Solve 4(1/2+1/4)div1^2+2^2/1/3^2

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

Evaluate

$$\frac{1}{15}\approx 0.066666667$$

Solution Steps

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

$$\frac{\frac{4\left(\frac{2}{4}+\frac{1}{4}\right)}{\frac{1^{2}+2^{2}}{1}}}{3^{2}}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

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

Cancel out 4 and 4.

$$\frac{\frac{3}{\frac{1^{2}+2^{2}}{1}}}{3^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\frac{3}{\frac{1+2^{2}}{1}}}{3^{2}}$$

Calculate 2 to the power of 2 and get 4.

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

Add 1 and 4 to get 5.

$$\frac{\frac{3}{\frac{5}{1}}}{3^{2}}$$

Anything divided by one gives itself.

$$\frac{\frac{3}{5}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{3}{5}}{9}$$

Express \frac{\frac{3}{5}}{9} as a single fraction.

$$\frac{3}{5\times 9}$$

Multiply 5 and 9 to get 45.

$$\frac{3}{45}$$

Reduce the fraction \frac{3}{45} to lowest terms by extracting and canceling out 3.

$$\frac{1}{15}$$

Factor

$$\frac{1}{3 \cdot 5} = 0.06666666666666667$$