Evaluate
21
Factor
3\times 7
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)525}\\\end{array}
Use the 1^{st} digit 5 from dividend 525
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)525}\\\end{array}
Since 5 is less than 25, use the next digit 2 from dividend 525 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)525}\\\end{array}
Use the 2^{nd} digit 2 from dividend 525
\begin{array}{l}\phantom{25)}02\phantom{4}\\25\overline{)525}\\\phantom{25)}\underline{\phantom{}50\phantom{9}}\\\phantom{25)9}2\\\end{array}
Find closest multiple of 25 to 52. We see that 2 \times 25 = 50 is the nearest. Now subtract 50 from 52 to get reminder 2. Add 2 to quotient.
\begin{array}{l}\phantom{25)}02\phantom{5}\\25\overline{)525}\\\phantom{25)}\underline{\phantom{}50\phantom{9}}\\\phantom{25)9}25\\\end{array}
Use the 3^{rd} digit 5 from dividend 525
\begin{array}{l}\phantom{25)}021\phantom{6}\\25\overline{)525}\\\phantom{25)}\underline{\phantom{}50\phantom{9}}\\\phantom{25)9}25\\\phantom{25)}\underline{\phantom{9}25\phantom{}}\\\phantom{25)999}0\\\end{array}
Find closest multiple of 25 to 25. We see that 1 \times 25 = 25 is the nearest. Now subtract 25 from 25 to get reminder 0. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }0
Since 0 is less than 25, stop the division. The reminder is 0. The topmost line 021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}