Evaluate
\frac{156}{5}=31.2
Factor
\frac{2 ^ {2} \cdot 3 \cdot 13}{5} = 31\frac{1}{5} = 31.2
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)3120}\\\end{array}
Use the 1^{st} digit 3 from dividend 3120
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)3120}\\\end{array}
Since 3 is less than 100, use the next digit 1 from dividend 3120 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)3120}\\\end{array}
Use the 2^{nd} digit 1 from dividend 3120
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)3120}\\\end{array}
Since 31 is less than 100, use the next digit 2 from dividend 3120 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)3120}\\\end{array}
Use the 3^{rd} digit 2 from dividend 3120
\begin{array}{l}\phantom{100)}003\phantom{6}\\100\overline{)3120}\\\phantom{100)}\underline{\phantom{}300\phantom{9}}\\\phantom{100)9}12\\\end{array}
Find closest multiple of 100 to 312. We see that 3 \times 100 = 300 is the nearest. Now subtract 300 from 312 to get reminder 12. Add 3 to quotient.
\begin{array}{l}\phantom{100)}003\phantom{7}\\100\overline{)3120}\\\phantom{100)}\underline{\phantom{}300\phantom{9}}\\\phantom{100)9}120\\\end{array}
Use the 4^{th} digit 0 from dividend 3120
\begin{array}{l}\phantom{100)}0031\phantom{8}\\100\overline{)3120}\\\phantom{100)}\underline{\phantom{}300\phantom{9}}\\\phantom{100)9}120\\\phantom{100)}\underline{\phantom{9}100\phantom{}}\\\phantom{100)99}20\\\end{array}
Find closest multiple of 100 to 120. We see that 1 \times 100 = 100 is the nearest. Now subtract 100 from 120 to get reminder 20. Add 1 to quotient.
\text{Quotient: }31 \text{Reminder: }20
Since 20 is less than 100, stop the division. The reminder is 20. The topmost line 0031 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 31.
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}