Evaluate
45
Factor
3^{2}\times 5
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\lceil \frac{1125}{25}-\frac{23}{25}\rceil
Convert 45 to fraction \frac{1125}{25}.
\lceil \frac{1125-23}{25}\rceil
Since \frac{1125}{25} and \frac{23}{25} have the same denominator, subtract them by subtracting their numerators.
\lceil \frac{1102}{25}\rceil
Subtract 23 from 1125 to get 1102.
\lceil 44+\frac{2}{25}\rceil
Dividing 1102 by 25 gives 44 and remainder 2. Rewrite \frac{1102}{25} as 44+\frac{2}{25}.
45
The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 44+\frac{2}{25} is 45.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}