Solve 53/553/5-22/522/5

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

Evaluate

$$\frac{128}{5}=25.6$$

Solution Steps

Multiply \frac{5\times 5+3}{5} and \frac{5\times 5+3}{5} to get \left(\frac{5\times 5+3}{5}\right)^{2}.

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

Multiply \frac{2\times 5+2}{5} and \frac{2\times 5+2}{5} to get \left(\frac{2\times 5+2}{5}\right)^{2}.

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

Multiply 5 and 5 to get 25.

$$\left(\frac{25+3}{5}\right)^{2}-\left(\frac{2\times 5+2}{5}\right)^{2}$$

Add 25 and 3 to get 28.

$$\left(\frac{28}{5}\right)^{2}-\left(\frac{2\times 5+2}{5}\right)^{2}$$

Calculate \frac{28}{5} to the power of 2 and get \frac{784}{25}.

$$\frac{784}{25}-\left(\frac{2\times 5+2}{5}\right)^{2}$$

Multiply 2 and 5 to get 10.

$$\frac{784}{25}-\left(\frac{10+2}{5}\right)^{2}$$

Add 10 and 2 to get 12.

$$\frac{784}{25}-\left(\frac{12}{5}\right)^{2}$$

Calculate \frac{12}{5} to the power of 2 and get \frac{144}{25}.

$$\frac{784}{25}-\frac{144}{25}$$

Since \frac{784}{25} and \frac{144}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{784-144}{25}$$

Subtract 144 from 784 to get 640.

$$\frac{640}{25}$$

Reduce the fraction \frac{640}{25} to lowest terms by extracting and canceling out 5.

$$\frac{128}{5}$$

Factor

$$\frac{2 ^ {7}}{5} = 25\frac{3}{5} = 25.6$$