Solve (58/9:117/26+11/4):41/5

$$( 5 \frac { 8 } { 9 } : 1 \frac { 17 } { 26 } + 1 \frac { 1 } { 4 } ) : 4 \frac { 1 } { 5 }$$

Evaluate

$$\frac{37235}{32508}\approx 1.145410361$$

Solution Steps

Divide \frac{5\times 9+8}{9} by \frac{1\times 26+17}{26} by multiplying \frac{5\times 9+8}{9} by the reciprocal of \frac{1\times 26+17}{26}.

$$\frac{\frac{\left(5\times 9+8\right)\times 26}{9\left(1\times 26+17\right)}+\frac{1\times 4+1}{4}}{\frac{4\times 5+1}{5}}$$

Multiply 5 and 9 to get 45.

$$\frac{\frac{\left(45+8\right)\times 26}{9\left(1\times 26+17\right)}+\frac{1\times 4+1}{4}}{\frac{4\times 5+1}{5}}$$

Add 45 and 8 to get 53.

$$\frac{\frac{53\times 26}{9\left(1\times 26+17\right)}+\frac{1\times 4+1}{4}}{\frac{4\times 5+1}{5}}$$

Multiply 53 and 26 to get 1378.

$$\frac{\frac{1378}{9\left(1\times 26+17\right)}+\frac{1\times 4+1}{4}}{\frac{4\times 5+1}{5}}$$

Multiply 1 and 26 to get 26.

$$\frac{\frac{1378}{9\left(26+17\right)}+\frac{1\times 4+1}{4}}{\frac{4\times 5+1}{5}}$$

Add 26 and 17 to get 43.

$$\frac{\frac{1378}{9\times 43}+\frac{1\times 4+1}{4}}{\frac{4\times 5+1}{5}}$$

Multiply 9 and 43 to get 387.

$$\frac{\frac{1378}{387}+\frac{1\times 4+1}{4}}{\frac{4\times 5+1}{5}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{1378}{387}+\frac{4+1}{4}}{\frac{4\times 5+1}{5}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{1378}{387}+\frac{5}{4}}{\frac{4\times 5+1}{5}}$$

Least common multiple of 387 and 4 is 1548. Convert \frac{1378}{387} and \frac{5}{4} to fractions with denominator 1548.

$$\frac{\frac{5512}{1548}+\frac{1935}{1548}}{\frac{4\times 5+1}{5}}$$

Since \frac{5512}{1548} and \frac{1935}{1548} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5512+1935}{1548}}{\frac{4\times 5+1}{5}}$$

Add 5512 and 1935 to get 7447.

$$\frac{\frac{7447}{1548}}{\frac{4\times 5+1}{5}}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{7447}{1548}}{\frac{20+1}{5}}$$

Add 20 and 1 to get 21.

$$\frac{\frac{7447}{1548}}{\frac{21}{5}}$$

Divide \frac{7447}{1548} by \frac{21}{5} by multiplying \frac{7447}{1548} by the reciprocal of \frac{21}{5}.

$$\frac{7447}{1548}\times \frac{5}{21}$$

Multiply \frac{7447}{1548} times \frac{5}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7447\times 5}{1548\times 21}$$

Do the multiplications in the fraction \frac{7447\times 5}{1548\times 21}.

$$\frac{37235}{32508}$$

Factor

$$\frac{5 \cdot 11 \cdot 677}{2 ^ {2} \cdot 3 ^ {3} \cdot 7 \cdot 43} = 1\frac{4727}{32508} = 1.1454103605266397$$