Evaluate
\frac{1706}{21}\approx 81.238095238
Factor
\frac{2 \cdot 853}{3 \cdot 7} = 81\frac{5}{21} = 81.23809523809524
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)3412}\\\end{array}
Use the 1^{st} digit 3 from dividend 3412
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)3412}\\\end{array}
Since 3 is less than 42, use the next digit 4 from dividend 3412 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)3412}\\\end{array}
Use the 2^{nd} digit 4 from dividend 3412
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)3412}\\\end{array}
Since 34 is less than 42, use the next digit 1 from dividend 3412 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)3412}\\\end{array}
Use the 3^{rd} digit 1 from dividend 3412
\begin{array}{l}\phantom{42)}008\phantom{6}\\42\overline{)3412}\\\phantom{42)}\underline{\phantom{}336\phantom{9}}\\\phantom{42)99}5\\\end{array}
Find closest multiple of 42 to 341. We see that 8 \times 42 = 336 is the nearest. Now subtract 336 from 341 to get reminder 5. Add 8 to quotient.
\begin{array}{l}\phantom{42)}008\phantom{7}\\42\overline{)3412}\\\phantom{42)}\underline{\phantom{}336\phantom{9}}\\\phantom{42)99}52\\\end{array}
Use the 4^{th} digit 2 from dividend 3412
\begin{array}{l}\phantom{42)}0081\phantom{8}\\42\overline{)3412}\\\phantom{42)}\underline{\phantom{}336\phantom{9}}\\\phantom{42)99}52\\\phantom{42)}\underline{\phantom{99}42\phantom{}}\\\phantom{42)99}10\\\end{array}
Find closest multiple of 42 to 52. We see that 1 \times 42 = 42 is the nearest. Now subtract 42 from 52 to get reminder 10. Add 1 to quotient.
\text{Quotient: }81 \text{Reminder: }10
Since 10 is less than 42, stop the division. The reminder is 10. The topmost line 0081 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 81.
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}