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Sagot :
To solve the division of [tex]\( 44823 \)[/tex] by [tex]\( 9 \)[/tex], we will perform long division step-by-step.
1. Set up the problem:
We place [tex]\( 9 \)[/tex] on the outside of the division bar and [tex]\( 44823 \)[/tex] on the inside.
[tex]\[ 9 \ \bigg) \overline{44823} \][/tex]
2. Divide the first digit:
- Look at the first digit of [tex]\( 44823 \)[/tex], which is [tex]\( 4 \)[/tex].
- [tex]\( 9 \)[/tex] does not go into [tex]\( 4 \)[/tex], so we consider the first two digits, which are [tex]\( 44 \)[/tex].
3. Divide [tex]\( 44 \)[/tex] by [tex]\( 9 \)[/tex]:
- [tex]\( 9 \)[/tex] goes into [tex]\( 44 \)[/tex] a total of [tex]\( 4 \)[/tex] times (since [tex]\( 9 \times 4 = 36 \)[/tex] and [tex]\( 9 \times 5 = 45 \)[/tex] which is too large).
- Place [tex]\( 4 \)[/tex] above the division bar.
[tex]\[ \begin{array}{c} \phantom{0}4 \\ 9 \ \bigg) \overline{44823} \\ - 36\phantom{88} \\ \phantom{8}82\phantom{8} \end{array} \][/tex]
4. Subtract and bring down the next digit:
- Subtract [tex]\( 36 \)[/tex] from [tex]\( 44 \)[/tex] to get [tex]\( 8 \)[/tex].
- Bring down the next digit, [tex]\( 8 \)[/tex], making it [tex]\( 88 \)[/tex].
5. Divide [tex]\( 88 \)[/tex] by [tex]\( 9 \)[/tex]:
- [tex]\( 9 \)[/tex] goes into [tex]\( 88 \)[/tex] a total of [tex]\( 9 \)[/tex] times (since [tex]\( 9 \times 9 = 81 \)[/tex]).
- Place [tex]\( 9 \)[/tex] above the division bar.
[tex]\[ \begin{array}{c} \phantom{0}49 \\ 9 \ \bigg) \overline{44823} \\ - 36\phantom{88} \\ \phantom{8}8823 \\ - 81\phantom{8} \end{array} \][/tex]
6. Subtract and bring down the next digit:
- Subtract [tex]\( 81 \)[/tex] from [tex]\( 88 \)[/tex] to get [tex]\( 7 \)[/tex].
- Bring down the next digit, [tex]\( 2 \)[/tex], making it [tex]\( 72 \)[/tex].
7. Divide [tex]\( 72 \)[/tex] by [tex]\( 9 \)[/tex]:
- [tex]\( 9 \)[/tex] goes into [tex]\( 72 \)[/tex] a total of [tex]\( 8 \)[/tex] times (since [tex]\( 9 \times 8 = 72 \)[/tex]).
- Place [tex]\( 8 \)[/tex] above the division bar.
[tex]\[ \begin{array}{c} \phantom{0}498 \\ 9 \ \bigg) \overline{44823} \\ - 36\phantom{88} \\ \phantom{8}8823 \\ - 81\phantom{88} \\ \phantom{8}723 \\ - 72\phantom{8} \end{array} \][/tex]
8. Subtract and bring down the next digit:
- Subtract [tex]\( 72 \)[/tex] from [tex]\( 72 \)[/tex] to get [tex]\( 0 \)[/tex].
- Bring down the final digit, [tex]\( 3 \)[/tex], making it [tex]\( 3 \)[/tex].
9. Divide [tex]\( 3 \)[/tex] by [tex]\( 9 \)[/tex]:
- [tex]\( 9 \)[/tex] does not go into [tex]\( 3 \)[/tex], so we place [tex]\( 0 \)[/tex] above the division bar.
- Leave the remainder [tex]\( 3 \)[/tex].
[tex]\[ \begin{array}{c} \phantom{0}4980 \\ 9 \ \bigg) \overline{44823} \\ - 36\phantom{88} \\ \phantom{8}8823 \\ - 81\phantom{88} \\ \phantom{8}723 \\ - 72\phantom{88} \\ \phantom{3}3 \\ \end{array} \][/tex]
Thus, the quotient is [tex]\( 4980 \)[/tex] and the remainder is [tex]\( 3 \)[/tex].
