Solve {l}{(2/3+1/12)*(7/10+1/4)}{(24+3)*(28+10)}

$$\left. \begin{array} { l } { ( \frac { 2 } { 3 } + \frac { 1 } { 12 } ) \cdot ( \frac { 7 } { 10 } + \frac { 1 } { 4 } ) } \\ { ( 24 + 3 ) \cdot ( 28 + 10 ) } \end{array} \right.$$

Sort

$$\frac{57}{80},\ 1026$$

Solution Steps

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{1}{12} to fractions with denominator 12.

$$sort(\left(\frac{8}{12}+\frac{1}{12}\right)\left(\frac{7}{10}+\frac{1}{4}\right),\left(24+3\right)\left(28+10\right))$$

Since \frac{8}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$sort(\frac{8+1}{12}\left(\frac{7}{10}+\frac{1}{4}\right),\left(24+3\right)\left(28+10\right))$$

Add 8 and 1 to get 9.

$$sort(\frac{9}{12}\left(\frac{7}{10}+\frac{1}{4}\right),\left(24+3\right)\left(28+10\right))$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$sort(\frac{3}{4}\left(\frac{7}{10}+\frac{1}{4}\right),\left(24+3\right)\left(28+10\right))$$

Least common multiple of 10 and 4 is 20. Convert \frac{7}{10} and \frac{1}{4} to fractions with denominator 20.

$$sort(\frac{3}{4}\left(\frac{14}{20}+\frac{5}{20}\right),\left(24+3\right)\left(28+10\right))$$

Since \frac{14}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$sort(\frac{3}{4}\times \frac{14+5}{20},\left(24+3\right)\left(28+10\right))$$

Add 14 and 5 to get 19.

$$sort(\frac{3}{4}\times \frac{19}{20},\left(24+3\right)\left(28+10\right))$$

Multiply \frac{3}{4} times \frac{19}{20} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{3\times 19}{4\times 20},\left(24+3\right)\left(28+10\right))$$

Do the multiplications in the fraction \frac{3\times 19}{4\times 20}.

$$sort(\frac{57}{80},\left(24+3\right)\left(28+10\right))$$

Add 24 and 3 to get 27.

$$sort(\frac{57}{80},27\left(28+10\right))$$

Add 28 and 10 to get 38.

$$sort(\frac{57}{80},27\times 38)$$

Multiply 27 and 38 to get 1026.

$$sort(\frac{57}{80},1026)$$

Convert decimal numbers in the list \frac{57}{80},1026 to fractions.

$$\frac{57}{80},1026$$

Evaluate

$$\frac{57}{80},\ 1026$$