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

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!

Re: parent needing help with math homework with child

Either. Multiplying both sides by 3 is a good move no matter when.

Re: parent needing help with math homework with child

are muliplying 3 to get rid of the whole 3 or the denominator of 3? thanks for the help!

Re: parent needing help with math homework with child

aidenluver said:

are muliplying 3 to get rid of the whole 3 or the denominator of 3? thanks for the help!

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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!!

Re: parent needing help with math homework with child

aidenluver said:

are muliplying 3 to get rid of the whole 3 or the denominator of 3? thanks for the help!

Click to expand...

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.)

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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.

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Cheers,

~ Mark