Solving Equations with Fractions

How do I solve this?
1/3(7y-1)+1/6(4y+7)

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Solving Equations with Fractions

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Jan 14, 2012
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starstarstarstarstar 		Solving Equations with Fraction NEW
by: Karin

I added the explanation to the end of the original problem and hopefully this will explain the problem more clearly. See the original post for a complete explanation.
Jan 14, 2012
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starstarstarstarstar 		Problem solving1/3(7y-1)+1/6(4y+7)
by: Anonymous

Show me how you got 18/6y+5/6
Dec 20, 2011
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starstarstarstarstar 		Solving Equations with Fractions
by: Karin

Yes, you are correct! Sorry about that - my mind was in equation mode and without multiplying the other side by 6, we need to divide by 6 at the end in order to complete the simplification.
Dec 20, 2011
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starstarstarstarstar 		completion of equation
by: Anonymous

Karen, your logic is good, but incomplete. You must return to the part of the equation where you multiplied by 6, and divide each item by 6 to complete the calculation.

(18y/6)+(5/6)
=3y+5/6
Sep 06, 2010
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starstarstarstarstar 		Solving Equations with Fractions
by: Karin

I would love to help you solve this equation, however, we need to have an equal sign with an answer:

1/3(7y-1) + 1/6(4y + 7) = ???

If the directions are to simplify, then we can:

Step 1: Get rid of the fractions by multiplying all terms by 6.

6[1/3(7y-1) + 1/6(4y +7)]
2(7y-1) +1(4y+7)

Step 2: Use the distributive property:
2(7y-1) +1(4y+7)
14y -2 + 4y + 7

Step 3: Write like terms together:
14y -2 + 4y + 7
14y + 4y - 2 + 7

Step 4: Combine like terms:
14y + 4y - 2 + 7
18y + 5

Step 5: Since we are simplifying an expression (and not solving an equation where we would keep the equation balanced by multiplying by 6 on both sides), we need to divide our answer by 6.

We multiplied by 6 initially to get rid of the fractions and now we must divide our answer by 6 in order to keep it balanced.

18y/6 + 5/6

Simplifies to 3y + 5/6

Hope this helps,
Karin

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