Solve (31/3+13/5):311/22

$$( 3 \frac { 1 } { 3 } + 1 \frac { 3 } { 5 } ) : 3 \frac { 11 } { 22 }$$

Evaluate

$$\frac{148}{105}\approx 1.40952381$$

Solution Steps

Multiply 3 and 3 to get 9.

$$\frac{\frac{9+1}{3}+\frac{1\times 5+3}{5}}{\frac{3\times 22+11}{22}}$$

Add 9 and 1 to get 10.

$$\frac{\frac{10}{3}+\frac{1\times 5+3}{5}}{\frac{3\times 22+11}{22}}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{10}{3}+\frac{5+3}{5}}{\frac{3\times 22+11}{22}}$$

Add 5 and 3 to get 8.

$$\frac{\frac{10}{3}+\frac{8}{5}}{\frac{3\times 22+11}{22}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{10}{3} and \frac{8}{5} to fractions with denominator 15.

$$\frac{\frac{50}{15}+\frac{24}{15}}{\frac{3\times 22+11}{22}}$$

Since \frac{50}{15} and \frac{24}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{50+24}{15}}{\frac{3\times 22+11}{22}}$$

Add 50 and 24 to get 74.

$$\frac{\frac{74}{15}}{\frac{3\times 22+11}{22}}$$

Multiply 3 and 22 to get 66.

$$\frac{\frac{74}{15}}{\frac{66+11}{22}}$$

Add 66 and 11 to get 77.

$$\frac{\frac{74}{15}}{\frac{77}{22}}$$

Reduce the fraction \frac{77}{22} to lowest terms by extracting and canceling out 11.

$$\frac{\frac{74}{15}}{\frac{7}{2}}$$

Divide \frac{74}{15} by \frac{7}{2} by multiplying \frac{74}{15} by the reciprocal of \frac{7}{2}.

$$\frac{74}{15}\times \frac{2}{7}$$

Multiply \frac{74}{15} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{74\times 2}{15\times 7}$$

Do the multiplications in the fraction \frac{74\times 2}{15\times 7}.

$$\frac{148}{105}$$

Factor

$$\frac{2 ^ {2} \cdot 37}{3 \cdot 5 \cdot 7} = 1\frac{43}{105} = 1.4095238095238096$$