Question Divide 9,876 by 123 using long division. Find the quotient and remainder.

Studdy Solution

STEP 1

Assumptions
1. We are performing a long division of two numbers: $9,876$ (dividend) and $123$ (divisor).
2. The result will include a quotient and possibly a remainder.

STEP 2

Set up the long division by writing the dividend ( $9,876$ ) inside the division bracket and the divisor ( $123$ ) outside, to the left.
$\begin{array}{r} \phantom{0} \\ 123 \overline{)9,876} \\ \end{array}$

STEP 3

Determine how many times the divisor $123$ can fit into the first digit of the dividend ( $9$ ). Since $123$ is larger than $9$ , we cannot divide $123$ into $9$ . Therefore, we consider the first two digits of the dividend ( $98$ ).
$\begin{array}{r} \phantom{0} \\ 123 \overline{)9,876} \\ \end{array}$

STEP 4

Determine how many times $123$ can fit into $98$ . Since $123$ is still larger than $98$ , we cannot divide $123$ into $98$ either. Thus, we consider the first three digits of the dividend ( $987$ ).
$\begin{array}{r} \phantom{0} \\ 123 \overline{)9,876} \\ \end{array}$

STEP 5

Estimate how many times $123$ can fit into $987$ . Since $123 \times 8 = 984$ , which is less than $987$ , we can use $8$ as the first digit of our quotient.
$\begin{array}{r} \phantom{0}8 \\ 123 \overline{)9,876} \\ \end{array}$

STEP 6

Multiply the divisor $123$ by the first digit of the quotient $8$ and write the result under the first three digits of the dividend.
$\begin{array}{r} \phantom{0}8 \\ 123 \overline{)9,876} \\ \phantom{0}984 \\ \end{array}$

STEP 7

Subtract $984$ from $987$ and write the result below.
$\begin{array}{r} \phantom{0}8 \\ 123 \overline{)9,876} \\ \phantom{0}984 \\ \phantom{0}--- \\ \phantom{0}003 \\ \end{array}$

STEP 8

Bring down the next digit of the dividend ( $6$ ) to the right of the remainder ( $3$ ) to form the number $36$ .
$\begin{array}{r} \phantom{0}8 \\ 123 \overline{)9,876} \\ \phantom{0}984 \\ \phantom{0}--- \\ \phantom{0}0036 \\ \end{array}$

STEP 9

Determine how many times $123$ can fit into $36$ . Since $123$ is larger than $36$ , it cannot fit into $36$ at all. Therefore, the quotient is $80$ and the remainder is $36$ .
$\begin{array}{r} \phantom{0}80 \\ 123 \overline{)9,876} \\ \phantom{0}984 \\ \phantom{0}--- \\ \phantom{0}0036 \\ \end{array}$

STEP 10

Write down the final quotient and remainder.
The quotient is $80$ and the remainder is $36$ .
So, $9,876 \div 123 = 80$ with a remainder of $36$ .

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