Evaluate
125
Factor
5^{3}
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)7500}\\\end{array}
Use the 1^{st} digit 7 from dividend 7500
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)7500}\\\end{array}
Since 7 is less than 60, use the next digit 5 from dividend 7500 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)7500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 7500
\begin{array}{l}\phantom{60)}01\phantom{4}\\60\overline{)7500}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)}15\\\end{array}
Find closest multiple of 60 to 75. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 75 to get reminder 15. Add 1 to quotient.
\begin{array}{l}\phantom{60)}01\phantom{5}\\60\overline{)7500}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)}150\\\end{array}
Use the 3^{rd} digit 0 from dividend 7500
\begin{array}{l}\phantom{60)}012\phantom{6}\\60\overline{)7500}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)}150\\\phantom{60)}\underline{\phantom{}120\phantom{9}}\\\phantom{60)9}30\\\end{array}
Find closest multiple of 60 to 150. We see that 2 \times 60 = 120 is the nearest. Now subtract 120 from 150 to get reminder 30. Add 2 to quotient.
\begin{array}{l}\phantom{60)}012\phantom{7}\\60\overline{)7500}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)}150\\\phantom{60)}\underline{\phantom{}120\phantom{9}}\\\phantom{60)9}300\\\end{array}
Use the 4^{th} digit 0 from dividend 7500
\begin{array}{l}\phantom{60)}0125\phantom{8}\\60\overline{)7500}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)}150\\\phantom{60)}\underline{\phantom{}120\phantom{9}}\\\phantom{60)9}300\\\phantom{60)}\underline{\phantom{9}300\phantom{}}\\\phantom{60)9999}0\\\end{array}
Find closest multiple of 60 to 300. We see that 5 \times 60 = 300 is the nearest. Now subtract 300 from 300 to get reminder 0. Add 5 to quotient.
\text{Quotient: }125 \text{Reminder: }0
Since 0 is less than 60, stop the division. The reminder is 0. The topmost line 0125 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 125.
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}