Therefore, the result of [tex]\( 44823 \div 9 \)[/tex] is:
[tex]\[ 4980 \text{ R } 3 \][/tex]
1. Set up the problem:
We place [tex]\( 9 \)[/tex] on the outside of the division bar and [tex]\( 44823 \)[/tex] on the inside.
[tex]\[ 9 \ \bigg) \overline{44823} \][/tex]
2. Divide the first digit:
- Look at the first digit of [tex]\( 44823 \)[/tex], which is [tex]\( 4 \)[/tex].
- [tex]\( 9 \)[/tex] does not go into [tex]\( 4 \)[/tex], so we consider the first two digits, which are [tex]\( 44 \)[/tex].
3. Divide [tex]\( 44 \)[/tex] by [tex]\( 9 \)[/tex]:
- [tex]\( 9 \)[/tex] goes into [tex]\( 44 \)[/tex] a total of [tex]\( 4 \)[/tex] times (since [tex]\( 9 \times 4 = 36 \)[/tex] and [tex]\( 9 \times 5 = 45 \)[/tex] which is too large).
- Place [tex]\( 4 \)[/tex] above the division bar.
[tex]\[ \begin{array}{c} \phantom{0}4 \\ 9 \ \bigg) \overline{44823} \\ - 36\phantom{88} \\ \phantom{8}82\phantom{8} \end{array} \][/tex]
4. Subtract and bring down the next digit:
- Subtract [tex]\( 36 \)[/tex] from [tex]\( 44 \)[/tex] to get [tex]\( 8 \)[/tex].
- Bring down the next digit, [tex]\( 8 \)[/tex], making it [tex]\( 88 \)[/tex].
5. Divide [tex]\( 88 \)[/tex] by [tex]\( 9 \)[/tex]:
- [tex]\( 9 \)[/tex] goes into [tex]\( 88 \)[/tex] a total of [tex]\( 9 \)[/tex] times (since [tex]\( 9 \times 9 = 81 \)[/tex]).
- Place [tex]\( 9 \)[/tex] above the division bar.
[tex]\[ \begin{array}{c} \phantom{0}49 \\ 9 \ \bigg) \overline{44823} \\ - 36\phantom{88} \\ \phantom{8}8823 \\ - 81\phantom{8} \end{array} \][/tex]
6. Subtract and bring down the next digit:
- Subtract [tex]\( 81 \)[/tex] from [tex]\( 88 \)[/tex] to get [tex]\( 7 \)[/tex].
- Bring down the next digit, [tex]\( 2 \)[/tex], making it [tex]\( 72 \)[/tex].
7. Divide [tex]\( 72 \)[/tex] by [tex]\( 9 \)[/tex]:
- [tex]\( 9 \)[/tex] goes into [tex]\( 72 \)[/tex] a total of [tex]\( 8 \)[/tex] times (since [tex]\( 9 \times 8 = 72 \)[/tex]).
- Place [tex]\( 8 \)[/tex] above the division bar.
[tex]\[ \begin{array}{c} \phantom{0}498 \\ 9 \ \bigg) \overline{44823} \\ - 36\phantom{88} \\ \phantom{8}8823 \\ - 81\phantom{88} \\ \phantom{8}723 \\ - 72\phantom{8} \end{array} \][/tex]
8. Subtract and bring down the next digit:
- Subtract [tex]\( 72 \)[/tex] from [tex]\( 72 \)[/tex] to get [tex]\( 0 \)[/tex].
- Bring down the final digit, [tex]\( 3 \)[/tex], making it [tex]\( 3 \)[/tex].
9. Divide [tex]\( 3 \)[/tex] by [tex]\( 9 \)[/tex]:
- [tex]\( 9 \)[/tex] does not go into [tex]\( 3 \)[/tex], so we place [tex]\( 0 \)[/tex] above the division bar.
- Leave the remainder [tex]\( 3 \)[/tex].
[tex]\[ \begin{array}{c} \phantom{0}4980 \\ 9 \ \bigg) \overline{44823} \\ - 36\phantom{88} \\ \phantom{8}8823 \\ - 81\phantom{88} \\ \phantom{8}723 \\ - 72\phantom{88} \\ \phantom{3}3 \\ \end{array} \][/tex]
Thus, the quotient is [tex]\( 4980 \)[/tex] and the remainder is [tex]\( 3 \)[/tex].
Therefore, the result of [tex]\( 44823 \div 9 \)[/tex] is:
[tex]\[ 4980 \text{ R } 3 \][/tex]
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