Solve for m (2/3)÷(m/n)=6/15

Math
23÷mn=615
Factor each term.
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To divide by a fraction, multiply by its reciprocal.
23⋅nm=615
Multiply 23 and nm.
2n3m=615
Cancel the common factor of 6 and 15.
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Factor 3 out of 6.
2n3m=3(2)15
Cancel the common factors.
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Factor 3 out of 15.
2n3m=3⋅23⋅5
Cancel the common factor.
2n3m=3⋅23⋅5
Rewrite the expression.
2n3m=25
2n3m=25
2n3m=25
2n3m=25
Set up the rational expression with the same denominator over the entire equation.
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Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 15m. The 2n3m expression needs to be multiplied by 55 to make the denominator 15m. The 25 expression needs to be multiplied by 3m3m to make the denominator 15m.
2n3m⋅55=25⋅3m3m
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 15m.
2n(5)
Multiply 5 by 2.
10n15m=25⋅3m3m
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 15m.
2(3m)
Multiply 3 by 2.
10n15m=6m15m
10n15m=6m15m
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
10n=6m
Rewrite the equation as 6m=10n.
6m=10n
Divide each term by 6 and simplify.
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Divide each term in 6m=10n by 6.
6m6=10n6
Cancel the common factor of 6.
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Cancel the common factor.
6m6=10n6
Divide m by 1.
m=10n6
m=10n6
Cancel the common factor of 10 and 6.
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Factor 2 out of 10n.
m=2(5n)6
Cancel the common factors.
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Factor 2 out of 6.
m=2(5n)2(3)
Cancel the common factor.
m=2(5n)2⋅3
Rewrite the expression.
m=5n3
m=5n3
m=5n3
m=5n3
Solve for m (2/3)÷(m/n)=6/15

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