How to solve X. 471000/1000

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve X. 471000/1000 | Equatix

Use the $1^{st}$ digit $4$ from dividend $471000$

$$\begin{array}{l}\phantom{1000)}\phantom{1}\\1000\overline{)471000}\\\end{array}$$

Since $4$ is less than $1000$, use the next digit $7$ from dividend $471000$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{1000)}0\phantom{2}\\1000\overline{)471000}\\\end{array}$$

Use the $2^{nd}$ digit $7$ from dividend $471000$

$$\begin{array}{l}\phantom{1000)}0\phantom{3}\\1000\overline{)471000}\\\end{array}$$

Since $47$ is less than $1000$, use the next digit $1$ from dividend $471000$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{1000)}00\phantom{4}\\1000\overline{)471000}\\\end{array}$$

Use the $3^{rd}$ digit $1$ from dividend $471000$

$$\begin{array}{l}\phantom{1000)}00\phantom{5}\\1000\overline{)471000}\\\end{array}$$

Since $471$ is less than $1000$, use the next digit $0$ from dividend $471000$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{1000)}000\phantom{6}\\1000\overline{)471000}\\\end{array}$$

Use the $4^{th}$ digit $0$ from dividend $471000$

$$\begin{array}{l}\phantom{1000)}000\phantom{7}\\1000\overline{)471000}\\\end{array}$$

Find closest multiple of $1000$ to $4710$. We see that $4 \times 1000 = 4000$ is the nearest. Now subtract $4000$ from $4710$ to get reminder $710$. Add $4$ to quotient.

$$\begin{array}{l}\phantom{1000)}0004\phantom{8}\\1000\overline{)471000}\\\phantom{1000)}\underline{\phantom{}4000\phantom{99}}\\\phantom{1000)9}710\\\end{array}$$

Use the $5^{th}$ digit $0$ from dividend $471000$

$$\begin{array}{l}\phantom{1000)}0004\phantom{9}\\1000\overline{)471000}\\\phantom{1000)}\underline{\phantom{}4000\phantom{99}}\\\phantom{1000)9}7100\\\end{array}$$

Find closest multiple of $1000$ to $7100$. We see that $7 \times 1000 = 7000$ is the nearest. Now subtract $7000$ from $7100$ to get reminder $100$. Add $7$ to quotient.

$$\begin{array}{l}\phantom{1000)}00047\phantom{10}\\1000\overline{)471000}\\\phantom{1000)}\underline{\phantom{}4000\phantom{99}}\\\phantom{1000)9}7100\\\phantom{1000)}\underline{\phantom{9}7000\phantom{9}}\\\phantom{1000)99}100\\\end{array}$$

Use the $6^{th}$ digit $0$ from dividend $471000$

$$\begin{array}{l}\phantom{1000)}00047\phantom{11}\\1000\overline{)471000}\\\phantom{1000)}\underline{\phantom{}4000\phantom{99}}\\\phantom{1000)9}7100\\\phantom{1000)}\underline{\phantom{9}7000\phantom{9}}\\\phantom{1000)99}1000\\\end{array}$$

Find closest multiple of $1000$ to $1000$. We see that $1 \times 1000 = 1000$ is the nearest. Now subtract $1000$ from $1000$ to get reminder $0$. Add $1$ to quotient.

$$\begin{array}{l}\phantom{1000)}000471\phantom{12}\\1000\overline{)471000}\\\phantom{1000)}\underline{\phantom{}4000\phantom{99}}\\\phantom{1000)9}7100\\\phantom{1000)}\underline{\phantom{9}7000\phantom{9}}\\\phantom{1000)99}1000\\\phantom{1000)}\underline{\phantom{99}1000\phantom{}}\\\phantom{1000)999999}0\\\end{array}$$

Since $0$ is less than $1000$, stop the division. The reminder is $0$. The topmost line $000471$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $471$.

$$\text{Quotient: }471$$ $$\text{Reminder: }0$$

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