Evaluate
45
Factor
3^{2}\times 5
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)1125}\\\end{array}
Use the 1^{st} digit 1 from dividend 1125
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)1125}\\\end{array}
Since 1 is less than 25, use the next digit 1 from dividend 1125 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)1125}\\\end{array}
Use the 2^{nd} digit 1 from dividend 1125
\begin{array}{l}\phantom{25)}00\phantom{4}\\25\overline{)1125}\\\end{array}
Since 11 is less than 25, use the next digit 2 from dividend 1125 and add 0 to the quotient
\begin{array}{l}\phantom{25)}00\phantom{5}\\25\overline{)1125}\\\end{array}
Use the 3^{rd} digit 2 from dividend 1125
\begin{array}{l}\phantom{25)}004\phantom{6}\\25\overline{)1125}\\\phantom{25)}\underline{\phantom{}100\phantom{9}}\\\phantom{25)9}12\\\end{array}
Find closest multiple of 25 to 112. We see that 4 \times 25 = 100 is the nearest. Now subtract 100 from 112 to get reminder 12. Add 4 to quotient.
\begin{array}{l}\phantom{25)}004\phantom{7}\\25\overline{)1125}\\\phantom{25)}\underline{\phantom{}100\phantom{9}}\\\phantom{25)9}125\\\end{array}
Use the 4^{th} digit 5 from dividend 1125
\begin{array}{l}\phantom{25)}0045\phantom{8}\\25\overline{)1125}\\\phantom{25)}\underline{\phantom{}100\phantom{9}}\\\phantom{25)9}125\\\phantom{25)}\underline{\phantom{9}125\phantom{}}\\\phantom{25)9999}0\\\end{array}
Find closest multiple of 25 to 125. We see that 5 \times 25 = 125 is the nearest. Now subtract 125 from 125 to get reminder 0. Add 5 to quotient.
\text{Quotient: }45 \text{Reminder: }0
Since 0 is less than 25, stop the division. The reminder is 0. The topmost line 0045 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 45.
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}