Solve 4(1/2+1/4)div2/3^2+2^2

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

Evaluate

$$\frac{35}{2}=17.5$$

Solution Steps

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

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

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

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

Add 2 and 1 to get 3.

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

Cancel out 4 and 4.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{3}{\frac{2}{9}}+2^{2}$$

Divide 3 by \frac{2}{9} by multiplying 3 by the reciprocal of \frac{2}{9}.

$$3\times \frac{9}{2}+2^{2}$$

Express 3\times \frac{9}{2} as a single fraction.

$$\frac{3\times 9}{2}+2^{2}$$

Multiply 3 and 9 to get 27.

$$\frac{27}{2}+2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{27}{2}+4$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{27}{2}+\frac{8}{2}$$

Since \frac{27}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{27+8}{2}$$

Add 27 and 8 to get 35.

$$\frac{35}{2}$$

Factor

$$\frac{5 \cdot 7}{2} = 17\frac{1}{2} = 17.5$$