Solve n/4frac{1{5}}=62/7/3frac{1{4}}

$$\frac { n } { 4 \frac { 1 } { 5 } } = \frac { 6 \frac { 2 } { 7 } } { 3 \frac { 1 } { 4 } }$$

Solve for n

$$n = \frac{528}{65} = 8\frac{8}{65} \approx 8.123076923$$

Steps for Solving Linear Equation

Divide n by \frac{4\times 5+1}{5} by multiplying n by the reciprocal of \frac{4\times 5+1}{5}.

$$\frac{n\times 5}{4\times 5+1}=\frac{\frac{6\times 7+2}{7}}{\frac{3\times 4+1}{4}}$$

Multiply 4 and 5 to get 20.

$$\frac{n\times 5}{20+1}=\frac{\frac{6\times 7+2}{7}}{\frac{3\times 4+1}{4}}$$

Add 20 and 1 to get 21.

$$\frac{n\times 5}{21}=\frac{\frac{6\times 7+2}{7}}{\frac{3\times 4+1}{4}}$$

Divide \frac{6\times 7+2}{7} by \frac{3\times 4+1}{4} by multiplying \frac{6\times 7+2}{7} by the reciprocal of \frac{3\times 4+1}{4}.

$$\frac{n\times 5}{21}=\frac{\left(6\times 7+2\right)\times 4}{7\left(3\times 4+1\right)}$$

Multiply 6 and 7 to get 42.

$$\frac{n\times 5}{21}=\frac{\left(42+2\right)\times 4}{7\left(3\times 4+1\right)}$$

Add 42 and 2 to get 44.

$$\frac{n\times 5}{21}=\frac{44\times 4}{7\left(3\times 4+1\right)}$$

Multiply 44 and 4 to get 176.

$$\frac{n\times 5}{21}=\frac{176}{7\left(3\times 4+1\right)}$$

Multiply 3 and 4 to get 12.

$$\frac{n\times 5}{21}=\frac{176}{7\left(12+1\right)}$$

Add 12 and 1 to get 13.

$$\frac{n\times 5}{21}=\frac{176}{7\times 13}$$

Multiply 7 and 13 to get 91.

$$\frac{n\times 5}{21}=\frac{176}{91}$$

Multiply both sides by 21.

$$n\times 5=\frac{176}{91}\times 21$$

Express \frac{176}{91}\times 21 as a single fraction.

$$n\times 5=\frac{176\times 21}{91}$$

Multiply 176 and 21 to get 3696.

$$n\times 5=\frac{3696}{91}$$

Reduce the fraction \frac{3696}{91} to lowest terms by extracting and canceling out 7.

$$n\times 5=\frac{528}{13}$$

Divide both sides by 5.

$$n=\frac{\frac{528}{13}}{5}$$

Express \frac{\frac{528}{13}}{5} as a single fraction.

$$n=\frac{528}{13\times 5}$$

Multiply 13 and 5 to get 65.

$$n=\frac{528}{65}$$