Evaluate
\frac{39}{4}=9.75
Factor
\frac{3 \cdot 13}{2 ^ {2}} = 9\frac{3}{4} = 9.75
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)975}\\\end{array}
Use the 1^{st} digit 9 from dividend 975
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)975}\\\end{array}
Since 9 is less than 100, use the next digit 7 from dividend 975 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)975}\\\end{array}
Use the 2^{nd} digit 7 from dividend 975
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)975}\\\end{array}
Since 97 is less than 100, use the next digit 5 from dividend 975 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)975}\\\end{array}
Use the 3^{rd} digit 5 from dividend 975
\begin{array}{l}\phantom{100)}009\phantom{6}\\100\overline{)975}\\\phantom{100)}\underline{\phantom{}900\phantom{}}\\\phantom{100)9}75\\\end{array}
Find closest multiple of 100 to 975. We see that 9 \times 100 = 900 is the nearest. Now subtract 900 from 975 to get reminder 75. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }75
Since 75 is less than 100, stop the division. The reminder is 75. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}