solve each proportion

Question

solve each proportion in math

1.x-4/6=x+2/12

2.4/y+2=10/5y

3. y+2/y+7=11/31

Answer 1

Hi Abby,

Many students solve proportions by cross-multiplying, which means multiplying the numerators by the denominators ACROSS the equals sign.  Another way to think about this is that you are clearing the denominators by multiplying both sides of the equation by them.  There are some shortcuts and tricks, but the method I described works every time.

1:  12*(x-4) = 6*(x+2)  Distribute to clear the parentheses...

12x - 48 = 6x + 12  Subtract 6x from both sides and add 48 to both sides...

6x = 60  Divide both sides by 6 and your solution for x is 10.

2:  4*5y = 10*(y+2)  Follow the steps described above and you'll get y = 2

3:  31*(y+2) = 11*(y+7)  When you follow the same steps you'll get y = 15/20, reduce to 3/4

Answer 2

x-4/6=x+2/12 ; x-4/1=x+2/2 ; 2x-8=x+2 ; x=10

4/y+2=10/5y ; 4/y+2=2/y ; 2/y+2=1/y; 2y=y+2 ; y=2

31y+62=11y+77; 20y=77-62; y=15/20; y=3/4