Answer:
2/5
Step-by-step explanation:
There are several ways to work this. One is to simplify the equation first.
[tex]\dfrac{\ \dfrac{1}{2}\ }{\dfrac{3}{5}}=\dfrac{\ \dfrac{1}{3}\ }{m}\\\\\dfrac{1\cdot5}{2\cdot3}=\dfrac{1}{3m}\qquad\text{simplify fractions}\\\\m=\dfrac{6}{5}\cdot\dfrac{1}{3}\qquad\text{multiply by $\dfrac{6}{5}m$}\\\\\boxed{m=\dfrac{2}{5}}\qquad\text{simplify}[/tex]
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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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