Evaluate
125
Factor
5^{3}
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)2500}\\\end{array}
Use the 1^{st} digit 2 from dividend 2500
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)2500}\\\end{array}
Since 2 is less than 20, use the next digit 5 from dividend 2500 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)2500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 2500
\begin{array}{l}\phantom{20)}01\phantom{4}\\20\overline{)2500}\\\phantom{20)}\underline{\phantom{}20\phantom{99}}\\\phantom{20)9}5\\\end{array}
Find closest multiple of 20 to 25. We see that 1 \times 20 = 20 is the nearest. Now subtract 20 from 25 to get reminder 5. Add 1 to quotient.
\begin{array}{l}\phantom{20)}01\phantom{5}\\20\overline{)2500}\\\phantom{20)}\underline{\phantom{}20\phantom{99}}\\\phantom{20)9}50\\\end{array}
Use the 3^{rd} digit 0 from dividend 2500
\begin{array}{l}\phantom{20)}012\phantom{6}\\20\overline{)2500}\\\phantom{20)}\underline{\phantom{}20\phantom{99}}\\\phantom{20)9}50\\\phantom{20)}\underline{\phantom{9}40\phantom{9}}\\\phantom{20)9}10\\\end{array}
Find closest multiple of 20 to 50. We see that 2 \times 20 = 40 is the nearest. Now subtract 40 from 50 to get reminder 10. Add 2 to quotient.
\begin{array}{l}\phantom{20)}012\phantom{7}\\20\overline{)2500}\\\phantom{20)}\underline{\phantom{}20\phantom{99}}\\\phantom{20)9}50\\\phantom{20)}\underline{\phantom{9}40\phantom{9}}\\\phantom{20)9}100\\\end{array}
Use the 4^{th} digit 0 from dividend 2500
\begin{array}{l}\phantom{20)}0125\phantom{8}\\20\overline{)2500}\\\phantom{20)}\underline{\phantom{}20\phantom{99}}\\\phantom{20)9}50\\\phantom{20)}\underline{\phantom{9}40\phantom{9}}\\\phantom{20)9}100\\\phantom{20)}\underline{\phantom{9}100\phantom{}}\\\phantom{20)9999}0\\\end{array}
Find closest multiple of 20 to 100. We see that 5 \times 20 = 100 is the nearest. Now subtract 100 from 100 to get reminder 0. Add 5 to quotient.
\text{Quotient: }125 \text{Reminder: }0
Since 0 is less than 20, stop the division. The reminder is 0. The topmost line 0125 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 125.
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}