Solve 7/4+19/700:(4-8/10:5/10-frac{1}{2})

$$\frac { 7 } { 4 } + \frac { 19 } { 700 } : ( 4 - \frac { 8 } { 10 } : \frac { 5 } { 10 } - \frac { 1 } { 2 } )$$

Evaluate

$$\frac{247}{140}\approx 1.764285714$$

Solution Steps

Divide \frac{8}{10} by \frac{5}{10} by multiplying \frac{8}{10} by the reciprocal of \frac{5}{10}.

$$\frac{7}{4}+\frac{\frac{19}{700}}{4-\frac{8\times 10}{10\times 5}-\frac{1}{2}}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{7}{4}+\frac{\frac{19}{700}}{4-\frac{2\times 4}{5}-\frac{1}{2}}$$

Multiply 2 and 4 to get 8.

$$\frac{7}{4}+\frac{\frac{19}{700}}{4-\frac{8}{5}-\frac{1}{2}}$$

Convert 4 to fraction \frac{20}{5}.

$$\frac{7}{4}+\frac{\frac{19}{700}}{\frac{20}{5}-\frac{8}{5}-\frac{1}{2}}$$

Since \frac{20}{5} and \frac{8}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}+\frac{\frac{19}{700}}{\frac{20-8}{5}-\frac{1}{2}}$$

Subtract 8 from 20 to get 12.

$$\frac{7}{4}+\frac{\frac{19}{700}}{\frac{12}{5}-\frac{1}{2}}$$

Least common multiple of 5 and 2 is 10. Convert \frac{12}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{7}{4}+\frac{\frac{19}{700}}{\frac{24}{10}-\frac{5}{10}}$$

Since \frac{24}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{4}+\frac{\frac{19}{700}}{\frac{24-5}{10}}$$

Subtract 5 from 24 to get 19.

$$\frac{7}{4}+\frac{\frac{19}{700}}{\frac{19}{10}}$$

Divide \frac{19}{700} by \frac{19}{10} by multiplying \frac{19}{700} by the reciprocal of \frac{19}{10}.

$$\frac{7}{4}+\frac{19}{700}\times \frac{10}{19}$$

Multiply \frac{19}{700} times \frac{10}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{4}+\frac{19\times 10}{700\times 19}$$

Cancel out 19 in both numerator and denominator.

$$\frac{7}{4}+\frac{10}{700}$$

Reduce the fraction \frac{10}{700} to lowest terms by extracting and canceling out 10.

$$\frac{7}{4}+\frac{1}{70}$$

Least common multiple of 4 and 70 is 140. Convert \frac{7}{4} and \frac{1}{70} to fractions with denominator 140.

$$\frac{245}{140}+\frac{2}{140}$$

Since \frac{245}{140} and \frac{2}{140} have the same denominator, add them by adding their numerators.

$$\frac{245+2}{140}$$

Add 245 and 2 to get 247.

$$\frac{247}{140}$$

Factor

$$\frac{13 \cdot 19}{2 ^ {2} \cdot 5 \cdot 7} = 1\frac{107}{140} = 1.7642857142857142$$