15 - \lceil 7 - ( 2 \frac { 1 } { 4 }
Evaluate
10
Factor
2\times 5
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15-\lceil 7-\frac{8+1}{4}\rceil
Multiply 2 and 4 to get 8.
15-\lceil 7-\frac{9}{4}\rceil
Add 8 and 1 to get 9.
15-\lceil \frac{28}{4}-\frac{9}{4}\rceil
Convert 7 to fraction \frac{28}{4}.
15-\lceil \frac{28-9}{4}\rceil
Since \frac{28}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.
15-\lceil \frac{19}{4}\rceil
Subtract 9 from 28 to get 19.
15-\lceil 4+\frac{3}{4}\rceil
Dividing 19 by 4 gives 4 and remainder 3. Rewrite \frac{19}{4} as 4+\frac{3}{4}.
15-5
The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 4+\frac{3}{4} is 5.
10
Subtract 5 from 15 to get 10.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
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}