Evaluate
47
Factor
47
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\begin{array}{l}\phantom{14)}\phantom{1}\\14\overline{)658}\\\end{array}
Use the 1^{st} digit 6 from dividend 658
\begin{array}{l}\phantom{14)}0\phantom{2}\\14\overline{)658}\\\end{array}
Since 6 is less than 14, use the next digit 5 from dividend 658 and add 0 to the quotient
\begin{array}{l}\phantom{14)}0\phantom{3}\\14\overline{)658}\\\end{array}
Use the 2^{nd} digit 5 from dividend 658
\begin{array}{l}\phantom{14)}04\phantom{4}\\14\overline{)658}\\\phantom{14)}\underline{\phantom{}56\phantom{9}}\\\phantom{14)9}9\\\end{array}
Find closest multiple of 14 to 65. We see that 4 \times 14 = 56 is the nearest. Now subtract 56 from 65 to get reminder 9. Add 4 to quotient.
\begin{array}{l}\phantom{14)}04\phantom{5}\\14\overline{)658}\\\phantom{14)}\underline{\phantom{}56\phantom{9}}\\\phantom{14)9}98\\\end{array}
Use the 3^{rd} digit 8 from dividend 658
\begin{array}{l}\phantom{14)}047\phantom{6}\\14\overline{)658}\\\phantom{14)}\underline{\phantom{}56\phantom{9}}\\\phantom{14)9}98\\\phantom{14)}\underline{\phantom{9}98\phantom{}}\\\phantom{14)999}0\\\end{array}
Find closest multiple of 14 to 98. We see that 7 \times 14 = 98 is the nearest. Now subtract 98 from 98 to get reminder 0. Add 7 to quotient.
\text{Quotient: }47 \text{Reminder: }0
Since 0 is less than 14, stop the division. The reminder is 0. The topmost line 047 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 47.
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}