Solve {l}{670*7/11+670*1/3}{7/5*(-3/8)+frac{3}{4}*frac{7}{5}}

$$\left. \begin{array} { l } { 670 \times \frac { 7 } { 11 } + 670 \times \frac { 1 } { 3 } } \\ { \frac { 7 } { 5 } \times ( \frac { - 3 } { 8 } ) + \frac { 3 } { 4 } \times \frac { 7 } { 5 } } \end{array} \right.$$

Sort

$$\frac{21}{40},\frac{21440}{33}$$

Solution Steps

Express 670\times \frac{7}{11} as a single fraction.

$$sort(\frac{670\times 7}{11}+670\times \frac{1}{3},\frac{7}{5}\times \frac{-3}{8}+\frac{3}{4}\times \frac{7}{5})$$

Multiply 670 and 7 to get 4690.

$$sort(\frac{4690}{11}+670\times \frac{1}{3},\frac{7}{5}\times \frac{-3}{8}+\frac{3}{4}\times \frac{7}{5})$$

Multiply 670 and \frac{1}{3} to get \frac{670}{3}.

$$sort(\frac{4690}{11}+\frac{670}{3},\frac{7}{5}\times \frac{-3}{8}+\frac{3}{4}\times \frac{7}{5})$$

Least common multiple of 11 and 3 is 33. Convert \frac{4690}{11} and \frac{670}{3} to fractions with denominator 33.

$$sort(\frac{14070}{33}+\frac{7370}{33},\frac{7}{5}\times \frac{-3}{8}+\frac{3}{4}\times \frac{7}{5})$$

Since \frac{14070}{33} and \frac{7370}{33} have the same denominator, add them by adding their numerators.

$$sort(\frac{14070+7370}{33},\frac{7}{5}\times \frac{-3}{8}+\frac{3}{4}\times \frac{7}{5})$$

Add 14070 and 7370 to get 21440.

$$sort(\frac{21440}{33},\frac{7}{5}\times \frac{-3}{8}+\frac{3}{4}\times \frac{7}{5})$$

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$sort(\frac{21440}{33},\frac{7}{5}\left(-\frac{3}{8}\right)+\frac{3}{4}\times \frac{7}{5})$$

Multiply \frac{7}{5} times -\frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{21440}{33},\frac{7\left(-3\right)}{5\times 8}+\frac{3}{4}\times \frac{7}{5})$$

Do the multiplications in the fraction \frac{7\left(-3\right)}{5\times 8}.

$$sort(\frac{21440}{33},\frac{-21}{40}+\frac{3}{4}\times \frac{7}{5})$$

Fraction \frac{-21}{40} can be rewritten as -\frac{21}{40} by extracting the negative sign.

$$sort(\frac{21440}{33},-\frac{21}{40}+\frac{3}{4}\times \frac{7}{5})$$

Multiply \frac{3}{4} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{21440}{33},-\frac{21}{40}+\frac{3\times 7}{4\times 5})$$

Do the multiplications in the fraction \frac{3\times 7}{4\times 5}.

$$sort(\frac{21440}{33},-\frac{21}{40}+\frac{21}{20})$$

Least common multiple of 40 and 20 is 40. Convert -\frac{21}{40} and \frac{21}{20} to fractions with denominator 40.

$$sort(\frac{21440}{33},-\frac{21}{40}+\frac{42}{40})$$

Since -\frac{21}{40} and \frac{42}{40} have the same denominator, add them by adding their numerators.

$$sort(\frac{21440}{33},\frac{-21+42}{40})$$

Add -21 and 42 to get 21.

$$sort(\frac{21440}{33},\frac{21}{40})$$

Least common denominator of the numbers in the list \frac{21440}{33},\frac{21}{40} is 1320. Convert numbers in the list to fractions with denominator 1320.

$$\frac{857600}{1320},\frac{693}{1320}$$

To sort the list, start from a single element \frac{857600}{1320}.

$$\frac{857600}{1320}$$

Insert \frac{693}{1320} to the appropriate location in the new list.

$$\frac{693}{1320},\frac{857600}{1320}$$

Replace the obtained fractions with the initial values.

$$\frac{21}{40},\frac{21440}{33}$$

Evaluate

$$\frac{21440}{33},\ \frac{21}{40}$$