Evaluate
3
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3
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)75}\\\end{array}
Use the 1^{st} digit 7 from dividend 75
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)75}\\\end{array}
Since 7 is less than 25, use the next digit 5 from dividend 75 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)75}\\\end{array}
Use the 2^{nd} digit 5 from dividend 75
\begin{array}{l}\phantom{25)}03\phantom{4}\\25\overline{)75}\\\phantom{25)}\underline{\phantom{}75\phantom{}}\\\phantom{25)99}0\\\end{array}
Find closest multiple of 25 to 75. We see that 3 \times 25 = 75 is the nearest. Now subtract 75 from 75 to get reminder 0. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }0
Since 0 is less than 25, stop the division. The reminder is 0. The topmost line 03 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}