How to solve for variable when it is in a fraction

Question

Solve for Y

y/5 + y/3 = 8/9

Answer 1

There are two ways we can solve this problem, (1) using the least common denominator or (2) getting rid of the fractions.

(1) Using the least common denominator:

The least common denominator for 5, 3, 9 would be 45 because 5 x 9 = 45. To change the denominator to 45, we have to multiply the first fraction by 9/9, the second fraction by 15/15, and the third fraction by 5/5, so we get:

9y/45 + 15y/45 = 40/45

Then, we can combine the fractions on the left:

24y/45 = 40/45

Multiply both sides by 45:

24y = 40

y = 40/24 = 5/3

(2) Getting rid of the fractions:

Multiply the whole equation by 45

45(y/5 + y/3 = 8/9)

9y + 15y = 40

24y = 40

y = 40/24 = 5/3

Both methods are efficient and get you the right answer, which is y = 5/3.

Answer 2

y/5+y/3=8/9

LCD=15 (for the left side)

y/5=3y/15 and y/3=5y/15

3y/15+5y/15=8/9

8y/15=8/9

multiply both sides of the equation by 15/8

(15/8)(8/15)y=(15/8)(8/9)

y=15/9 (the 8s cancel)

simplify

y=5/3

check your work

Answer 3

Remove the fractions by multiplying by the least common multiple of 3, 5, and 9. That number is 9 × 5, or 45:

9y + 15y = 40

Combine like terms:

24y = 40

Divide by the coefficient of y:

y = 5/3

Plug this value back into the original equation to check. You can use a calculator and compare the decimal fractions to verify that this is the correct answer.