Evaluate
42
Factor
2\times 3\times 7
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\begin{array}{l}\phantom{69)}\phantom{1}\\69\overline{)2898}\\\end{array}
Use the 1^{st} digit 2 from dividend 2898
\begin{array}{l}\phantom{69)}0\phantom{2}\\69\overline{)2898}\\\end{array}
Since 2 is less than 69, use the next digit 8 from dividend 2898 and add 0 to the quotient
\begin{array}{l}\phantom{69)}0\phantom{3}\\69\overline{)2898}\\\end{array}
Use the 2^{nd} digit 8 from dividend 2898
\begin{array}{l}\phantom{69)}00\phantom{4}\\69\overline{)2898}\\\end{array}
Since 28 is less than 69, use the next digit 9 from dividend 2898 and add 0 to the quotient
\begin{array}{l}\phantom{69)}00\phantom{5}\\69\overline{)2898}\\\end{array}
Use the 3^{rd} digit 9 from dividend 2898
\begin{array}{l}\phantom{69)}004\phantom{6}\\69\overline{)2898}\\\phantom{69)}\underline{\phantom{}276\phantom{9}}\\\phantom{69)9}13\\\end{array}
Find closest multiple of 69 to 289. We see that 4 \times 69 = 276 is the nearest. Now subtract 276 from 289 to get reminder 13. Add 4 to quotient.
\begin{array}{l}\phantom{69)}004\phantom{7}\\69\overline{)2898}\\\phantom{69)}\underline{\phantom{}276\phantom{9}}\\\phantom{69)9}138\\\end{array}
Use the 4^{th} digit 8 from dividend 2898
\begin{array}{l}\phantom{69)}0042\phantom{8}\\69\overline{)2898}\\\phantom{69)}\underline{\phantom{}276\phantom{9}}\\\phantom{69)9}138\\\phantom{69)}\underline{\phantom{9}138\phantom{}}\\\phantom{69)9999}0\\\end{array}
Find closest multiple of 69 to 138. We see that 2 \times 69 = 138 is the nearest. Now subtract 138 from 138 to get reminder 0. Add 2 to quotient.
\text{Quotient: }42 \text{Reminder: }0
Since 0 is less than 69, 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}