Evaluate
\frac{2378}{43}\approx 55.302325581
Factor
\frac{2 \cdot 29 \cdot 41}{43} = 55\frac{13}{43} = 55.30232558139535
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\begin{array}{l}\phantom{43)}\phantom{1}\\43\overline{)2378}\\\end{array}
Use the 1^{st} digit 2 from dividend 2378
\begin{array}{l}\phantom{43)}0\phantom{2}\\43\overline{)2378}\\\end{array}
Since 2 is less than 43, use the next digit 3 from dividend 2378 and add 0 to the quotient
\begin{array}{l}\phantom{43)}0\phantom{3}\\43\overline{)2378}\\\end{array}
Use the 2^{nd} digit 3 from dividend 2378
\begin{array}{l}\phantom{43)}00\phantom{4}\\43\overline{)2378}\\\end{array}
Since 23 is less than 43, use the next digit 7 from dividend 2378 and add 0 to the quotient
\begin{array}{l}\phantom{43)}00\phantom{5}\\43\overline{)2378}\\\end{array}
Use the 3^{rd} digit 7 from dividend 2378
\begin{array}{l}\phantom{43)}005\phantom{6}\\43\overline{)2378}\\\phantom{43)}\underline{\phantom{}215\phantom{9}}\\\phantom{43)9}22\\\end{array}
Find closest multiple of 43 to 237. We see that 5 \times 43 = 215 is the nearest. Now subtract 215 from 237 to get reminder 22. Add 5 to quotient.
\begin{array}{l}\phantom{43)}005\phantom{7}\\43\overline{)2378}\\\phantom{43)}\underline{\phantom{}215\phantom{9}}\\\phantom{43)9}228\\\end{array}
Use the 4^{th} digit 8 from dividend 2378
\begin{array}{l}\phantom{43)}0055\phantom{8}\\43\overline{)2378}\\\phantom{43)}\underline{\phantom{}215\phantom{9}}\\\phantom{43)9}228\\\phantom{43)}\underline{\phantom{9}215\phantom{}}\\\phantom{43)99}13\\\end{array}
Find closest multiple of 43 to 228. We see that 5 \times 43 = 215 is the nearest. Now subtract 215 from 228 to get reminder 13. Add 5 to quotient.
\text{Quotient: }55 \text{Reminder: }13
Since 13 is less than 43, stop the division. The reminder is 13. The topmost line 0055 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 55.
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}