Evaluate
42
Factor
2\times 3\times 7
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\begin{array}{l}\phantom{56)}\phantom{1}\\56\overline{)2352}\\\end{array}
Use the 1^{st} digit 2 from dividend 2352
\begin{array}{l}\phantom{56)}0\phantom{2}\\56\overline{)2352}\\\end{array}
Since 2 is less than 56, use the next digit 3 from dividend 2352 and add 0 to the quotient
\begin{array}{l}\phantom{56)}0\phantom{3}\\56\overline{)2352}\\\end{array}
Use the 2^{nd} digit 3 from dividend 2352
\begin{array}{l}\phantom{56)}00\phantom{4}\\56\overline{)2352}\\\end{array}
Since 23 is less than 56, use the next digit 5 from dividend 2352 and add 0 to the quotient
\begin{array}{l}\phantom{56)}00\phantom{5}\\56\overline{)2352}\\\end{array}
Use the 3^{rd} digit 5 from dividend 2352
\begin{array}{l}\phantom{56)}004\phantom{6}\\56\overline{)2352}\\\phantom{56)}\underline{\phantom{}224\phantom{9}}\\\phantom{56)9}11\\\end{array}
Find closest multiple of 56 to 235. We see that 4 \times 56 = 224 is the nearest. Now subtract 224 from 235 to get reminder 11. Add 4 to quotient.
\begin{array}{l}\phantom{56)}004\phantom{7}\\56\overline{)2352}\\\phantom{56)}\underline{\phantom{}224\phantom{9}}\\\phantom{56)9}112\\\end{array}
Use the 4^{th} digit 2 from dividend 2352
\begin{array}{l}\phantom{56)}0042\phantom{8}\\56\overline{)2352}\\\phantom{56)}\underline{\phantom{}224\phantom{9}}\\\phantom{56)9}112\\\phantom{56)}\underline{\phantom{9}112\phantom{}}\\\phantom{56)9999}0\\\end{array}
Find closest multiple of 56 to 112. We see that 2 \times 56 = 112 is the nearest. Now subtract 112 from 112 to get reminder 0. Add 2 to quotient.
\text{Quotient: }42 \text{Reminder: }0
Since 0 is less than 56, stop the division. The reminder is 0. The topmost line 0042 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 42.
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}