fefetasprites
  • fefetasprites
22. 1/2+3/t=5/8
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
You can multiply both sides by the LCD to get rid of all denominators. What is the LCD of 2, t, and 8?
fefetasprites
  • fefetasprites
It's 2t, right? That's what I used and the answer came out weird. Is it 8t?
fefetasprites
  • fefetasprites
@mathstudent55

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mathstudent55
  • mathstudent55
No. You need the smallest quantity that is divisible by 2, t, and 8. 2t is divisible by 2 and t, but it is not divisible by 8. What is the smallest quantity that is divisible by 2, t, and 8?
fefetasprites
  • fefetasprites
Is it 8t then?
mathstudent55
  • mathstudent55
Yes. Now we multiply both sides by 8t. This way we will get rid of all denominators. \(8t \left( \dfrac{1}{2} + \dfrac{3}{t} \right)= 8t \left( \dfrac{5}{8} \right)\) Ok?
mathstudent55
  • mathstudent55
Now we distribute the 8t on the left, and we multiply the 8t on the right. \(\dfrac{8t}{1} \left( \dfrac{1}{2} + \dfrac{3}{t} \right)= \dfrac{8t}{1} \left( \dfrac{5}{8} \right)\) \( \dfrac{8t}{2} + \dfrac{8t \times 3}{t} = \dfrac{8t \times 5}{8} \)
fefetasprites
  • fefetasprites
Distribute and multiply? How I learned was to cancel out like terms. So in this question, I would cancel out the t in 8t and 3t, and cancel out the 8 in 8t and the 8 in 5/8. Does that end up with the same thing? Or am I doing something wrong?
mathstudent55
  • mathstudent55
Your idea of canceling is ok, but you need to be careful how you do it.
mathstudent55
  • mathstudent55
Now we cancel out all denominators with factors in the numerators. \( \dfrac{\cancel{8}4t}{\cancel{2}1} + \dfrac{8\cancel{t} \times 3}{\cancel{t} 1} = \dfrac{\cancel{8}t \times 5}{\cancel{8}1} \) \(4t + 24 = 5t\)
fefetasprites
  • fefetasprites
Alright, so now you just do basic algebra and solve t, right?
mathstudent55
  • mathstudent55
You are correct that the 8t on the left multiplies the fraction 3/t. the t's cancel out leaving just 3 * 8 = 24. You can;t forget to also multiply 8t by the fraction 1/2. That is why it is a good idea to distribute first, then cancel.
mathstudent55
  • mathstudent55
Yes.
fefetasprites
  • fefetasprites
Okay, thank you!
mathstudent55
  • mathstudent55
You're welcome.

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