Evaluate
\frac{426}{89}\approx 4.786516854
Factor
\frac{2 \cdot 3 \cdot 71}{89} = 4\frac{70}{89} = 4.786516853932584
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\begin{array}{l}\phantom{89)}\phantom{1}\\89\overline{)426}\\\end{array}
Use the 1^{st} digit 4 from dividend 426
\begin{array}{l}\phantom{89)}0\phantom{2}\\89\overline{)426}\\\end{array}
Since 4 is less than 89, use the next digit 2 from dividend 426 and add 0 to the quotient
\begin{array}{l}\phantom{89)}0\phantom{3}\\89\overline{)426}\\\end{array}
Use the 2^{nd} digit 2 from dividend 426
\begin{array}{l}\phantom{89)}00\phantom{4}\\89\overline{)426}\\\end{array}
Since 42 is less than 89, use the next digit 6 from dividend 426 and add 0 to the quotient
\begin{array}{l}\phantom{89)}00\phantom{5}\\89\overline{)426}\\\end{array}
Use the 3^{rd} digit 6 from dividend 426
\begin{array}{l}\phantom{89)}004\phantom{6}\\89\overline{)426}\\\phantom{89)}\underline{\phantom{}356\phantom{}}\\\phantom{89)9}70\\\end{array}
Find closest multiple of 89 to 426. We see that 4 \times 89 = 356 is the nearest. Now subtract 356 from 426 to get reminder 70. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }70
Since 70 is less than 89, stop the division. The reminder is 70. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}