Solve (12/3+41/2+25/6):(43/10+3frac{1}{5}+1frac{7}{20})

$$( 1 \frac { 2 } { 3 } + 4 \frac { 1 } { 2 } + 2 \frac { 5 } { 6 } ) : ( 4 \frac { 3 } { 10 } + 3 \frac { 1 } { 5 } + 1 \frac { 7 } { 20 } )$$

Evaluate

$$\frac{60}{59}\approx 1.016949153$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{\frac{3+2}{3}+\frac{4\times 2+1}{2}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{3}+\frac{4\times 2+1}{2}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{5}{3}+\frac{8+1}{2}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{5}{3}+\frac{9}{2}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{9}{2} to fractions with denominator 6.

$$\frac{\frac{10}{6}+\frac{27}{6}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Since \frac{10}{6} and \frac{27}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+27}{6}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Add 10 and 27 to get 37.

$$\frac{\frac{37}{6}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Multiply 2 and 6 to get 12.

$$\frac{\frac{37}{6}+\frac{12+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Add 12 and 5 to get 17.

$$\frac{\frac{37}{6}+\frac{17}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Since \frac{37}{6} and \frac{17}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{37+17}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Add 37 and 17 to get 54.

$$\frac{\frac{54}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Divide 54 by 6 to get 9.

$$\frac{9}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Multiply 4 and 10 to get 40.

$$\frac{9}{\frac{40+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Add 40 and 3 to get 43.

$$\frac{9}{\frac{43}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Multiply 3 and 5 to get 15.

$$\frac{9}{\frac{43}{10}+\frac{15+1}{5}+\frac{1\times 20+7}{20}}$$

Add 15 and 1 to get 16.

$$\frac{9}{\frac{43}{10}+\frac{16}{5}+\frac{1\times 20+7}{20}}$$

Least common multiple of 10 and 5 is 10. Convert \frac{43}{10} and \frac{16}{5} to fractions with denominator 10.

$$\frac{9}{\frac{43}{10}+\frac{32}{10}+\frac{1\times 20+7}{20}}$$

Since \frac{43}{10} and \frac{32}{10} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{43+32}{10}+\frac{1\times 20+7}{20}}$$

Add 43 and 32 to get 75.

$$\frac{9}{\frac{75}{10}+\frac{1\times 20+7}{20}}$$

Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{9}{\frac{15}{2}+\frac{1\times 20+7}{20}}$$

Multiply 1 and 20 to get 20.

$$\frac{9}{\frac{15}{2}+\frac{20+7}{20}}$$

Add 20 and 7 to get 27.

$$\frac{9}{\frac{15}{2}+\frac{27}{20}}$$

Least common multiple of 2 and 20 is 20. Convert \frac{15}{2} and \frac{27}{20} to fractions with denominator 20.

$$\frac{9}{\frac{150}{20}+\frac{27}{20}}$$

Since \frac{150}{20} and \frac{27}{20} have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{150+27}{20}}$$

Add 150 and 27 to get 177.

$$\frac{9}{\frac{177}{20}}$$

Divide 9 by \frac{177}{20} by multiplying 9 by the reciprocal of \frac{177}{20}.

$$9\times \frac{20}{177}$$

Express 9\times \frac{20}{177} as a single fraction.

$$\frac{9\times 20}{177}$$

Multiply 9 and 20 to get 180.

$$\frac{180}{177}$$

Reduce the fraction \frac{180}{177} to lowest terms by extracting and canceling out 3.

$$\frac{60}{59}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 5}{59} = 1\frac{1}{59} = 1.0169491525423728$$