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fefetasprites

  • one year ago

22. 1/2+3/t=5/8

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  1. mathstudent55
    • one year ago
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    You can multiply both sides by the LCD to get rid of all denominators. What is the LCD of 2, t, and 8?

  2. fefetasprites
    • one year ago
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    It's 2t, right? That's what I used and the answer came out weird. Is it 8t?

  3. fefetasprites
    • one year ago
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    @mathstudent55

  4. mathstudent55
    • one year ago
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    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?

  5. fefetasprites
    • one year ago
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    Is it 8t then?

  6. mathstudent55
    • one year ago
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    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?

  7. mathstudent55
    • one year ago
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    Now we distribute the 8t on the left, and we multiply the 8t on the right. \(\dfrac{8t}{1} \left( \dfrac{1}{2} + \dfrac{3}{t} \right)= \dfrac{8t}{1} \left( \dfrac{5}{8} \right)\) \( \dfrac{8t}{2} + \dfrac{8t \times 3}{t} = \dfrac{8t \times 5}{8} \)

  8. fefetasprites
    • one year ago
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    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?

  9. mathstudent55
    • one year ago
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    Your idea of canceling is ok, but you need to be careful how you do it.

  10. mathstudent55
    • one year ago
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    Now we cancel out all denominators with factors in the numerators. \( \dfrac{\cancel{8}4t}{\cancel{2}1} + \dfrac{8\cancel{t} \times 3}{\cancel{t} 1} = \dfrac{\cancel{8}t \times 5}{\cancel{8}1} \) \(4t + 24 = 5t\)

  11. fefetasprites
    • one year ago
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    Alright, so now you just do basic algebra and solve t, right?

  12. mathstudent55
    • one year ago
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    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.

  13. mathstudent55
    • one year ago
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    Yes.

  14. fefetasprites
    • one year ago
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    Okay, thank you!

  15. mathstudent55
    • one year ago
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    You're welcome.

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