Mathematics
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OpenStudy (diamond77108):
will medal & fan
2/9v+4−2/3v=5
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OpenStudy (shadowlegendx):
\[\frac{ 2 }{ 9 }v + 4 - \frac{ 2 }{ 3 }v = 5\]
OpenStudy (shadowlegendx):
Do you know what the first step would be?
OpenStudy (diamond77108):
combine like terms
OpenStudy (shadowlegendx):
Correct, so how would we do that with these fractions?
OpenStudy (diamond77108):
\[\frac{ 2 }{ 9 }-\frac{ 2 }{ 3 }\]
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OpenStudy (shadowlegendx):
Yes, but in order to add/subtract with fractions, what is required?
OpenStudy (diamond77108):
least common denominators which is 9
OpenStudy (shadowlegendx):
Yes, so how would we get 2/3 to fulfill that requirement?
OpenStudy (diamond77108):
\[\frac{ 6 }{ 9 }\]
OpenStudy (shadowlegendx):
Remember,
\[-\frac{ 2 }{ 3 } \times \frac{ 3 }{ 3 } = - \frac{ 6 }{ 9 }\]
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OpenStudy (shadowlegendx):
Negative
OpenStudy (shadowlegendx):
So we have \[\frac{ 2 }{ 9 }v + 4 - \frac{ 6 }{ 9 }v = 5\]
OpenStudy (shadowlegendx):
What now?
OpenStudy (diamond77108):
subtract the two fractions
OpenStudy (shadowlegendx):
What do you get?
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OpenStudy (diamond77108):
\[\frac{ -8 }{ 9? }\]
OpenStudy (diamond77108):
positive 8
OpenStudy (shadowlegendx):
\[\frac{ 2 }{ 9 }v - \frac{ 6 }{ 9 }v\]
OpenStudy (diamond77108):
\[\frac{ -4 }{ 9 }\]
OpenStudy (shadowlegendx):
Yep
\[-\frac{ 4 }{ 9 }v\]
So we have,
\[-\frac{ 4 }{ 9 }v + 4 = 5\]
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OpenStudy (diamond77108):
so now we subtrac the 4 on both sides
OpenStudy (shadowlegendx):
Yes,
We get..
\[-\frac{ 4 }{ 9 }v = 1\]
OpenStudy (diamond77108):
v=-4/9
OpenStudy (shadowlegendx):
Wait...
OpenStudy (shadowlegendx):
You multiply both sides by -9, you get 4v = -9, then divide by 4
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OpenStudy (shadowlegendx):
\[v = -\frac{ 9 }{ 4 }\]
OpenStudy (diamond77108):
2 1/4
OpenStudy (shadowlegendx):
Keep it in the earlier form unless your teacher wants it in that form
OpenStudy (shadowlegendx):
Mixed fractions are kind of informal and used usually in just elementary school
OpenStudy (diamond77108):
its neg rigtht
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OpenStudy (shadowlegendx):
Yes
OpenStudy (diamond77108):
thx
OpenStudy (shadowlegendx):
No problem