Evaluate
\frac{5478}{43}\approx 127.395348837
Factor
\frac{2 \cdot 3 \cdot 11 \cdot 83}{43} = 127\frac{17}{43} = 127.3953488372093
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\begin{array}{l}\phantom{43)}\phantom{1}\\43\overline{)5478}\\\end{array}
Use the 1^{st} digit 5 from dividend 5478
\begin{array}{l}\phantom{43)}0\phantom{2}\\43\overline{)5478}\\\end{array}
Since 5 is less than 43, use the next digit 4 from dividend 5478 and add 0 to the quotient
\begin{array}{l}\phantom{43)}0\phantom{3}\\43\overline{)5478}\\\end{array}
Use the 2^{nd} digit 4 from dividend 5478
\begin{array}{l}\phantom{43)}01\phantom{4}\\43\overline{)5478}\\\phantom{43)}\underline{\phantom{}43\phantom{99}}\\\phantom{43)}11\\\end{array}
Find closest multiple of 43 to 54. We see that 1 \times 43 = 43 is the nearest. Now subtract 43 from 54 to get reminder 11. Add 1 to quotient.
\begin{array}{l}\phantom{43)}01\phantom{5}\\43\overline{)5478}\\\phantom{43)}\underline{\phantom{}43\phantom{99}}\\\phantom{43)}117\\\end{array}
Use the 3^{rd} digit 7 from dividend 5478
\begin{array}{l}\phantom{43)}012\phantom{6}\\43\overline{)5478}\\\phantom{43)}\underline{\phantom{}43\phantom{99}}\\\phantom{43)}117\\\phantom{43)}\underline{\phantom{9}86\phantom{9}}\\\phantom{43)9}31\\\end{array}
Find closest multiple of 43 to 117. We see that 2 \times 43 = 86 is the nearest. Now subtract 86 from 117 to get reminder 31. Add 2 to quotient.
\begin{array}{l}\phantom{43)}012\phantom{7}\\43\overline{)5478}\\\phantom{43)}\underline{\phantom{}43\phantom{99}}\\\phantom{43)}117\\\phantom{43)}\underline{\phantom{9}86\phantom{9}}\\\phantom{43)9}318\\\end{array}
Use the 4^{th} digit 8 from dividend 5478
\begin{array}{l}\phantom{43)}0127\phantom{8}\\43\overline{)5478}\\\phantom{43)}\underline{\phantom{}43\phantom{99}}\\\phantom{43)}117\\\phantom{43)}\underline{\phantom{9}86\phantom{9}}\\\phantom{43)9}318\\\phantom{43)}\underline{\phantom{9}301\phantom{}}\\\phantom{43)99}17\\\end{array}
Find closest multiple of 43 to 318. We see that 7 \times 43 = 301 is the nearest. Now subtract 301 from 318 to get reminder 17. Add 7 to quotient.
\text{Quotient: }127 \text{Reminder: }17
Since 17 is less than 43, stop the division. The reminder is 17. The topmost line 0127 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 127.
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}