Solve 1+1/4/frac{frac{1{2}}{1+2/3}-1-frac{1/4}{frac{1}{3}}}*(10frac{1}{3}-3frac{2}{3})

$$\frac { 1 + \frac { 1 } { 4 } } { \frac { \frac { 1 } { 2 } } { 1 + \frac { 2 } { 3 } } - \frac { 1 - \frac { 1 } { 4 } } { \frac { 1 } { 3 } } } \times ( 10 \frac { 1 } { 3 } - 3 \frac { 2 } { 3 } )$$

Evaluate

$$-\frac{500}{117}\approx -4.273504274$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{4}{4}+\frac{1}{4}}{\frac{\frac{1}{2}}{1+\frac{2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+1}{4}}{\frac{\frac{1}{2}}{1+\frac{2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Add 4 and 1 to get 5.

$$\frac{\frac{5}{4}}{\frac{\frac{1}{2}}{1+\frac{2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{5}{4}}{\frac{\frac{1}{2}}{\frac{3}{3}+\frac{2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{4}}{\frac{\frac{1}{2}}{\frac{3+2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{4}}{\frac{\frac{1}{2}}{\frac{5}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Divide \frac{1}{2} by \frac{5}{3} by multiplying \frac{1}{2} by the reciprocal of \frac{5}{3}.

$$\frac{\frac{5}{4}}{\frac{1}{2}\times \frac{3}{5}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Multiply \frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{4}}{\frac{1\times 3}{2\times 5}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 5}.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{\frac{4}{4}-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{\frac{4-1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{\frac{3}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Divide \frac{3}{4} by \frac{1}{3} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{3}.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{3}{4}\times 3}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Express \frac{3}{4}\times 3 as a single fraction.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{3\times 3}{4}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{9}{4}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Least common multiple of 10 and 4 is 20. Convert \frac{3}{10} and \frac{9}{4} to fractions with denominator 20.

$$\frac{\frac{5}{4}}{\frac{6}{20}-\frac{45}{20}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Since \frac{6}{20} and \frac{45}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{4}}{\frac{6-45}{20}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Subtract 45 from 6 to get -39.

$$\frac{\frac{5}{4}}{-\frac{39}{20}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Divide \frac{5}{4} by -\frac{39}{20} by multiplying \frac{5}{4} by the reciprocal of -\frac{39}{20}.

$$\frac{5}{4}\left(-\frac{20}{39}\right)\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Multiply \frac{5}{4} times -\frac{20}{39} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-20\right)}{4\times 39}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Do the multiplications in the fraction \frac{5\left(-20\right)}{4\times 39}.

$$\frac{-100}{156}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Reduce the fraction \frac{-100}{156} to lowest terms by extracting and canceling out 4.

$$-\frac{25}{39}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Multiply 10 and 3 to get 30.

$$-\frac{25}{39}\left(\frac{30+1}{3}-\frac{3\times 3+2}{3}\right)$$

Add 30 and 1 to get 31.

$$-\frac{25}{39}\left(\frac{31}{3}-\frac{3\times 3+2}{3}\right)$$

Multiply 3 and 3 to get 9.

$$-\frac{25}{39}\left(\frac{31}{3}-\frac{9+2}{3}\right)$$

Add 9 and 2 to get 11.

$$-\frac{25}{39}\left(\frac{31}{3}-\frac{11}{3}\right)$$

Since \frac{31}{3} and \frac{11}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{25}{39}\times \frac{31-11}{3}$$

Subtract 11 from 31 to get 20.

$$-\frac{25}{39}\times \frac{20}{3}$$

Multiply -\frac{25}{39} times \frac{20}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-25\times 20}{39\times 3}$$

Do the multiplications in the fraction \frac{-25\times 20}{39\times 3}.

$$\frac{-500}{117}$$

Fraction \frac{-500}{117} can be rewritten as -\frac{500}{117} by extracting the negative sign.

$$-\frac{500}{117}$$

Factor

$$-\frac{500}{117} = -4\frac{32}{117} = -4.273504273504273$$