Evaluate
\frac{46}{7}\approx 6.571428571
Factor
\frac{2 \cdot 23}{7} = 6\frac{4}{7} = 6.571428571428571
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)230}\\\end{array}
Use the 1^{st} digit 2 from dividend 230
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)230}\\\end{array}
Since 2 is less than 35, use the next digit 3 from dividend 230 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)230}\\\end{array}
Use the 2^{nd} digit 3 from dividend 230
\begin{array}{l}\phantom{35)}00\phantom{4}\\35\overline{)230}\\\end{array}
Since 23 is less than 35, use the next digit 0 from dividend 230 and add 0 to the quotient
\begin{array}{l}\phantom{35)}00\phantom{5}\\35\overline{)230}\\\end{array}
Use the 3^{rd} digit 0 from dividend 230
\begin{array}{l}\phantom{35)}006\phantom{6}\\35\overline{)230}\\\phantom{35)}\underline{\phantom{}210\phantom{}}\\\phantom{35)9}20\\\end{array}
Find closest multiple of 35 to 230. We see that 6 \times 35 = 210 is the nearest. Now subtract 210 from 230 to get reminder 20. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }20
Since 20 is less than 35, stop the division. The reminder is 20. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}