Solve 5/4/7+5-1/2/3-frac{4{5}}

$$\frac { \frac { 5 } { 4 } } { 7 } + 5 - \frac { \frac { 1 } { 2 } } { 3 - \frac { 4 } { 5 } }$$

Evaluate

$$\frac{1525}{308}\approx 4.951298701$$

Solution Steps

Express \frac{\frac{5}{4}}{7} as a single fraction.

$$\frac{5}{4\times 7}+5-\frac{\frac{1}{2}}{3-\frac{4}{5}}$$

Multiply 4 and 7 to get 28.

$$\frac{5}{28}+5-\frac{\frac{1}{2}}{3-\frac{4}{5}}$$

Convert 5 to fraction \frac{140}{28}.

$$\frac{5}{28}+\frac{140}{28}-\frac{\frac{1}{2}}{3-\frac{4}{5}}$$

Since \frac{5}{28} and \frac{140}{28} have the same denominator, add them by adding their numerators.

$$\frac{5+140}{28}-\frac{\frac{1}{2}}{3-\frac{4}{5}}$$

Add 5 and 140 to get 145.

$$\frac{145}{28}-\frac{\frac{1}{2}}{3-\frac{4}{5}}$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{145}{28}-\frac{\frac{1}{2}}{\frac{15}{5}-\frac{4}{5}}$$

Since \frac{15}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{145}{28}-\frac{\frac{1}{2}}{\frac{15-4}{5}}$$

Subtract 4 from 15 to get 11.

$$\frac{145}{28}-\frac{\frac{1}{2}}{\frac{11}{5}}$$

Divide \frac{1}{2} by \frac{11}{5} by multiplying \frac{1}{2} by the reciprocal of \frac{11}{5}.

$$\frac{145}{28}-\frac{1}{2}\times \frac{5}{11}$$

Multiply \frac{1}{2} times \frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{145}{28}-\frac{1\times 5}{2\times 11}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 11}.

$$\frac{145}{28}-\frac{5}{22}$$

Least common multiple of 28 and 22 is 308. Convert \frac{145}{28} and \frac{5}{22} to fractions with denominator 308.

$$\frac{1595}{308}-\frac{70}{308}$$

Since \frac{1595}{308} and \frac{70}{308} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1595-70}{308}$$

Subtract 70 from 1595 to get 1525.

$$\frac{1525}{308}$$

Factor

$$\frac{5 ^ {2} \cdot 61}{2 ^ {2} \cdot 7 \cdot 11} = 4\frac{293}{308} = 4.951298701298701$$