Evaluate
54
Factor
2\times 3^{3}
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)1242}\\\end{array}
Use the 1^{st} digit 1 from dividend 1242
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)1242}\\\end{array}
Since 1 is less than 23, use the next digit 2 from dividend 1242 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)1242}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1242
\begin{array}{l}\phantom{23)}00\phantom{4}\\23\overline{)1242}\\\end{array}
Since 12 is less than 23, use the next digit 4 from dividend 1242 and add 0 to the quotient
\begin{array}{l}\phantom{23)}00\phantom{5}\\23\overline{)1242}\\\end{array}
Use the 3^{rd} digit 4 from dividend 1242
\begin{array}{l}\phantom{23)}005\phantom{6}\\23\overline{)1242}\\\phantom{23)}\underline{\phantom{}115\phantom{9}}\\\phantom{23)99}9\\\end{array}
Find closest multiple of 23 to 124. We see that 5 \times 23 = 115 is the nearest. Now subtract 115 from 124 to get reminder 9. Add 5 to quotient.
\begin{array}{l}\phantom{23)}005\phantom{7}\\23\overline{)1242}\\\phantom{23)}\underline{\phantom{}115\phantom{9}}\\\phantom{23)99}92\\\end{array}
Use the 4^{th} digit 2 from dividend 1242
\begin{array}{l}\phantom{23)}0054\phantom{8}\\23\overline{)1242}\\\phantom{23)}\underline{\phantom{}115\phantom{9}}\\\phantom{23)99}92\\\phantom{23)}\underline{\phantom{99}92\phantom{}}\\\phantom{23)9999}0\\\end{array}
Find closest multiple of 23 to 92. We see that 4 \times 23 = 92 is the nearest. Now subtract 92 from 92 to get reminder 0. Add 4 to quotient.
\text{Quotient: }54 \text{Reminder: }0
Since 0 is less than 23, stop the division. The reminder is 0. The topmost line 0054 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 54.
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}