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

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

Evaluate

$$\frac{4273}{2280}\approx 1.874122807$$

Solution Steps

Multiply 1 and 4 to get 4.

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

Add 4 and 1 to get 5.

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

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

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

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

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

Add 7 and 10 to get 17.

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

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

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

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

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

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

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

Multiply 2 and 1 to get 2.

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

Add 2 and 1 to get 3.

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

Anything divided by one gives itself.

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

Multiply 1 and 10 to get 10.

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

Add 10 and 1 to get 11.

$$\frac{17}{8}-\frac{\frac{2}{3}}{3-\frac{11}{10}}+\frac{1}{14}\times \frac{7}{5}$$

Convert 3 to fraction \frac{30}{10}.

$$\frac{17}{8}-\frac{\frac{2}{3}}{\frac{30}{10}-\frac{11}{10}}+\frac{1}{14}\times \frac{7}{5}$$

Since \frac{30}{10} and \frac{11}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{8}-\frac{\frac{2}{3}}{\frac{30-11}{10}}+\frac{1}{14}\times \frac{7}{5}$$

Subtract 11 from 30 to get 19.

$$\frac{17}{8}-\frac{\frac{2}{3}}{\frac{19}{10}}+\frac{1}{14}\times \frac{7}{5}$$

Divide \frac{2}{3} by \frac{19}{10} by multiplying \frac{2}{3} by the reciprocal of \frac{19}{10}.

$$\frac{17}{8}-\frac{2}{3}\times \frac{10}{19}+\frac{1}{14}\times \frac{7}{5}$$

Multiply \frac{2}{3} times \frac{10}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17}{8}-\frac{2\times 10}{3\times 19}+\frac{1}{14}\times \frac{7}{5}$$

Do the multiplications in the fraction \frac{2\times 10}{3\times 19}.

$$\frac{17}{8}-\frac{20}{57}+\frac{1}{14}\times \frac{7}{5}$$

Least common multiple of 8 and 57 is 456. Convert \frac{17}{8} and \frac{20}{57} to fractions with denominator 456.

$$\frac{969}{456}-\frac{160}{456}+\frac{1}{14}\times \frac{7}{5}$$

Since \frac{969}{456} and \frac{160}{456} have the same denominator, subtract them by subtracting their numerators.

$$\frac{969-160}{456}+\frac{1}{14}\times \frac{7}{5}$$

Subtract 160 from 969 to get 809.

$$\frac{809}{456}+\frac{1}{14}\times \frac{7}{5}$$

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

$$\frac{809}{456}+\frac{1\times 7}{14\times 5}$$

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

$$\frac{809}{456}+\frac{7}{70}$$

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

$$\frac{809}{456}+\frac{1}{10}$$

Least common multiple of 456 and 10 is 2280. Convert \frac{809}{456} and \frac{1}{10} to fractions with denominator 2280.

$$\frac{4045}{2280}+\frac{228}{2280}$$

Since \frac{4045}{2280} and \frac{228}{2280} have the same denominator, add them by adding their numerators.

$$\frac{4045+228}{2280}$$

Add 4045 and 228 to get 4273.

$$\frac{4273}{2280}$$

Factor

$$\frac{4273}{2 ^ {3} \cdot 3 \cdot 5 \cdot 19} = 1\frac{1993}{2280} = 1.874122807017544$$