Solve 77div25/51+22^2-25

$$77 \div \frac{ 25 }{ 51+ { 22 }^{ 2 } } -25$$

Evaluate

$$\frac{8114}{5}=1622.8$$

Solution Steps

Divide 77 by \frac{25}{51+22^{2}} by multiplying 77 by the reciprocal of \frac{25}{51+22^{2}}.

$$\frac{77\left(51+22^{2}\right)}{25}-25$$

Calculate 22 to the power of 2 and get 484.

$$\frac{77\left(51+484\right)}{25}-25$$

Add 51 and 484 to get 535.

$$\frac{77\times 535}{25}-25$$

Multiply 77 and 535 to get 41195.

$$\frac{41195}{25}-25$$

Reduce the fraction \frac{41195}{25} to lowest terms by extracting and canceling out 5.

$$\frac{8239}{5}-25$$

Convert 25 to fraction \frac{125}{5}.

$$\frac{8239}{5}-\frac{125}{5}$$

Since \frac{8239}{5} and \frac{125}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8239-125}{5}$$

Subtract 125 from 8239 to get 8114.

$$\frac{8114}{5}$$

Factor

$$\frac{2 \cdot 4057}{5} = 1622\frac{4}{5} = 1622.8$$