Solve {l}{5quad45quad5/5}{25/7+3/10-4(-69/70)}

$$\left. \begin{array} { l } { 5 \quad 45 \quad \frac { 5 } { 5 } } \\ { 2 \frac { 5 } { 7 } + \frac { 3 } { 10 } - 4 ( \frac { - 69 } { 70 } ) } \end{array} \right.$$

Sort

$$\frac{487}{70},230$$

Solution Steps

Multiply 45 and 5 to get 225.

$$sort(5\times \frac{225+5}{5},\frac{2\times 7+5}{7}+\frac{3}{10}-4\times \frac{-69}{70})$$

Add 225 and 5 to get 230.

$$sort(5\times \frac{230}{5},\frac{2\times 7+5}{7}+\frac{3}{10}-4\times \frac{-69}{70})$$

Divide 230 by 5 to get 46.

$$sort(5\times 46,\frac{2\times 7+5}{7}+\frac{3}{10}-4\times \frac{-69}{70})$$

Multiply 5 and 46 to get 230.

$$sort(230,\frac{2\times 7+5}{7}+\frac{3}{10}-4\times \frac{-69}{70})$$

Multiply 2 and 7 to get 14.

$$sort(230,\frac{14+5}{7}+\frac{3}{10}-4\times \frac{-69}{70})$$

Add 14 and 5 to get 19.

$$sort(230,\frac{19}{7}+\frac{3}{10}-4\times \frac{-69}{70})$$

Least common multiple of 7 and 10 is 70. Convert \frac{19}{7} and \frac{3}{10} to fractions with denominator 70.

$$sort(230,\frac{190}{70}+\frac{21}{70}-4\times \frac{-69}{70})$$

Since \frac{190}{70} and \frac{21}{70} have the same denominator, add them by adding their numerators.

$$sort(230,\frac{190+21}{70}-4\times \frac{-69}{70})$$

Add 190 and 21 to get 211.

$$sort(230,\frac{211}{70}-4\times \frac{-69}{70})$$

Fraction \frac{-69}{70} can be rewritten as -\frac{69}{70} by extracting the negative sign.

$$sort(230,\frac{211}{70}-4\left(-\frac{69}{70}\right))$$

Express 4\left(-\frac{69}{70}\right) as a single fraction.

$$sort(230,\frac{211}{70}-\frac{4\left(-69\right)}{70})$$

Multiply 4 and -69 to get -276.

$$sort(230,\frac{211}{70}-\frac{-276}{70})$$

Reduce the fraction \frac{-276}{70} to lowest terms by extracting and canceling out 2.

$$sort(230,\frac{211}{70}-\left(-\frac{138}{35}\right))$$

The opposite of -\frac{138}{35} is \frac{138}{35}.

$$sort(230,\frac{211}{70}+\frac{138}{35})$$

Least common multiple of 70 and 35 is 70. Convert \frac{211}{70} and \frac{138}{35} to fractions with denominator 70.

$$sort(230,\frac{211}{70}+\frac{276}{70})$$

Since \frac{211}{70} and \frac{276}{70} have the same denominator, add them by adding their numerators.

$$sort(230,\frac{211+276}{70})$$

Add 211 and 276 to get 487.

$$sort(230,\frac{487}{70})$$

Convert decimal numbers in the list 230,\frac{487}{70} to fractions.

$$230,\frac{487}{70}$$

To sort the list, start from a single element 230.

$$230$$

Insert \frac{487}{70} to the appropriate location in the new list.

$$\frac{487}{70},230$$

Evaluate

$$230,\ \frac{487}{70}$$