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I was given this question and not sure how to do the second part

Part 1: Evaluate the following 2/7 divided by ¾

Answer = 2/7 multiplied by 4/3 = 8/21

Part 2: Now explain why you calculation (the algorithm you used) is correct? This is where I am stuck.

Appreciate any help. Thank you.

JMoravitz
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tfa
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  • You're being asked to make an argument why $\frac{2}{7} \div \frac{3}{4} = \frac{8}{21}$. That really has to come from you. Maybe you could express it in terms of areas? – Matthew Leingang Oct 22 '19 at 17:00
  • I am not not sure what the lecture is asking in the second part I think he maybe looking for a theorem that uses x and y and proves why this is correct – tfa Oct 22 '19 at 17:01
  • It would help if you give us an idea of what you do know about division of rational numbers, multiplying rational numbers, equality of rational numbers, and multiplicative inverses in general. We could go in depth with the various formal ways of defining these things, but it will be meaningless to you if you don't use the same formal definitions that we do. – JMoravitz Oct 22 '19 at 17:01
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    The explanation I like best that avoids some of the formality... I could say that division is informally defined as multiplying by the multiplicative inverse, $a\div b = a\times b^{-1}$ (much like how subtraction is adding by the additive inverse, $a-b = a+(-b)$). Next, I would point out how the multiplicative inverse of a fraction $\frac{c}{d}$ is the fraction $\frac{d}{c}$ since these multiplied together simplify to $1$, seen however you prefer. – JMoravitz Oct 22 '19 at 17:07
  • Thank you for your replies yes JMoravitz your answer makes sense I will come back here when the lecture gives the solution and hopefully yours JMoravitz is what he is looking for. Thanks again. – tfa Oct 22 '19 at 19:32

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