Solve 7/8+11/4-3/2*frac{4/9}{2frac{1}{2}-1frac{1}{10}+frac{1}{14}*frac{7}{5}}

$$\frac { \frac { 7 } { 8 } + 1 \frac { 1 } { 4 } - \frac { 3 } { 2 } \times \frac { 4 } { 9 } } { 2 \frac { 1 } { 2 } - 1 \frac { 1 } { 10 } + \frac { 1 } { 14 } \times \frac { 7 } { 5 } }$$

Evaluate

$$\frac{35}{36}\approx 0.972222222$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{\frac{7}{8}+\frac{4+1}{4}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{7}{8}+\frac{5}{4}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Least common multiple of 8 and 4 is 8. Convert \frac{7}{8} and \frac{5}{4} to fractions with denominator 8.

$$\frac{\frac{7}{8}+\frac{10}{8}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Since \frac{7}{8} and \frac{10}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7+10}{8}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Add 7 and 10 to get 17.

$$\frac{\frac{17}{8}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Multiply \frac{3}{2} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{17}{8}-\frac{3\times 4}{2\times 9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Do the multiplications in the fraction \frac{3\times 4}{2\times 9}.

$$\frac{\frac{17}{8}-\frac{12}{18}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{17}{8}-\frac{2}{3}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Least common multiple of 8 and 3 is 24. Convert \frac{17}{8} and \frac{2}{3} to fractions with denominator 24.

$$\frac{\frac{51}{24}-\frac{16}{24}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Since \frac{51}{24} and \frac{16}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{51-16}{24}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Subtract 16 from 51 to get 35.

$$\frac{\frac{35}{24}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{35}{24}}{\frac{4+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{35}{24}}{\frac{5}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Multiply 1 and 10 to get 10.

$$\frac{\frac{35}{24}}{\frac{5}{2}-\frac{10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{35}{24}}{\frac{5}{2}-\frac{11}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Least common multiple of 2 and 10 is 10. Convert \frac{5}{2} and \frac{11}{10} to fractions with denominator 10.

$$\frac{\frac{35}{24}}{\frac{25}{10}-\frac{11}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Since \frac{25}{10} and \frac{11}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{35}{24}}{\frac{25-11}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Subtract 11 from 25 to get 14.

$$\frac{\frac{35}{24}}{\frac{14}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{35}{24}}{\frac{7}{5}+\frac{1}{14}\times \frac{7}{5}}$$

Multiply \frac{1}{14} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{35}{24}}{\frac{7}{5}+\frac{1\times 7}{14\times 5}}$$

Do the multiplications in the fraction \frac{1\times 7}{14\times 5}.

$$\frac{\frac{35}{24}}{\frac{7}{5}+\frac{7}{70}}$$

Reduce the fraction \frac{7}{70} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{35}{24}}{\frac{7}{5}+\frac{1}{10}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{7}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{\frac{35}{24}}{\frac{14}{10}+\frac{1}{10}}$$

Since \frac{14}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{35}{24}}{\frac{14+1}{10}}$$

Add 14 and 1 to get 15.

$$\frac{\frac{35}{24}}{\frac{15}{10}}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{35}{24}}{\frac{3}{2}}$$

Divide \frac{35}{24} by \frac{3}{2} by multiplying \frac{35}{24} by the reciprocal of \frac{3}{2}.

$$\frac{35}{24}\times \frac{2}{3}$$

Multiply \frac{35}{24} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 2}{24\times 3}$$

Do the multiplications in the fraction \frac{35\times 2}{24\times 3}.

$$\frac{70}{72}$$

Reduce the fraction \frac{70}{72} to lowest terms by extracting and canceling out 2.

$$\frac{35}{36}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {2} \cdot 3 ^ {2}} = 0.9722222222222222$$