Evaluate
\frac{325}{3}\approx 108.333333333
Factor
\frac{5 ^ {2} \cdot 13}{3} = 108\frac{1}{3} = 108.33333333333333
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)1300}\\\end{array}
Use the 1^{st} digit 1 from dividend 1300
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)1300}\\\end{array}
Since 1 is less than 12, use the next digit 3 from dividend 1300 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)1300}\\\end{array}
Use the 2^{nd} digit 3 from dividend 1300
\begin{array}{l}\phantom{12)}01\phantom{4}\\12\overline{)1300}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}1\\\end{array}
Find closest multiple of 12 to 13. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 13 to get reminder 1. Add 1 to quotient.
\begin{array}{l}\phantom{12)}01\phantom{5}\\12\overline{)1300}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}10\\\end{array}
Use the 3^{rd} digit 0 from dividend 1300
\begin{array}{l}\phantom{12)}010\phantom{6}\\12\overline{)1300}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}10\\\end{array}
Since 10 is less than 12, use the next digit 0 from dividend 1300 and add 0 to the quotient
\begin{array}{l}\phantom{12)}010\phantom{7}\\12\overline{)1300}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}100\\\end{array}
Use the 4^{th} digit 0 from dividend 1300
\begin{array}{l}\phantom{12)}0108\phantom{8}\\12\overline{)1300}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)9}100\\\phantom{12)}\underline{\phantom{99}96\phantom{}}\\\phantom{12)999}4\\\end{array}
Find closest multiple of 12 to 100. We see that 8 \times 12 = 96 is the nearest. Now subtract 96 from 100 to get reminder 4. Add 8 to quotient.
\text{Quotient: }108 \text{Reminder: }4
Since 4 is less than 12, stop the division. The reminder is 4. The topmost line 0108 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 108.
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}