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

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

Evaluate

$$9$$

Solution Steps

Divide 1 by 1 to get 1.

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

Convert 1 to fraction \frac{4}{4}.

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

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

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

Add 4 and 1 to get 5.

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

Cancel out 4 and 4.

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

Calculate 1 to the power of 2 and get 1.

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

Calculate 2 to the power of 2 and get 4.

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

Add 1 and 4 to get 5.

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

Calculate 3 to the power of 2 and get 9.

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

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

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

Cancel out 5 and 5.

$$9$$

Factor

$$3^{2}$$