Solve (2/3+3/4)*1/2+4/2+frac{1}{4}:3^2

$$( \frac { 2 } { 3 } + \frac { 3 } { 4 } ) \cdot \frac { 1 } { 2 } + \frac { 4 } { 2 } + \frac { 1 } { 4 } : 3 ^ { 2 }$$

Evaluate

$$\frac{197}{72}\approx 2.736111111$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$\left(\frac{8}{12}+\frac{9}{12}\right)\times \frac{1}{2}+\frac{4}{2}+\frac{\frac{1}{4}}{3^{2}}$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+9}{12}\times \frac{1}{2}+\frac{4}{2}+\frac{\frac{1}{4}}{3^{2}}$$

Add 8 and 9 to get 17.

$$\frac{17}{12}\times \frac{1}{2}+\frac{4}{2}+\frac{\frac{1}{4}}{3^{2}}$$

Multiply \frac{17}{12} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 1}{12\times 2}+\frac{4}{2}+\frac{\frac{1}{4}}{3^{2}}$$

Do the multiplications in the fraction \frac{17\times 1}{12\times 2}.

$$\frac{17}{24}+\frac{4}{2}+\frac{\frac{1}{4}}{3^{2}}$$

Divide 4 by 2 to get 2.

$$\frac{17}{24}+2+\frac{\frac{1}{4}}{3^{2}}$$

Convert 2 to fraction \frac{48}{24}.

$$\frac{17}{24}+\frac{48}{24}+\frac{\frac{1}{4}}{3^{2}}$$

Since \frac{17}{24} and \frac{48}{24} have the same denominator, add them by adding their numerators.

$$\frac{17+48}{24}+\frac{\frac{1}{4}}{3^{2}}$$

Add 17 and 48 to get 65.

$$\frac{65}{24}+\frac{\frac{1}{4}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{65}{24}+\frac{\frac{1}{4}}{9}$$

Express \frac{\frac{1}{4}}{9} as a single fraction.

$$\frac{65}{24}+\frac{1}{4\times 9}$$

Multiply 4 and 9 to get 36.

$$\frac{65}{24}+\frac{1}{36}$$

Least common multiple of 24 and 36 is 72. Convert \frac{65}{24} and \frac{1}{36} to fractions with denominator 72.

$$\frac{195}{72}+\frac{2}{72}$$

Since \frac{195}{72} and \frac{2}{72} have the same denominator, add them by adding their numerators.

$$\frac{195+2}{72}$$

Add 195 and 2 to get 197.

$$\frac{197}{72}$$

Factor

$$\frac{197}{2 ^ {3} \cdot 3 ^ {2}} = 2\frac{53}{72} = 2.736111111111111$$