The value of [tex]\dfrac{m}{n}[/tex] is [tex]\boxed{\frac{m}{n} = \frac{{49}}{9}}.[/tex]
Further explanation:
Given:
The equation is [tex]\dfrac{3}{7}m = \dfrac{7}{3}n.[/tex]
Explanation:
We have to find the value of [tex]\dfrac{m}{n}.[/tex]
The left hand side of the equation is [tex]\dfrac{3}{7}m.[/tex]
The right hand side of the equation is [tex]\dfrac{7}{3}n.[/tex]
Consider the left hand side and the right hand side of the equation as A.
The value of m can be obtained as follows,
[tex]\begin{aligned}\frac{3}{7}m&= A\hfill\\m&= \frac{7}{3}A\hfill\\\end{aligned}[/tex]
The value of [tex]n[/tex] can be obtained as follows,
[tex]\begin{aligned}\frac{7}{3}n&= A\hfill\\n&= \frac{3}{7}A \hfill\\\end{aligned}[/tex]
The value [tex]\dfrac{m}{n}[/tex] can be calculated as follows,
[tex]\begin{aligned}\dfrac{m}{n}&=\dfrac{{\dfrac{7}{3}A}}{{\dfrac{3}{7}A}}\\&= \dfrac{{\dfrac{7}{3}}}{{\dfrac{3}{7}}}\\&= \dfrac{{7 \times 7}}{{3 \times 3}}\\&= \dfrac{{49}}{9}\\\end{aligned}[/tex]
The value of [tex]\dfrac{m}{n}\: {\text{is}\: \boxed{\frac{m}{n} = \dfrac{{49}}{9}}.[/tex]
Learn more
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
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3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Fractions
Keywords: fraction, simplify, m/n,[tex]3/7m=7/3n[/tex] add, subtraction, denominators, numerators,value.
