Solve {l}{12.5*5/18-5/14*5/18+8.3}{*5/18}

$$\left. \begin{array} { l } { 12.5 \times \frac { 5 } { 18 } - \frac { 5 } { 14 } \times \frac { 5 } { 18 } + 8.3 } \\ { \times \frac { 5 } { 18 } } \end{array} \right.$$

Evaluate

$$\frac{159}{28}\approx 5.678571429$$

Solution Steps

Convert decimal number 12.5 to fraction \frac{125}{10}. Reduce the fraction \frac{125}{10} to lowest terms by extracting and canceling out 5.

$$\frac{25}{2}\times \frac{5}{18}-\frac{5}{14}\times \frac{5}{18}+8.3\times \frac{5}{18}$$

Multiply \frac{25}{2} times \frac{5}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 5}{2\times 18}-\frac{5}{14}\times \frac{5}{18}+8.3\times \frac{5}{18}$$

Do the multiplications in the fraction \frac{25\times 5}{2\times 18}.

$$\frac{125}{36}-\frac{5}{14}\times \frac{5}{18}+8.3\times \frac{5}{18}$$

Multiply \frac{5}{14} times \frac{5}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{125}{36}-\frac{5\times 5}{14\times 18}+8.3\times \frac{5}{18}$$

Do the multiplications in the fraction \frac{5\times 5}{14\times 18}.

$$\frac{125}{36}-\frac{25}{252}+8.3\times \frac{5}{18}$$

Least common multiple of 36 and 252 is 252. Convert \frac{125}{36} and \frac{25}{252} to fractions with denominator 252.

$$\frac{875}{252}-\frac{25}{252}+8.3\times \frac{5}{18}$$

Since \frac{875}{252} and \frac{25}{252} have the same denominator, subtract them by subtracting their numerators.

$$\frac{875-25}{252}+8.3\times \frac{5}{18}$$

Subtract 25 from 875 to get 850.

$$\frac{850}{252}+8.3\times \frac{5}{18}$$

Reduce the fraction \frac{850}{252} to lowest terms by extracting and canceling out 2.

$$\frac{425}{126}+8.3\times \frac{5}{18}$$

Convert decimal number 8.3 to fraction \frac{83}{10}.

$$\frac{425}{126}+\frac{83}{10}\times \frac{5}{18}$$

Multiply \frac{83}{10} times \frac{5}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{425}{126}+\frac{83\times 5}{10\times 18}$$

Do the multiplications in the fraction \frac{83\times 5}{10\times 18}.

$$\frac{425}{126}+\frac{415}{180}$$

Reduce the fraction \frac{415}{180} to lowest terms by extracting and canceling out 5.

$$\frac{425}{126}+\frac{83}{36}$$

Least common multiple of 126 and 36 is 252. Convert \frac{425}{126} and \frac{83}{36} to fractions with denominator 252.

$$\frac{850}{252}+\frac{581}{252}$$

Since \frac{850}{252} and \frac{581}{252} have the same denominator, add them by adding their numerators.

$$\frac{850+581}{252}$$

Add 850 and 581 to get 1431.

$$\frac{1431}{252}$$

Reduce the fraction \frac{1431}{252} to lowest terms by extracting and canceling out 9.

$$\frac{159}{28}$$

Factor

$$\frac{3 \cdot 53}{7 \cdot 2 ^ {2}} = 5\frac{19}{28} = 5.678571428571429$$