Solve 1/5lceil420-1/5rceil(30*65

$$\frac{ 1 }{ 5 } \lceil 420- \frac{ 1 }{ 5 } \rceil (30 \times 65$$

Evaluate

$$163800$$

Solution Steps

Convert 420 to fraction \frac{2100}{5}.

$$\frac{1}{5}\lceil \frac{2100}{5}-\frac{1}{5}\rceil \times 30\times 65$$

Since \frac{2100}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}\lceil \frac{2100-1}{5}\rceil \times 30\times 65$$

Subtract 1 from 2100 to get 2099.

$$\frac{1}{5}\lceil \frac{2099}{5}\rceil \times 30\times 65$$

Dividing 2099 by 5 gives 419 and remainder 4. Rewrite \frac{2099}{5} as 419+\frac{4}{5}.

$$\frac{1}{5}\lceil 419+\frac{4}{5}\rceil \times 30\times 65$$

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 419+\frac{4}{5} is 420.

$$\frac{1}{5}\times 420\times 30\times 65$$

Multiply \frac{1}{5} and 420 to get \frac{420}{5}.

$$\frac{420}{5}\times 30\times 65$$

Divide 420 by 5 to get 84.

$$84\times 30\times 65$$

Multiply 84 and 30 to get 2520.

$$2520\times 65$$

Multiply 2520 and 65 to get 163800.

$$163800$$

Factor

$$2^{3}\times 3^{2}\times 5^{2}\times 7\times 13$$