Question

Can anyone help me with this problem please?

Answer 1

2/5

Explanation:

There are several ways to work this. One is to simplify the equation first.

`(\ (1)/(2)\ )/((3)/(5))=(\ (1)/(3)\ )/(m)\\\\(1\cdot5)/(2\cdot3)=(1)/(3m)\qquad\text{simplify fractions}\\\\m=(6)/(5)\cdot(1)/(3)\qquad\text{multiply by $(6)/(5)m$}\\\\\boxed{m=(2)/(5)}\qquad\text{simplify}`

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Alternate solution

You know that the solution to ...

a/b = c/m

can be found by cross-multiplying, then dividing by the coefficient of m:

am = bc

m = bc/a

You can go there directly with the values in this problem: a=1/2, b=3/5, c=1/3.

m = (b)(c)(1/a) = (3/5)(1/3)(2/1) = (1/5)(2/1) = 2/5

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