Evaluate
\frac{231}{5}=46.2
Factor
\frac{3 \cdot 7 \cdot 11}{5} = 46\frac{1}{5} = 46.2
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)1617}\\\end{array}
Use the 1^{st} digit 1 from dividend 1617
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)1617}\\\end{array}
Since 1 is less than 35, use the next digit 6 from dividend 1617 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)1617}\\\end{array}
Use the 2^{nd} digit 6 from dividend 1617
\begin{array}{l}\phantom{35)}00\phantom{4}\\35\overline{)1617}\\\end{array}
Since 16 is less than 35, use the next digit 1 from dividend 1617 and add 0 to the quotient
\begin{array}{l}\phantom{35)}00\phantom{5}\\35\overline{)1617}\\\end{array}
Use the 3^{rd} digit 1 from dividend 1617
\begin{array}{l}\phantom{35)}004\phantom{6}\\35\overline{)1617}\\\phantom{35)}\underline{\phantom{}140\phantom{9}}\\\phantom{35)9}21\\\end{array}
Find closest multiple of 35 to 161. We see that 4 \times 35 = 140 is the nearest. Now subtract 140 from 161 to get reminder 21. Add 4 to quotient.
\begin{array}{l}\phantom{35)}004\phantom{7}\\35\overline{)1617}\\\phantom{35)}\underline{\phantom{}140\phantom{9}}\\\phantom{35)9}217\\\end{array}
Use the 4^{th} digit 7 from dividend 1617
\begin{array}{l}\phantom{35)}0046\phantom{8}\\35\overline{)1617}\\\phantom{35)}\underline{\phantom{}140\phantom{9}}\\\phantom{35)9}217\\\phantom{35)}\underline{\phantom{9}210\phantom{}}\\\phantom{35)999}7\\\end{array}
Find closest multiple of 35 to 217. We see that 6 \times 35 = 210 is the nearest. Now subtract 210 from 217 to get reminder 7. Add 6 to quotient.
\text{Quotient: }46 \text{Reminder: }7
Since 7 is less than 35, stop the division. The reminder is 7. The topmost line 0046 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 46.
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}