y+4/5=3/4
The goal is to get y by itself. Don’t be fooled by the fractions. This problem is very similar to x+4=10.
We want to get rid of the 4/5. Well, not actually get rid of it, but move it to the other side of the equal sign. The way we do that is to subtract it from both sides.
y+4/54/5=3/44/5
On the left side, 4/54/5 cancel out.
y = 3/4 4/5
Now, to subtract fractions, you need a common denominator. One common denominator is 4*5=20. Others are possible. If you use the lowest common denominator, there will be fewer steps later on.
Remember that 5/5 and 4/4 are both equal to 1. You can multiply anything by 1 and not change it. 1 is special that way.
y = (3/4) –(4/5) (Just rewritten for clarity)
y = (5/5)*(3/4) –(4/5)
That 5/5 doesn’t really change anything, but lets us change the denominator.
y = (15/20) –(4/5)
y = (15/20) –(4/4)*(4/5)
y = (15/20) –(16/20)
Now we have a common denominator and can subtract.
y = 1/20
This kind of problem can be confusing. There are 2 principles at work. First, you can multiply by 1 and not change anything. Second, you need a common denominator to add or subtract fractions. When we changed the denominators, like when we made 3/4 into 15/20, we didn’t change its value. Both are the same. The trick for getting that common denominator is to multiply one term by a special form of 1, like 4/4 or 5/5. The choice here is to use the denominator of the other term. For this problem, we converted 3/4 into 20ths using the 5/5 because 5 was in the denominator of the 4/5 term. And we used 4/4 to convert 4/5 into 20ths because 4 was in the denominator of the 3/4 term.
I hope this helps. You can use the comment feature to ask more questions if this is confusing.
9/27/2012

Robert C.
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