Evaluate
125
Factor
5^{3}
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)1500}\\\end{array}
Use the 1^{st} digit 1 from dividend 1500
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)1500}\\\end{array}
Since 1 is less than 12, use the next digit 5 from dividend 1500 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)1500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1500
\begin{array}{l}\phantom{12)}01\phantom{4}\\12\overline{)1500}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}3\\\end{array}
Find closest multiple of 12 to 15. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 15 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{12)}01\phantom{5}\\12\overline{)1500}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}30\\\end{array}
Use the 3^{rd} digit 0 from dividend 1500
\begin{array}{l}\phantom{12)}012\phantom{6}\\12\overline{)1500}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}30\\\phantom{12)}\underline{\phantom{9}24\phantom{9}}\\\phantom{12)99}6\\\end{array}
Find closest multiple of 12 to 30. We see that 2 \times 12 = 24 is the nearest. Now subtract 24 from 30 to get reminder 6. Add 2 to quotient.
\begin{array}{l}\phantom{12)}012\phantom{7}\\12\overline{)1500}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}30\\\phantom{12)}\underline{\phantom{9}24\phantom{9}}\\\phantom{12)99}60\\\end{array}
Use the 4^{th} digit 0 from dividend 1500
\begin{array}{l}\phantom{12)}0125\phantom{8}\\12\overline{)1500}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}30\\\phantom{12)}\underline{\phantom{9}24\phantom{9}}\\\phantom{12)99}60\\\phantom{12)}\underline{\phantom{99}60\phantom{}}\\\phantom{12)9999}0\\\end{array}
Find closest multiple of 12 to 60. We see that 5 \times 12 = 60 is the nearest. Now subtract 60 from 60 to get reminder 0. Add 5 to quotient.
\text{Quotient: }125 \text{Reminder: }0
Since 0 is less than 12, 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}