Evaluate
\frac{42}{25}=1.68
Factor
\frac{2 \cdot 3 \cdot 7}{5 ^ {2}} = 1\frac{17}{25} = 1.68
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)42}\\\end{array}
Use the 1^{st} digit 4 from dividend 42
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)42}\\\end{array}
Since 4 is less than 25, use the next digit 2 from dividend 42 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)42}\\\end{array}
Use the 2^{nd} digit 2 from dividend 42
\begin{array}{l}\phantom{25)}01\phantom{4}\\25\overline{)42}\\\phantom{25)}\underline{\phantom{}25\phantom{}}\\\phantom{25)}17\\\end{array}
Find closest multiple of 25 to 42. We see that 1 \times 25 = 25 is the nearest. Now subtract 25 from 42 to get reminder 17. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }17
Since 17 is less than 25, stop the division. The reminder is 17. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}