Evaluate
\frac{609}{5}=121.8
Factor
\frac{3 \cdot 7 \cdot 29}{5} = 121\frac{4}{5} = 121.8
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\begin{array}{l}\phantom{10)}\phantom{1}\\10\overline{)1218}\\\end{array}
Use the 1^{st} digit 1 from dividend 1218
\begin{array}{l}\phantom{10)}0\phantom{2}\\10\overline{)1218}\\\end{array}
Since 1 is less than 10, use the next digit 2 from dividend 1218 and add 0 to the quotient
\begin{array}{l}\phantom{10)}0\phantom{3}\\10\overline{)1218}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1218
\begin{array}{l}\phantom{10)}01\phantom{4}\\10\overline{)1218}\\\phantom{10)}\underline{\phantom{}10\phantom{99}}\\\phantom{10)9}2\\\end{array}
Find closest multiple of 10 to 12. We see that 1 \times 10 = 10 is the nearest. Now subtract 10 from 12 to get reminder 2. Add 1 to quotient.
\begin{array}{l}\phantom{10)}01\phantom{5}\\10\overline{)1218}\\\phantom{10)}\underline{\phantom{}10\phantom{99}}\\\phantom{10)9}21\\\end{array}
Use the 3^{rd} digit 1 from dividend 1218
\begin{array}{l}\phantom{10)}012\phantom{6}\\10\overline{)1218}\\\phantom{10)}\underline{\phantom{}10\phantom{99}}\\\phantom{10)9}21\\\phantom{10)}\underline{\phantom{9}20\phantom{9}}\\\phantom{10)99}1\\\end{array}
Find closest multiple of 10 to 21. We see that 2 \times 10 = 20 is the nearest. Now subtract 20 from 21 to get reminder 1. Add 2 to quotient.
\begin{array}{l}\phantom{10)}012\phantom{7}\\10\overline{)1218}\\\phantom{10)}\underline{\phantom{}10\phantom{99}}\\\phantom{10)9}21\\\phantom{10)}\underline{\phantom{9}20\phantom{9}}\\\phantom{10)99}18\\\end{array}
Use the 4^{th} digit 8 from dividend 1218
\begin{array}{l}\phantom{10)}0121\phantom{8}\\10\overline{)1218}\\\phantom{10)}\underline{\phantom{}10\phantom{99}}\\\phantom{10)9}21\\\phantom{10)}\underline{\phantom{9}20\phantom{9}}\\\phantom{10)99}18\\\phantom{10)}\underline{\phantom{99}10\phantom{}}\\\phantom{10)999}8\\\end{array}
Find closest multiple of 10 to 18. We see that 1 \times 10 = 10 is the nearest. Now subtract 10 from 18 to get reminder 8. Add 1 to quotient.
\text{Quotient: }121 \text{Reminder: }8
Since 8 is less than 10, stop the division. The reminder is 8. The topmost line 0121 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 121.
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}