Solve 1-2-frac{2/5/1-frac{3{10}}}{2+1/4}+frac{1/3-2}{frac{2}{3}-1}

$$\frac{ 1- \frac{ 2- \frac{ 2 }{ 5 } }{ 1- \frac{ 3 }{ 10 } } }{ 2+ \frac{ 1 }{ 4 } } + \frac{ \frac{ 1 }{ 3 } -2 }{ \frac{ 2 }{ 3 } -1 }$$

Evaluate

$$\frac{31}{7}\approx 4.428571429$$

Solution Steps

Convert 2 to fraction \frac{10}{5}.

$$\frac{1-\frac{\frac{10}{5}-\frac{2}{5}}{1-\frac{3}{10}}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Since \frac{10}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-\frac{\frac{10-2}{5}}{1-\frac{3}{10}}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Subtract 2 from 10 to get 8.

$$\frac{1-\frac{\frac{8}{5}}{1-\frac{3}{10}}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{1-\frac{\frac{8}{5}}{\frac{10}{10}-\frac{3}{10}}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Since \frac{10}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-\frac{\frac{8}{5}}{\frac{10-3}{10}}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Subtract 3 from 10 to get 7.

$$\frac{1-\frac{\frac{8}{5}}{\frac{7}{10}}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Divide \frac{8}{5} by \frac{7}{10} by multiplying \frac{8}{5} by the reciprocal of \frac{7}{10}.

$$\frac{1-\frac{8}{5}\times \frac{10}{7}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Multiply \frac{8}{5} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1-\frac{8\times 10}{5\times 7}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Do the multiplications in the fraction \frac{8\times 10}{5\times 7}.

$$\frac{1-\frac{80}{35}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Reduce the fraction \frac{80}{35} to lowest terms by extracting and canceling out 5.

$$\frac{1-\frac{16}{7}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{\frac{7}{7}-\frac{16}{7}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Since \frac{7}{7} and \frac{16}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-16}{7}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Subtract 16 from 7 to get -9.

$$\frac{-\frac{9}{7}}{2+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{-\frac{9}{7}}{\frac{8}{4}+\frac{1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Since \frac{8}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{9}{7}}{\frac{8+1}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Add 8 and 1 to get 9.

$$\frac{-\frac{9}{7}}{\frac{9}{4}}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Divide -\frac{9}{7} by \frac{9}{4} by multiplying -\frac{9}{7} by the reciprocal of \frac{9}{4}.

$$-\frac{9}{7}\times \frac{4}{9}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Multiply -\frac{9}{7} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9\times 4}{7\times 9}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Do the multiplications in the fraction \frac{-9\times 4}{7\times 9}.

$$\frac{-36}{63}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Reduce the fraction \frac{-36}{63} to lowest terms by extracting and canceling out 9.

$$-\frac{4}{7}+\frac{\frac{1}{3}-2}{\frac{2}{3}-1}$$

Convert 2 to fraction \frac{6}{3}.

$$-\frac{4}{7}+\frac{\frac{1}{3}-\frac{6}{3}}{\frac{2}{3}-1}$$

Since \frac{1}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{4}{7}+\frac{\frac{1-6}{3}}{\frac{2}{3}-1}$$

Subtract 6 from 1 to get -5.

$$-\frac{4}{7}+\frac{-\frac{5}{3}}{\frac{2}{3}-1}$$

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

$$-\frac{4}{7}+\frac{-\frac{5}{3}}{\frac{2}{3}-\frac{3}{3}}$$

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

$$-\frac{4}{7}+\frac{-\frac{5}{3}}{\frac{2-3}{3}}$$

Subtract 3 from 2 to get -1.

$$-\frac{4}{7}+\frac{-\frac{5}{3}}{-\frac{1}{3}}$$

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

$$-\frac{4}{7}-\frac{5}{3}\left(-3\right)$$

Express -\frac{5}{3}\left(-3\right) as a single fraction.

$$-\frac{4}{7}+\frac{-5\left(-3\right)}{3}$$

Multiply -5 and -3 to get 15.

$$-\frac{4}{7}+\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$-\frac{4}{7}+5$$

Convert 5 to fraction \frac{35}{7}.

$$-\frac{4}{7}+\frac{35}{7}$$

Since -\frac{4}{7} and \frac{35}{7} have the same denominator, add them by adding their numerators.

$$\frac{-4+35}{7}$$

Add -4 and 35 to get 31.

$$\frac{31}{7}$$

Factor

$$\frac{31}{7} = 4\frac{3}{7} = 4.428571428571429$$