Ch. 7.4 Equations with Fractions and Decimals

To solve an equation with fractions:

• Find the least common denominator (LCD) of all fraction terms on both sides of the equation.

• Multiply each term on both sides of the equation by the LCD. This should remove all fractions from the equation.

• Solve the resulting equation using the methods from earlier sections.

Solve:

• LCD = 20, so multiply both sides by 20.

3 45

4 20

x

3 4520 20

4 20

5 3 1 45

1

1

5 45

15

53

5

5

1

4

x

x

x

x

x

Solve:

• LCD = 12, so multiply each term by 12

3 13

4 6 12

x

3 1312 12 12

4 6 12

3 3 2 1 13

9 2 13

9 2 13

2 4

2

9 9

x

x

x

x

x

x

Solve:

18 18 18

24

9 62

49 6

4 72 3

4 72 3

72

72

4 4

x x

x x

x x

x x

x

x

x x

Tip: Equations containing fractions and decimal numbers can lead to messy computations. To avoid such messy computations, be

sure to follow these tips.

• When clearing an equation containing fractions, be sure to multiply every term on each side of the equation by the LCD.

• When clearing an equation containing decimals, be sure to multiply every term on each side of the equation by an appropriate power of 10. Choose the smallest exponent on 10 needed to eliminate the decimals.

Solving Linear Equations

Solving an Equation with Fractions

Multiply by LCD: 8.

58

m 34

m 12

m– 10 = +

58

m 34

m 12

m– 10 = + 8 8

58

m 34

m 12

m– 10 = +

8 88 8 Distribute.

5m – 80 = 6m + 4m Multiply.

Now use the four steps to solve this equivalent equation.

Combine terms.

Subtract 5m.

5m – 80 = 6m + 4m

Divide by 5.

Step 1

Step 2

Step 3

5m – 80 = 10m

5m – 80 – 5m = 10m – 5m

– 80 = 5m Combine terms.– 80 5m=

5 5

– 16 = m

Check by substituting –16 for m in the original equation.Step 4

? Let m = –16.

? Multiply.

True

The solution to the equation is –16.

58

m 34

m 12

m– 10 = + 5

8(–16) 3

4(–16) 1

2(–16)– 10 = +

–10 – 10 = –12 – 8

–20 = –20

Solving an Equation with Decimals

0.2v – 0.03 ( 11 + v ) = – 0.06 ( 31 )

Multiply by 100.20v – 3 ( 11 + v ) = – 6 ( 31 )

Distribute.20v – 3 ( 11) – 3 ( v ) = – 186

20v – 33 – 3v = – 186 Multiply.

17v – 33 = – 186 Combine terms.

17v – 33 + 33 = – 186 + 33 Add 33.

17v = – 153 Combine terms.

Divide by 17.

v = – 9

17 1717v – 153

=

Step 1

Step 2

Step 3

Check to confirm that – 9 is the solution.