Solve lceil-1+(2^2-5*6)rceildiv(5+2)+1

$$\lceil -1+( { 2 }^{ 2 } -5 \times 6) \rceil \div (5+2)+1$$

Evaluate

$$-\frac{20}{7}\approx -2.857142857$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{\lceil -1+4-5\times 6\rceil }{5+2}+1$$

Multiply 5 and 6 to get 30.

$$\frac{\lceil -1+4-30\rceil }{5+2}+1$$

Subtract 30 from 4 to get -26.

$$\frac{\lceil -1-26\rceil }{5+2}+1$$

Subtract 26 from -1 to get -27.

$$\frac{\lceil -27\rceil }{5+2}+1$$

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of -27 is -27.

$$\frac{-27}{5+2}+1$$

Add 5 and 2 to get 7.

$$\frac{-27}{7}+1$$

Fraction \frac{-27}{7} can be rewritten as -\frac{27}{7} by extracting the negative sign.

$$-\frac{27}{7}+1$$

Convert 1 to fraction \frac{7}{7}.

$$-\frac{27}{7}+\frac{7}{7}$$

Since -\frac{27}{7} and \frac{7}{7} have the same denominator, add them by adding their numerators.

$$\frac{-27+7}{7}$$

Add -27 and 7 to get -20.

$$-\frac{20}{7}$$

Factor

$$-\frac{20}{7} = -2\frac{6}{7} = -2.857142857142857$$