Evaluate
125
Factor
5^{3}
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)1875}\\\end{array}
Use the 1^{st} digit 1 from dividend 1875
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)1875}\\\end{array}
Since 1 is less than 15, use the next digit 8 from dividend 1875 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)1875}\\\end{array}
Use the 2^{nd} digit 8 from dividend 1875
\begin{array}{l}\phantom{15)}01\phantom{4}\\15\overline{)1875}\\\phantom{15)}\underline{\phantom{}15\phantom{99}}\\\phantom{15)9}3\\\end{array}
Find closest multiple of 15 to 18. We see that 1 \times 15 = 15 is the nearest. Now subtract 15 from 18 to get reminder 3. Add 1 to quotient.
\begin{array}{l}\phantom{15)}01\phantom{5}\\15\overline{)1875}\\\phantom{15)}\underline{\phantom{}15\phantom{99}}\\\phantom{15)9}37\\\end{array}
Use the 3^{rd} digit 7 from dividend 1875
\begin{array}{l}\phantom{15)}012\phantom{6}\\15\overline{)1875}\\\phantom{15)}\underline{\phantom{}15\phantom{99}}\\\phantom{15)9}37\\\phantom{15)}\underline{\phantom{9}30\phantom{9}}\\\phantom{15)99}7\\\end{array}
Find closest multiple of 15 to 37. We see that 2 \times 15 = 30 is the nearest. Now subtract 30 from 37 to get reminder 7. Add 2 to quotient.
\begin{array}{l}\phantom{15)}012\phantom{7}\\15\overline{)1875}\\\phantom{15)}\underline{\phantom{}15\phantom{99}}\\\phantom{15)9}37\\\phantom{15)}\underline{\phantom{9}30\phantom{9}}\\\phantom{15)99}75\\\end{array}
Use the 4^{th} digit 5 from dividend 1875
\begin{array}{l}\phantom{15)}0125\phantom{8}\\15\overline{)1875}\\\phantom{15)}\underline{\phantom{}15\phantom{99}}\\\phantom{15)9}37\\\phantom{15)}\underline{\phantom{9}30\phantom{9}}\\\phantom{15)99}75\\\phantom{15)}\underline{\phantom{99}75\phantom{}}\\\phantom{15)9999}0\\\end{array}
Find closest multiple of 15 to 75. We see that 5 \times 15 = 75 is the nearest. Now subtract 75 from 75 to get reminder 0. Add 5 to quotient.
\text{Quotient: }125 \text{Reminder: }0
Since 0 is less than 15, 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}