Solve {c}{471/5:12-20:63/7}{35}

$$\left. \begin{array} { c } { 47 \frac { 1 } { 5 } : 12 - 20 : 6 \frac { 3 } { 7 } } \\ { 35 } \end{array} \right.$$

Sort

$$\frac{37}{45},\ 35$$

Solution Steps

Express \frac{\frac{47\times 5+1}{5}}{12} as a single fraction.

$$sort(\frac{47\times 5+1}{5\times 12}-\frac{20}{\frac{6\times 7+3}{7}},35)$$

Multiply 47 and 5 to get 235.

$$sort(\frac{235+1}{5\times 12}-\frac{20}{\frac{6\times 7+3}{7}},35)$$

Add 235 and 1 to get 236.

$$sort(\frac{236}{5\times 12}-\frac{20}{\frac{6\times 7+3}{7}},35)$$

Multiply 5 and 12 to get 60.

$$sort(\frac{236}{60}-\frac{20}{\frac{6\times 7+3}{7}},35)$$

Reduce the fraction \frac{236}{60} to lowest terms by extracting and canceling out 4.

$$sort(\frac{59}{15}-\frac{20}{\frac{6\times 7+3}{7}},35)$$

Divide 20 by \frac{6\times 7+3}{7} by multiplying 20 by the reciprocal of \frac{6\times 7+3}{7}.

$$sort(\frac{59}{15}-\frac{20\times 7}{6\times 7+3},35)$$

Multiply 20 and 7 to get 140.

$$sort(\frac{59}{15}-\frac{140}{6\times 7+3},35)$$

Multiply 6 and 7 to get 42.

$$sort(\frac{59}{15}-\frac{140}{42+3},35)$$

Add 42 and 3 to get 45.

$$sort(\frac{59}{15}-\frac{140}{45},35)$$

Reduce the fraction \frac{140}{45} to lowest terms by extracting and canceling out 5.

$$sort(\frac{59}{15}-\frac{28}{9},35)$$

Least common multiple of 15 and 9 is 45. Convert \frac{59}{15} and \frac{28}{9} to fractions with denominator 45.

$$sort(\frac{177}{45}-\frac{140}{45},35)$$

Since \frac{177}{45} and \frac{140}{45} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{177-140}{45},35)$$

Subtract 140 from 177 to get 37.

$$sort(\frac{37}{45},35)$$

Convert decimal numbers in the list \frac{37}{45},35 to fractions.

$$\frac{37}{45},35$$

Evaluate

$$\frac{37}{45},\ 35$$