Evaluate
\frac{1078}{25}=43.12
Factor
\frac{2 \cdot 7 ^ {2} \cdot 11}{5 ^ {2}} = 43\frac{3}{25} = 43.12
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)3234}\\\end{array}
Use the 1^{st} digit 3 from dividend 3234
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)3234}\\\end{array}
Since 3 is less than 75, use the next digit 2 from dividend 3234 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)3234}\\\end{array}
Use the 2^{nd} digit 2 from dividend 3234
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)3234}\\\end{array}
Since 32 is less than 75, use the next digit 3 from dividend 3234 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)3234}\\\end{array}
Use the 3^{rd} digit 3 from dividend 3234
\begin{array}{l}\phantom{75)}004\phantom{6}\\75\overline{)3234}\\\phantom{75)}\underline{\phantom{}300\phantom{9}}\\\phantom{75)9}23\\\end{array}
Find closest multiple of 75 to 323. We see that 4 \times 75 = 300 is the nearest. Now subtract 300 from 323 to get reminder 23. Add 4 to quotient.
\begin{array}{l}\phantom{75)}004\phantom{7}\\75\overline{)3234}\\\phantom{75)}\underline{\phantom{}300\phantom{9}}\\\phantom{75)9}234\\\end{array}
Use the 4^{th} digit 4 from dividend 3234
\begin{array}{l}\phantom{75)}0043\phantom{8}\\75\overline{)3234}\\\phantom{75)}\underline{\phantom{}300\phantom{9}}\\\phantom{75)9}234\\\phantom{75)}\underline{\phantom{9}225\phantom{}}\\\phantom{75)999}9\\\end{array}
Find closest multiple of 75 to 234. We see that 3 \times 75 = 225 is the nearest. Now subtract 225 from 234 to get reminder 9. Add 3 to quotient.
\text{Quotient: }43 \text{Reminder: }9
Since 9 is less than 75, stop the division. The reminder is 9. The topmost line 0043 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 43.
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}