Solve 5/6 x-1/2=7/8

Question

Solve 5/6 x-1/2=7/8

Answer 1

First you need to find a common denominator for the 3 fractions given:

 

5/6  

1/2

7/8

 

Ask yourself, what number is divisible by 6, 2, and 8?

 

The answer is 24, because

 

6 x 4= 24

2 x 12= 24

8 x 3= 24

 

After you find the common denominator, multiply the numerators by the same number you multiplied the denominators with to get your common denominator:

 

5 x 4= 20

1 x 12= 12

7 x 3 = 21

 

Your new equation should be rewritten as follows:

 

20/24x - 12/24 = 21/24

 

Because all the denominators are 24, you can omit them:

 

20x - 12 = 21

 

Solve for x by isolating it -- get rid of the 12 by adding 12 on both sides of the equal sign so that they cancel each other out:

 

20x - 12 = 21

     + 12  +12

____________

20x = 33

 

 

To isolate x from 20, divide by 20 on both sides of the equal sign:

 

 20x         33

____  =  ____

 

 20          20

 

 

 

20x/20= 1x or just x, therefore -- 

 

x = 33/20, however 33/20 can be simplified by writing it as a mixed number:

 

1) Divide -- how many times does 20 go into 33?

 

                              1 time, with a remainder of 13.

 

 

2) Rewrite it with the whole number (number of times denominator goes into numerator evenly) = 1

    Take the remainder and make it the numerator = 13

    Take the denominator of the improper fraction and make it the denominator of the mixed number = 20

 

Your answer as a mixed number is                      x = 1 ¹³⁄²°

Your answer as an improper fraction is                x = 33/20

 

 

 

 

 

 

 

Answer 2

If you get a common denominator of 24, you can re-write the equation as...

 

20x-12=21

 

Then solve for x, first by adding 21...

 

20x = 33

x = 33/20