Expert: Jeff White - 10/11/2004

Question
-------------------------
Followup To
Question -
I understand basic algebra equasions but I am having trouble understanding problems with fractions and parentheses.  My teacher will not answer questions today and this is due tomorrow.  I am in 7th grade gifted math and I was doing well but I am now falling behind.  I live in the Florida.  Please help.
Answer -
Hi Chris.  Have you learned about the distributive property yet?  It says that if you have something that looks like this:
a(b + c)
it is equal to this:
a*b + a*c

That will come into play on the first two problems.

Problem #1:
-24 = 3(-2y - 7)
-24 = -6y - 21
add 21 to both sides:
-3 = -6y
divide both sides by -6:
y = -3/-6 = 1/2


*I understand question #1.

Problem #2:
besides the distributive property you will also need to multiply both sides of the equation by the least common denominator to get rid of the fractions.

3(x - 1/4) = 3/4
3x - 3/4 = 3/4
Multiply both sides by 4:
12x - 3 = 3
12x = 6
x = 1/2

*I understand the beginning of this problem but I don't understand why you then multiply both sides by 4 or what comes next.  We need to show our work but I don't understand why you multiply by 4.  


Problem #3:
3/8 - (1/4)x = 1/16
Withouth the parentheses around the 1/4, it implies that the x is in the denominator, but I'm guessing that's not where you meant for it to be...so you need the parentheses to clarify.

Multiply both sides by 16 and simplify:
6 - 4x = 1
5 - 4x = 0
5 = 4x
x = 5/4

*I need the problem in words about how you solve the problem.  I'm just not understanding how your getting what you get.  THanks.

On all three problems, and in general, be sure to plug your answer back into your original equation and check to see that it works.  I didn't show that, but I found an error I had made when I checked, and chances are you will too at some point.

Hope this helps.

Jeff

Answer
When there are fractions involved, multiplying both sides of the equation by the least common denominator of all the fractions is the easiest way to make the fractions disappear.  By multiplying by the LCD, you guarantee that all of your denominators will divide into your new (after being multiplied) numerators evenly, so you are in effect converting from an equation containing fractions to one that does not contain any fractions.

On problem #2:
**new steps added
3(x - 1/4) = 3/4
3x - 3/4 = 3/4
Multiply both sides by 4:
** 4(3x - 3/4) = 4 * 3/4
**12x - 12/4 = 12/4
12x - 3 = 3 (bye-bye fractions)
12x = 6
x = 1/2

On problem #2:
**new steps added
3/8 - (1/4)x = 1/16
multiply both sides by the LCD, which is 16:
** 16*(3/8 - (1/4)x) = 16 * 1/16
then simplify:
** 48/8 - (16/4)x = 16/16
6 - 4x = 1
5 - 4x = 0
5 = 4x
x = 5/4

Do the added steps help explain it better?

Jeff