4

can someone review this and see if i've done it correctly please.

$$\frac{\frac {3x} {y}}{\frac {2x}{7}} $$

$$= \frac{3x}{y} . \frac{7}{2x}$$

$$= \frac{21x}{2xy} $$

$$= \frac {21}{2y} $$

Thank you for your time.

Aeonify
  • 71
  • 4
    You have done it correctly – Aakash Kumar Jul 27 '16 at 08:43
  • 3
    To be pedantic, you might want to add the restriction $x\ne 0$, since it can't be in the first equation and it can in the second. (Since you cancelled an x over x, and that's not legal if x is 0) – Alan Jul 27 '16 at 09:37

2 Answers2

2

As a picture is worth a thousand words:

enter image description here

Bernard
  • 175,478
1

Your answer and method look correct (but as pointed out in the comments, you need to add the restriction $x\ne 0$). I would have liked to have seen more steps though to demonstrate understanding.

$$\frac{\frac{3x}{y}}{\frac{2x}{7}}$$ $$= \color{red}{\frac{\frac{3x}{y}}{\frac{2x}{7}}\cdot\frac{\frac{7}{2x}}{\frac{7}{2x}}}$$ $$= \color{red}{\frac{\frac{3x}{y}\cdot\frac{7}{2x}}{\frac{2x}{7}\cdot\frac{7}{2x}}}$$ $$= \color{red}{\frac{\frac{3x}{y}\cdot\frac{7}{2x}}{\frac{14x}{14x}}}$$ $$= \color{red}{\frac{\frac{3x}{y}\cdot\frac{7}{2x}}{1}}$$ $$= \frac{3x}{y}\cdot\frac{7}{2x}$$ $$= \frac{21x}{2xy}$$ $$= \frac{21}{2y}$$

John Joy
  • 7,790
  • 1
    I don't believe all those steps in red are really necessary. We can go immediately from step 1 to step 6 (the first black text after the red) by using the fact that dividing by $a/b$ is the same as multiplying by $b/a$. –  Jul 27 '16 at 16:40
  • 1
    @tilper How does one reason that dividing by $a/b$ is the same as multiplying by $b/a$. As stated, it sounds like a proclamation than a statement of fact. – John Joy Jul 27 '16 at 16:47
  • Eh. It's definitely something worth explaining to the students, but if it's something that you'd expect them to write on their own homework then I guess we just disagree pedagogically. –  Jul 27 '16 at 16:52
  • 2
    @tilper You are correct in that I would definitely expect a student to omit those steps on their homework, unless the student would benefit from doing so. The fact that the OP asked whether or not the answer was correct, indicates uncertainty and that he/she would benefit. – John Joy Jul 27 '16 at 16:59