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View Full Version : solving equations involving mixed numbers: (3_1/3)x = -22

aidenluver
10-15-2008, 07:29 PM
My 8th grade child brought home some fractional equations home and we are both stuck. I was hoping someone could work one out with us and then we could figure it out the rest on our own. It has been a long time since I have tackled this. Any help someone can give us will be greatly appreciated.

Here is a problem:

3 1/3 x = -22

I am stuck on whether I need to multiply both sides by 3 first or if I need to make it an improper fraction.

Thanks! :D

Loren
10-15-2008, 07:41 PM
Either. Multiplying both sides by 3 is a good move no matter when.

aidenluver
10-15-2008, 08:09 PM
are muliplying 3 to get rid of the whole 3 or the denominator of 3? thanks for the help!

Mrspi
10-15-2008, 08:20 PM
are muliplying 3 to get rid of the whole 3 or the denominator of 3? thanks for the help!

I'd rewrite the mixed number as an improper fraction FIRST.... 3 1/3 is 3*3/3 + 1/3, or 9/3 + 1/3, or 10/3

Now, your equation is

(10/3)x = -22

If you multiply both sides of this equation by 3, you'll have

3*(10/3)x = 3*(-22)

or,

10x = -66

Take it from there!!

mmm4444bot
10-16-2008, 04:41 AM
are muliplying 3 to get rid of the whole 3 or the denominator of 3? thanks for the help!

Hello Parent:

To address your question above, we are mutliplying by 3 to get rid of the denominator, but be careful how you multiply 3-1/3 by 3, if you choose to do that.

3-1/3 means (3 + 1/3), so 3-1/3 times 3 is 3*(3 + 1/3) which is 3*3 + 3*(1/3) which is 9 + 1.

Mrspi's instruction is really the way to go, and that post answers your original question about whether to convert to an improper fraction. Starting with algebra onward, do NOT proceed with mixed numbers (in fact, don't use them at all, except perhaps for reporting certain final answers with some word problems.)

< unsolicited opinions mode on >

Shame on your child's instructor for writing that equation in the first place. It is non-standard at best, and counter-instructive at worst.

< unsolicited opinions mode off >

Cheers,

~ Mark :)