Solve 12/3/5.5+17/12/2.25-frac{8{15}}

$$\frac{ 1 \frac{ 2 }{ 3 } }{ 5.5 } + \frac{ 1 \frac{ 7 }{ 12 } }{ 2.25- \frac{ 8 }{ 15 } }$$

Evaluate

$$\frac{4165}{3399}\approx 1.2253604$$

Solution Steps

Express \frac{\frac{1\times 3+2}{3}}{5.5} as a single fraction.

$$\frac{1\times 3+2}{3\times 5.5}+\frac{\frac{1\times 12+7}{12}}{2.25-\frac{8}{15}}$$

Multiply 1 and 3 to get 3.

$$\frac{3+2}{3\times 5.5}+\frac{\frac{1\times 12+7}{12}}{2.25-\frac{8}{15}}$$

Add 3 and 2 to get 5.

$$\frac{5}{3\times 5.5}+\frac{\frac{1\times 12+7}{12}}{2.25-\frac{8}{15}}$$

Multiply 3 and 5.5 to get 16.5.

$$\frac{5}{16.5}+\frac{\frac{1\times 12+7}{12}}{2.25-\frac{8}{15}}$$

Expand \frac{5}{16.5} by multiplying both numerator and the denominator by 10.

$$\frac{50}{165}+\frac{\frac{1\times 12+7}{12}}{2.25-\frac{8}{15}}$$

Reduce the fraction \frac{50}{165} to lowest terms by extracting and canceling out 5.

$$\frac{10}{33}+\frac{\frac{1\times 12+7}{12}}{2.25-\frac{8}{15}}$$

Multiply 1 and 12 to get 12.

$$\frac{10}{33}+\frac{\frac{12+7}{12}}{2.25-\frac{8}{15}}$$

Add 12 and 7 to get 19.

$$\frac{10}{33}+\frac{\frac{19}{12}}{2.25-\frac{8}{15}}$$

Convert decimal number 2.25 to fraction \frac{225}{100}. Reduce the fraction \frac{225}{100} to lowest terms by extracting and canceling out 25.

$$\frac{10}{33}+\frac{\frac{19}{12}}{\frac{9}{4}-\frac{8}{15}}$$

Least common multiple of 4 and 15 is 60. Convert \frac{9}{4} and \frac{8}{15} to fractions with denominator 60.

$$\frac{10}{33}+\frac{\frac{19}{12}}{\frac{135}{60}-\frac{32}{60}}$$

Since \frac{135}{60} and \frac{32}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{33}+\frac{\frac{19}{12}}{\frac{135-32}{60}}$$

Subtract 32 from 135 to get 103.

$$\frac{10}{33}+\frac{\frac{19}{12}}{\frac{103}{60}}$$

Divide \frac{19}{12} by \frac{103}{60} by multiplying \frac{19}{12} by the reciprocal of \frac{103}{60}.

$$\frac{10}{33}+\frac{19}{12}\times \frac{60}{103}$$

Multiply \frac{19}{12} times \frac{60}{103} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10}{33}+\frac{19\times 60}{12\times 103}$$

Do the multiplications in the fraction \frac{19\times 60}{12\times 103}.

$$\frac{10}{33}+\frac{1140}{1236}$$

Reduce the fraction \frac{1140}{1236} to lowest terms by extracting and canceling out 12.

$$\frac{10}{33}+\frac{95}{103}$$

Least common multiple of 33 and 103 is 3399. Convert \frac{10}{33} and \frac{95}{103} to fractions with denominator 3399.

$$\frac{1030}{3399}+\frac{3135}{3399}$$

Since \frac{1030}{3399} and \frac{3135}{3399} have the same denominator, add them by adding their numerators.

$$\frac{1030+3135}{3399}$$

Add 1030 and 3135 to get 4165.

$$\frac{4165}{3399}$$

Factor

$$\frac{5 \cdot 17 \cdot 7 ^ {2}}{3 \cdot 11 \cdot 103} = 1\frac{766}{3399} = 1.2253604001176817$$