Evaluate
13
Factor
13
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\begin{array}{l}\phantom{120)}\phantom{1}\\120\overline{)1560}\\\end{array}
Use the 1^{st} digit 1 from dividend 1560
\begin{array}{l}\phantom{120)}0\phantom{2}\\120\overline{)1560}\\\end{array}
Since 1 is less than 120, use the next digit 5 from dividend 1560 and add 0 to the quotient
\begin{array}{l}\phantom{120)}0\phantom{3}\\120\overline{)1560}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1560
\begin{array}{l}\phantom{120)}00\phantom{4}\\120\overline{)1560}\\\end{array}
Since 15 is less than 120, use the next digit 6 from dividend 1560 and add 0 to the quotient
\begin{array}{l}\phantom{120)}00\phantom{5}\\120\overline{)1560}\\\end{array}
Use the 3^{rd} digit 6 from dividend 1560
\begin{array}{l}\phantom{120)}001\phantom{6}\\120\overline{)1560}\\\phantom{120)}\underline{\phantom{}120\phantom{9}}\\\phantom{120)9}36\\\end{array}
Find closest multiple of 120 to 156. We see that 1 \times 120 = 120 is the nearest. Now subtract 120 from 156 to get reminder 36. Add 1 to quotient.
\begin{array}{l}\phantom{120)}001\phantom{7}\\120\overline{)1560}\\\phantom{120)}\underline{\phantom{}120\phantom{9}}\\\phantom{120)9}360\\\end{array}
Use the 4^{th} digit 0 from dividend 1560
\begin{array}{l}\phantom{120)}0013\phantom{8}\\120\overline{)1560}\\\phantom{120)}\underline{\phantom{}120\phantom{9}}\\\phantom{120)9}360\\\phantom{120)}\underline{\phantom{9}360\phantom{}}\\\phantom{120)9999}0\\\end{array}
Find closest multiple of 120 to 360. We see that 3 \times 120 = 360 is the nearest. Now subtract 360 from 360 to get reminder 0. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }0
Since 0 is less than 120, stop the division. The reminder is 0. The topmost line 0013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}