Evaluate
\frac{21948}{985}\approx 22.282233503
Factor
\frac{2 ^ {2} \cdot 3 \cdot 31 \cdot 59}{5 \cdot 197} = 22\frac{278}{985} = 22.28223350253807
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\begin{array}{l}\phantom{1970)}\phantom{1}\\1970\overline{)43896}\\\end{array}
Use the 1^{st} digit 4 from dividend 43896
\begin{array}{l}\phantom{1970)}0\phantom{2}\\1970\overline{)43896}\\\end{array}
Since 4 is less than 1970, use the next digit 3 from dividend 43896 and add 0 to the quotient
\begin{array}{l}\phantom{1970)}0\phantom{3}\\1970\overline{)43896}\\\end{array}
Use the 2^{nd} digit 3 from dividend 43896
\begin{array}{l}\phantom{1970)}00\phantom{4}\\1970\overline{)43896}\\\end{array}
Since 43 is less than 1970, use the next digit 8 from dividend 43896 and add 0 to the quotient
\begin{array}{l}\phantom{1970)}00\phantom{5}\\1970\overline{)43896}\\\end{array}
Use the 3^{rd} digit 8 from dividend 43896
\begin{array}{l}\phantom{1970)}000\phantom{6}\\1970\overline{)43896}\\\end{array}
Since 438 is less than 1970, use the next digit 9 from dividend 43896 and add 0 to the quotient
\begin{array}{l}\phantom{1970)}000\phantom{7}\\1970\overline{)43896}\\\end{array}
Use the 4^{th} digit 9 from dividend 43896
\begin{array}{l}\phantom{1970)}0002\phantom{8}\\1970\overline{)43896}\\\phantom{1970)}\underline{\phantom{}3940\phantom{9}}\\\phantom{1970)9}449\\\end{array}
Find closest multiple of 1970 to 4389. We see that 2 \times 1970 = 3940 is the nearest. Now subtract 3940 from 4389 to get reminder 449. Add 2 to quotient.
\begin{array}{l}\phantom{1970)}0002\phantom{9}\\1970\overline{)43896}\\\phantom{1970)}\underline{\phantom{}3940\phantom{9}}\\\phantom{1970)9}4496\\\end{array}
Use the 5^{th} digit 6 from dividend 43896
\begin{array}{l}\phantom{1970)}00022\phantom{10}\\1970\overline{)43896}\\\phantom{1970)}\underline{\phantom{}3940\phantom{9}}\\\phantom{1970)9}4496\\\phantom{1970)}\underline{\phantom{9}3940\phantom{}}\\\phantom{1970)99}556\\\end{array}
Find closest multiple of 1970 to 4496. We see that 2 \times 1970 = 3940 is the nearest. Now subtract 3940 from 4496 to get reminder 556. Add 2 to quotient.
\text{Quotient: }22 \text{Reminder: }556
Since 556 is less than 1970, stop the division. The reminder is 556. The topmost line 00022 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 22.
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}