Solve 4(3/5)-(4/5)+1/4(frac{3{5})+(4/5)-1}

$$\frac { 4 ( \frac { 3 } { 5 } ) - ( \frac { 4 } { 5 } ) + 1 } { 4 ( \frac { 3 } { 5 } ) + ( \frac { 4 } { 5 } ) - 1 }$$

Evaluate

$$\frac{13}{11}\approx 1.181818182$$

Solution Steps

Express 4\times \frac{3}{5} as a single fraction.

$$\frac{\frac{4\times 3}{5}-\frac{4}{5}+1}{4\times \frac{3}{5}+\frac{4}{5}-1}$$

Multiply 4 and 3 to get 12.

$$\frac{\frac{12}{5}-\frac{4}{5}+1}{4\times \frac{3}{5}+\frac{4}{5}-1}$$

Since \frac{12}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12-4}{5}+1}{4\times \frac{3}{5}+\frac{4}{5}-1}$$

Subtract 4 from 12 to get 8.

$$\frac{\frac{8}{5}+1}{4\times \frac{3}{5}+\frac{4}{5}-1}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{\frac{8}{5}+\frac{5}{5}}{4\times \frac{3}{5}+\frac{4}{5}-1}$$

Since \frac{8}{5} and \frac{5}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8+5}{5}}{4\times \frac{3}{5}+\frac{4}{5}-1}$$

Add 8 and 5 to get 13.

$$\frac{\frac{13}{5}}{4\times \frac{3}{5}+\frac{4}{5}-1}$$

Express 4\times \frac{3}{5} as a single fraction.

$$\frac{\frac{13}{5}}{\frac{4\times 3}{5}+\frac{4}{5}-1}$$

Multiply 4 and 3 to get 12.

$$\frac{\frac{13}{5}}{\frac{12}{5}+\frac{4}{5}-1}$$

Since \frac{12}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{5}}{\frac{12+4}{5}-1}$$

Add 12 and 4 to get 16.

$$\frac{\frac{13}{5}}{\frac{16}{5}-1}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{\frac{13}{5}}{\frac{16}{5}-\frac{5}{5}}$$

Since \frac{16}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{5}}{\frac{16-5}{5}}$$

Subtract 5 from 16 to get 11.

$$\frac{\frac{13}{5}}{\frac{11}{5}}$$

Divide \frac{13}{5} by \frac{11}{5} by multiplying \frac{13}{5} by the reciprocal of \frac{11}{5}.

$$\frac{13}{5}\times \frac{5}{11}$$

Multiply \frac{13}{5} times \frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 5}{5\times 11}$$

Cancel out 5 in both numerator and denominator.

$$\frac{13}{11}$$

Factor

$$\frac{13}{11} = 1\frac{2}{11} = 1.1818181818181819$$