Evaluate
\frac{125}{16}=7.8125
Factor
\frac{5 ^ {3}}{2 ^ {4}} = 7\frac{13}{16} = 7.8125
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\begin{array}{l}\phantom{16)}\phantom{1}\\16\overline{)125}\\\end{array}
Use the 1^{st} digit 1 from dividend 125
\begin{array}{l}\phantom{16)}0\phantom{2}\\16\overline{)125}\\\end{array}
Since 1 is less than 16, use the next digit 2 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{16)}0\phantom{3}\\16\overline{)125}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125
\begin{array}{l}\phantom{16)}00\phantom{4}\\16\overline{)125}\\\end{array}
Since 12 is less than 16, use the next digit 5 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{16)}00\phantom{5}\\16\overline{)125}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125
\begin{array}{l}\phantom{16)}007\phantom{6}\\16\overline{)125}\\\phantom{16)}\underline{\phantom{}112\phantom{}}\\\phantom{16)9}13\\\end{array}
Find closest multiple of 16 to 125. We see that 7 \times 16 = 112 is the nearest. Now subtract 112 from 125 to get reminder 13. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }13
Since 13 is less than 16, stop the division. The reminder is 13. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}