How does one simplify...?

Question

y/6 + y/12 = 14/4?

or how about:

x/9 + 2x/3 = 8/12?

Just solving one would be great so I'll know how to solve the other on my own.

No silly/stupid answers. Please spare me.

Answer 1

the second one has fractions so i'll do that one

x/9 + 2x/3 = 8/12

you have to get a lowest common denominator in order to add fractions. so multiply 2x/3 by 3/3 and you get 6x/9.

x/9 + 6x/9 = 8/12

7x/9 = 8/12

this is where you can cross multiply to get x

(7x)(12) = (8)(9)

84x = 72

divide both sides by 84 to solve for x

x= 72/84

both can be divided by 12 so simplify

x = 6/7

Answer 2

2y + y = 42

3y = 42

y = 14

4x + 24x = 24

28x = 24

x = 24/28

x = 6/7

Answer 3

1)

y/6 + y/12 = 14/4

12(y/6 + y/12) = 12(7/2)

2y + y = 42

3y = 42

y = 42/3

y = 14

2)

x/9 + 2x/3 = 8/12

9(x/9 + 2x/3) = 9(2/3)

x + 6x = 6

7x = 6

x = 6/7

Answer 4

1/6 y + 1/12 y = 14/4

add common terms

1/4 y = 14 / 4

get the common factor of both sides of the equation

1/4 ( y ) = 1/4 ( 14 )

divided both sides with that common factor

y = 14

Answer 5

You need to get the denomenators of both fractions on the left hand side equal so that you can convert them into one fraction.

y/6 = 2y/12 (you can mjultiply top and bottom of a fraction by the same number - in this case 2)

2y/12 + y/12 = 14/4

(2y + y)/12 = 14/4 (when adding 2 fractions with the same numerators you simply add the tops and keep the same denomenators)

3y/12 = 14/4

3y = (14 x 12)/4 (multiply both sides by 12)

3y = 42

y = 14

hope that helps

Answer 6

y/6+y/12=14/4

=>2y/12+y/12=14/4

=>4{3y}=14*12

=>12y=14*12

=>y=14

Answer 7

hi

(2y+y)/12=14/4

3y/12=14/4

y/4=14/4

y=14

Answer 8

Multiply the first equation by the LCD, which is 12

it yields 2y+y=42

                    3y=42

                     y=14