Solve a/3+a^2-1/3div11/5*(1/5)^2

$$\frac { a } { 3 } + a ^ { 2 } - \frac { 1 } { 3 } \div 1 \frac { 1 } { 5 } \cdot ( \frac { 1 } { 5 } ) ^ { 2 }$$

Evaluate

$$a^{2}+\frac{a}{3}-\frac{1}{90}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a^{2} times \frac{3}{3}.

$$\frac{a}{3}+\frac{3a^{2}}{3}-\frac{\frac{1}{3}}{\frac{1\times 5+1}{5}}\times \left(\frac{1}{5}\right)^{2}$$

Since \frac{a}{3} and \frac{3a^{2}}{3} have the same denominator, add them by adding their numerators.

$$\frac{a+3a^{2}}{3}-\frac{\frac{1}{3}}{\frac{1\times 5+1}{5}}\times \left(\frac{1}{5}\right)^{2}$$

Divide \frac{1}{3} by \frac{1\times 5+1}{5} by multiplying \frac{1}{3} by the reciprocal of \frac{1\times 5+1}{5}.

$$\frac{a+3a^{2}}{3}-\frac{5}{3\left(1\times 5+1\right)}\times \left(\frac{1}{5}\right)^{2}$$

Multiply 1 and 5 to get 5.

$$\frac{a+3a^{2}}{3}-\frac{5}{3\left(5+1\right)}\times \left(\frac{1}{5}\right)^{2}$$

Add 5 and 1 to get 6.

$$\frac{a+3a^{2}}{3}-\frac{5}{3\times 6}\times \left(\frac{1}{5}\right)^{2}$$

Multiply 3 and 6 to get 18.

$$\frac{a+3a^{2}}{3}-\frac{5}{18}\times \left(\frac{1}{5}\right)^{2}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\frac{a+3a^{2}}{3}-\frac{5}{18}\times \frac{1}{25}$$

Multiply \frac{5}{18} and \frac{1}{25} to get \frac{1}{90}.

$$\frac{a+3a^{2}}{3}-\frac{1}{90}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 90 is 90. Multiply \frac{a+3a^{2}}{3} times \frac{30}{30}.

$$\frac{30\left(a+3a^{2}\right)}{90}-\frac{1}{90}$$

Since \frac{30\left(a+3a^{2}\right)}{90} and \frac{1}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30\left(a+3a^{2}\right)-1}{90}$$

Do the multiplications in 30\left(a+3a^{2}\right)-1.

$$\frac{30a+90a^{2}-1}{90}$$

Divide each term of 30a+90a^{2}-1 by 90 to get -\frac{1}{90}+\frac{1}{3}a+a^{2}.

$$-\frac{1}{90}+\frac{1}{3}a+a^{2}$$

Expand

$$a^{2}+\frac{a}{3}-\frac{1}{90}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a^{2} times \frac{3}{3}.

$$\frac{a}{3}+\frac{3a^{2}}{3}-\frac{\frac{1}{3}}{\frac{1\times 5+1}{5}}\times \left(\frac{1}{5}\right)^{2}$$

Since \frac{a}{3} and \frac{3a^{2}}{3} have the same denominator, add them by adding their numerators.

$$\frac{a+3a^{2}}{3}-\frac{\frac{1}{3}}{\frac{1\times 5+1}{5}}\times \left(\frac{1}{5}\right)^{2}$$

Divide \frac{1}{3} by \frac{1\times 5+1}{5} by multiplying \frac{1}{3} by the reciprocal of \frac{1\times 5+1}{5}.

$$\frac{a+3a^{2}}{3}-\frac{5}{3\left(1\times 5+1\right)}\times \left(\frac{1}{5}\right)^{2}$$

Multiply 1 and 5 to get 5.

$$\frac{a+3a^{2}}{3}-\frac{5}{3\left(5+1\right)}\times \left(\frac{1}{5}\right)^{2}$$

Add 5 and 1 to get 6.

$$\frac{a+3a^{2}}{3}-\frac{5}{3\times 6}\times \left(\frac{1}{5}\right)^{2}$$

Multiply 3 and 6 to get 18.

$$\frac{a+3a^{2}}{3}-\frac{5}{18}\times \left(\frac{1}{5}\right)^{2}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\frac{a+3a^{2}}{3}-\frac{5}{18}\times \frac{1}{25}$$

Multiply \frac{5}{18} and \frac{1}{25} to get \frac{1}{90}.

$$\frac{a+3a^{2}}{3}-\frac{1}{90}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 90 is 90. Multiply \frac{a+3a^{2}}{3} times \frac{30}{30}.

$$\frac{30\left(a+3a^{2}\right)}{90}-\frac{1}{90}$$

Since \frac{30\left(a+3a^{2}\right)}{90} and \frac{1}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30\left(a+3a^{2}\right)-1}{90}$$

Do the multiplications in 30\left(a+3a^{2}\right)-1.

$$\frac{30a+90a^{2}-1}{90}$$

Divide each term of 30a+90a^{2}-1 by 90 to get -\frac{1}{90}+\frac{1}{3}a+a^{2}.

$$-\frac{1}{90}+\frac{1}{3}a+a^{2}$$