1. 3.6 Clearing Fractions and Decimals
Algebra
3.6
Clearing Fractions and Decimals

2. Clearing the fractions
It is easier to deal with whole numbers in an equation than with fractions.
To clear the fractions out of the equation, follow these STEPS:
Identify all the fractions in the equation that are not inside grouping symbols.
Find the LCD of these fractions.
Multiply both sides of the equation by the LCD.
Solve as usual.

3. Clearing the fractions

4. Clearing the fractions
To clear the fraction, multiply
both sides of the equation by the denominator of 5.

5. Clearing the fractions
To clear the fraction, multiply
both sides of the equation by the denominator of 5.

6. Clearing the fractions
To clear the fraction, multiply
both sides of the equation by the denominator of 5.
The fraction is cleared. Solve as usual

7. Clearing the fractions
To clear the fraction, multiply
both sides of the equation by the denominator of 5.
The fraction is cleared. Solve as usual

8. Clearing the fractions
To clear the fraction, multiply
both sides of the equation by the denominator of 5.
The fraction is cleared. Solve as usual

9. Clearing the fractions
Find the LCD of the fractions in the equation. What is the LCD of 5 and 2?

10. Clearing the fractions
Find the LCD of the fractions in the equation. What is the LCD of 5 and 2?
Multiply both sides of the equation by the LCD of 10.
You must distribute to each term on both sides!

11. Clearing the fractions
Find the LCD of the fractions in the equation. What is the LCD of 5 and 2?
Multiply both sides of the equation by the LCD of 10.
You must distribute to each term on both sides!
The fractions are cleared. Now, solve as usual.

12. Clearing the fractions
Find the LCD of the fractions in the equation. What is the LCD of 5 and 2?
Multiply both sides of the equation by the LCD of 10.
You must distribute to each term on both sides!
The fractions are cleared. Now, solve as usual.

13. Clearing the fractions

14. Clearing the fractions
The LCD of 3 and 4 is 12

15. Clearing the fractions
The LCD of 3 and 4 is 12
Multiply both sides of the equation by the LCD of 12.

16. Clearing the fractions
The LCD of 3 and 4 is 12
Multiply both sides of the equation by the LCD of 12.
The fractions are cleared. Now, solve as usual.

17. Clearing the fractions
The LCD of 3 and 4 is 12
Multiply both sides of the equation by the LCD of 12.
The fractions are cleared. Now, solve as usual.

18. Clearing the fractions
The LCD of 3 and 4 is 12
Multiply both sides of the equation by the LCD of 12.
The fractions are cleared. Now, solve as usual.

19. Clearing the decimals
It is easier to deal with whole numbers in an equation than with decimals.
To clear the decimals out of the equation, follow these STEPS:
Identify all the decimals in the equation that are not inside grouping symbols.
Find the term with the most digits to the right of the decimal point.
Multiply both sides of the equation by the power of 10 that will make that term a whole number.
Solve as usual.

20. Clearing the decimals
4x –.24 = .56 – .8x There are 2 places to the right of the decimal point in 2 of the terms. So, multiply both sides of the equation by 100.
100 [4x ] = [.56 – .8x] 100
400x – 24 = 56 – 80x
480x = 80
x = 1/6

21. Clearing the decimals 1000 [.005x + .02] = [.01x – .025] 1000
.005x = .01x – There are 3 places to the right of the decimal point so multiply both sides of the equation by
1000 [.005x ] = [.01x – .025] 1000
5x = 10x – 25
45 = 5x
x = 9

22. Try these 1.

23. Try these 1.
Solution: x = -6

24. Try these 1.
Solution: x = -6
. 75x + 5 = 2.5x – 2 2.

25. Try these 1.
Solution: x = -6
. 75x + 5 = 2.5x – 2 2.
Solution: x = 4

26. Homework
Next year do some more on the hw with binomials In the numberator