Solve 41/232/3+1/4/2-frac{1{5}}

$$\frac { 4 \frac { 1 } { 2 } 3 \frac { 2 } { 3 } + \frac { 1 } { 4 } } { 2 - \frac { 1 } { 5 } }$$

Evaluate

$$\frac{335}{36}\approx 9.305555556$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{\frac{8+1}{2}\times \frac{3\times 3+2}{3}+\frac{1}{4}}{2-\frac{1}{5}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{9}{2}\times \frac{3\times 3+2}{3}+\frac{1}{4}}{2-\frac{1}{5}}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{9}{2}\times \frac{9+2}{3}+\frac{1}{4}}{2-\frac{1}{5}}$$

Add 9 and 2 to get 11.

$$\frac{\frac{9}{2}\times \frac{11}{3}+\frac{1}{4}}{2-\frac{1}{5}}$$

Multiply \frac{9}{2} times \frac{11}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\times 11}{2\times 3}+\frac{1}{4}}{2-\frac{1}{5}}$$

Do the multiplications in the fraction \frac{9\times 11}{2\times 3}.

$$\frac{\frac{99}{6}+\frac{1}{4}}{2-\frac{1}{5}}$$

Reduce the fraction \frac{99}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{33}{2}+\frac{1}{4}}{2-\frac{1}{5}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{33}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{\frac{66}{4}+\frac{1}{4}}{2-\frac{1}{5}}$$

Since \frac{66}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{66+1}{4}}{2-\frac{1}{5}}$$

Add 66 and 1 to get 67.

$$\frac{\frac{67}{4}}{2-\frac{1}{5}}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{67}{4}}{\frac{10}{5}-\frac{1}{5}}$$

Since \frac{10}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{67}{4}}{\frac{10-1}{5}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{67}{4}}{\frac{9}{5}}$$

Divide \frac{67}{4} by \frac{9}{5} by multiplying \frac{67}{4} by the reciprocal of \frac{9}{5}.

$$\frac{67}{4}\times \frac{5}{9}$$

Multiply \frac{67}{4} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{67\times 5}{4\times 9}$$

Do the multiplications in the fraction \frac{67\times 5}{4\times 9}.

$$\frac{335}{36}$$

Factor

$$\frac{5 \cdot 67}{2 ^ {2} \cdot 3 ^ {2}} = 9\frac{11}{36} = 9.305555555555555$$