3 • 24

4

Two-Step Equations With Fractions and DecimalsLESSON 7-3

Additional Examples

1

6

PRE-ALGEBRA

Solve y + 3 = .

y + 3 = 12

23

Multiply each side by 6, the LCM of 2 and 3.6 y + 3 = 12

6 23

3y + 18 – 18 = 4 – 18 Subtract 18 from each side.

3y = –14 Simplify.

3y + 18 = 4 Simplify.

Use the Distributive Property.6 • y + 6 • 3 =12 6

23

Divide each side by 3.3y3

–143=

Simplify.y = –423

23

12

Two-Step Equations With Fractions and DecimalsLESSON 7-3

Additional Examples

PRE-ALGEBRA

Example: Solve 0.6a + 18.65 = 22.85.100(0.6a + 18.65) = 100(22.85) The greatest number of decimal

places is two places, so multiply each

side by 102 or 100.

100(0.6a) + 100(18.65) = 100(22.85) Use the Distributive Property.

60a + 1865

= 2285 Simplify. 60a + 1865 = 2285

- 1865 - 1865 Subtract 1865 from each side. 60a = 420

Simplify.

a =7 Simplify.

= Divide each side by 60.

60a60

42060

How do you clear solve equations that involve decimal?

How do you clear decimals?

To solve equations involving decimals, it might be easier to clear the equation decimals first.

To clear decimals from both sides of an equation, multiply all of the terms by 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.

Two-Step Equations with Fractions

and Decimals (7-3)

PRE-ALGEBRA

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.

There are 135 minutes on your bill.

30 + 0.05x = 36.75

x = 135 Simplify.

3000 – 3000 + 5x = 3675 – 3000 Simplify and subtract 3000 from each side.

5x = 675 Simplify.

Divide each side by 0.05.=675

55x5

Two-Step Equations With Fractions and DecimalsLESSON 7-3

Additional Examples

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.

PRE-ALGEBRA

Solve each equation.

1. d + 13 = 20 2. (s – 8) = 9 3. 5 + = 14

4. 0.07x + 0.03 = 0.38 5. 0.015w – 1.85 = 1.615

16

35

2c4

42 23 18

5 231

Two-Step Equations With Fractions and DecimalsLESSON 7-3

Lesson Quiz