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3/4-1/3(1/2y-2)=3(y-1/4) ??? and how?

 Oct 12, 2014

Best Answer 

 #1
avatar+118587 
+10

3/4-1/3(1/2y-2)=3(y-1/4)

 

$$\\\frac{3}{4}-\frac{1}{3}(\frac{1}{2}y-2)=3(y-\frac{1}{4})\\\\
\frac{3}{4}-\frac{1}{3}(\frac{y}{2}-2)=3(y-\frac{1}{4})\\\\
\frac{3}{4}-\frac{y}{6}+\frac{2}{3}=3y-\frac{3}{4}\\\\
$Now it will be easier if there were no fractions$\\
$The lowest common multiple of 4,6 and 3 is 12$\\\\
$So multiply both sides by 12 to get rid of all the fractions$\\
12(\frac{3}{4}-\frac{y}{6}+\frac{2}{3})=12(3y-\frac{3}{4})\\\\
\frac{12*3}{4}-\frac{12y}{6}+\frac{12*2}{3}=12*3y-\frac{12*3}{4}\\\\
9-2y+8=36y-9\\\\
17=38y-9\\\\
26=38y\\\\$$

$$\\y=\frac{26}{38}\\\\
y=\frac{13}{19}\\\\$$

 Oct 12, 2014
 #1
avatar+118587 
+10
Best Answer

3/4-1/3(1/2y-2)=3(y-1/4)

 

$$\\\frac{3}{4}-\frac{1}{3}(\frac{1}{2}y-2)=3(y-\frac{1}{4})\\\\
\frac{3}{4}-\frac{1}{3}(\frac{y}{2}-2)=3(y-\frac{1}{4})\\\\
\frac{3}{4}-\frac{y}{6}+\frac{2}{3}=3y-\frac{3}{4}\\\\
$Now it will be easier if there were no fractions$\\
$The lowest common multiple of 4,6 and 3 is 12$\\\\
$So multiply both sides by 12 to get rid of all the fractions$\\
12(\frac{3}{4}-\frac{y}{6}+\frac{2}{3})=12(3y-\frac{3}{4})\\\\
\frac{12*3}{4}-\frac{12y}{6}+\frac{12*2}{3}=12*3y-\frac{12*3}{4}\\\\
9-2y+8=36y-9\\\\
17=38y-9\\\\
26=38y\\\\$$

$$\\y=\frac{26}{38}\\\\
y=\frac{13}{19}\\\\$$

Melody Oct 12, 2014
 #2
avatar+49 
0

thank you so much that really helped me out, i cant tell you how much clearer it is now

 Oct 12, 2014
 #3
avatar+49 
0

whats it called when you multiplyed it by 12? is there a term for it?

 Oct 12, 2014
 #4
avatar+118587 
0

Thank you, I am glad I helped you.

Well, you are multiplying by the lowest common denominator.  

 Oct 13, 2014

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