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# im confused y+4/5=3/4

algerbra question

I always liked doing the following way.

You have y + 4/5=3/4

Just remove the demoninators first. Multiply first by 5 to get

5y+4= 15/4

Multiple by four to get

20y+16=15

20y= (-1)

and divide by 20.

I find this easier because you don't have to add or subtract fractions or find lowest common denominators.

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+4/5-4/5=3/4-4/5

On the left side, 4/5-4/5 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.

You get two different answers depending on how the original question is framed.

If the question is y + 4/5 = 3/4, the answer is y=-1/20 as shown by Robert and Debra earlier.

However, if the question really is (y+4)/5 = 3/4 you have a completely different answer.  Parentheses are very important in math.

To solve the latter:

1- Get rid of the denominators by transferring them to both sides.  Essentially you are multiplying both sides by 20 (5 * 4).  20/5 is 4 and 20/4 is 5.

(y+4)*4 = 3*5

2- Then expand the left side equation to isolate y and solve the right side.

4y + 16 = 15

3- Move similar terms to the same side of the equation.  Subtract both sides by 16.  Remember with an equal sign in the middle, you have to do the same thing to both sides of the equation.

4y = 15 - 16

4y = -1

4- Divide both sides by 4 to simplify y.

y = -1/4

To test the solution and make sure your answer is correct, substitute y in the original equation as follows:

(y+4)/5 = 3/4

(-1/4 + 4)/5 = 3/4

(-1/4 + 16/4)/5 = 3/4

(15/4)/5 = 3/4

15/4 = 3/4*5

15/4 = 15/4

Cool?

Good point, however we all need to be careful not to add too much or possibly irrelevant information, as it can become very confusing for the student. The given problem is typical for an introduction to variables.

y+4/5=3/4

To solve this you need to find the lowest commmon denominator.  the LCD for 5 and 4 is 20.  So now that we have the LCD, we need to adjust the numerators (the top numbers in the fractions) by multiplying:

4/5*4/4 = 16/20

Always multiply the numerator by the same number as the denominator.  We do this again for the second fraction:

3/4*5/5=15/20

Now we look at the problem again using the new fractions:

y+16/20=15/20

Now simplify like terms, in this case the fractions (remember to always do the same to both sides of the equation):

16/20-16/20 = 0

15/20-16/20= -1/20

Giving us our answer:

y= -1/20