Evaluate
\frac{35467}{678}\approx 52.31120944
Factor
\frac{29 \cdot 1223}{2 \cdot 3 \cdot 113} = 52\frac{211}{678} = 52.31120943952802
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\begin{array}{l}\phantom{678)}\phantom{1}\\678\overline{)35467}\\\end{array}
Use the 1^{st} digit 3 from dividend 35467
\begin{array}{l}\phantom{678)}0\phantom{2}\\678\overline{)35467}\\\end{array}
Since 3 is less than 678, use the next digit 5 from dividend 35467 and add 0 to the quotient
\begin{array}{l}\phantom{678)}0\phantom{3}\\678\overline{)35467}\\\end{array}
Use the 2^{nd} digit 5 from dividend 35467
\begin{array}{l}\phantom{678)}00\phantom{4}\\678\overline{)35467}\\\end{array}
Since 35 is less than 678, use the next digit 4 from dividend 35467 and add 0 to the quotient
\begin{array}{l}\phantom{678)}00\phantom{5}\\678\overline{)35467}\\\end{array}
Use the 3^{rd} digit 4 from dividend 35467
\begin{array}{l}\phantom{678)}000\phantom{6}\\678\overline{)35467}\\\end{array}
Since 354 is less than 678, use the next digit 6 from dividend 35467 and add 0 to the quotient
\begin{array}{l}\phantom{678)}000\phantom{7}\\678\overline{)35467}\\\end{array}
Use the 4^{th} digit 6 from dividend 35467
\begin{array}{l}\phantom{678)}0005\phantom{8}\\678\overline{)35467}\\\phantom{678)}\underline{\phantom{}3390\phantom{9}}\\\phantom{678)9}156\\\end{array}
Find closest multiple of 678 to 3546. We see that 5 \times 678 = 3390 is the nearest. Now subtract 3390 from 3546 to get reminder 156. Add 5 to quotient.
\begin{array}{l}\phantom{678)}0005\phantom{9}\\678\overline{)35467}\\\phantom{678)}\underline{\phantom{}3390\phantom{9}}\\\phantom{678)9}1567\\\end{array}
Use the 5^{th} digit 7 from dividend 35467
\begin{array}{l}\phantom{678)}00052\phantom{10}\\678\overline{)35467}\\\phantom{678)}\underline{\phantom{}3390\phantom{9}}\\\phantom{678)9}1567\\\phantom{678)}\underline{\phantom{9}1356\phantom{}}\\\phantom{678)99}211\\\end{array}
Find closest multiple of 678 to 1567. We see that 2 \times 678 = 1356 is the nearest. Now subtract 1356 from 1567 to get reminder 211. Add 2 to quotient.
\text{Quotient: }52 \text{Reminder: }211
Since 211 is less than 678, stop the division. The reminder is 211. The topmost line 00052 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 52.
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}