Evaluate
\frac{8562}{25}=342.48
Factor
\frac{2 \cdot 3 \cdot 1427}{5 ^ {2}} = 342\frac{12}{25} = 342.48
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)8562}\\\end{array}
Use the 1^{st} digit 8 from dividend 8562
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)8562}\\\end{array}
Since 8 is less than 25, use the next digit 5 from dividend 8562 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)8562}\\\end{array}
Use the 2^{nd} digit 5 from dividend 8562
\begin{array}{l}\phantom{25)}03\phantom{4}\\25\overline{)8562}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)}10\\\end{array}
Find closest multiple of 25 to 85. We see that 3 \times 25 = 75 is the nearest. Now subtract 75 from 85 to get reminder 10. Add 3 to quotient.
\begin{array}{l}\phantom{25)}03\phantom{5}\\25\overline{)8562}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)}106\\\end{array}
Use the 3^{rd} digit 6 from dividend 8562
\begin{array}{l}\phantom{25)}034\phantom{6}\\25\overline{)8562}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)}106\\\phantom{25)}\underline{\phantom{}100\phantom{9}}\\\phantom{25)99}6\\\end{array}
Find closest multiple of 25 to 106. We see that 4 \times 25 = 100 is the nearest. Now subtract 100 from 106 to get reminder 6. Add 4 to quotient.
\begin{array}{l}\phantom{25)}034\phantom{7}\\25\overline{)8562}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)}106\\\phantom{25)}\underline{\phantom{}100\phantom{9}}\\\phantom{25)99}62\\\end{array}
Use the 4^{th} digit 2 from dividend 8562
\begin{array}{l}\phantom{25)}0342\phantom{8}\\25\overline{)8562}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)}106\\\phantom{25)}\underline{\phantom{}100\phantom{9}}\\\phantom{25)99}62\\\phantom{25)}\underline{\phantom{99}50\phantom{}}\\\phantom{25)99}12\\\end{array}
Find closest multiple of 25 to 62. We see that 2 \times 25 = 50 is the nearest. Now subtract 50 from 62 to get reminder 12. Add 2 to quotient.
\text{Quotient: }342 \text{Reminder: }12
Since 12 is less than 25, stop the division. The reminder is 12. The topmost line 0342 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 342.
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}