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Answer :
We need to divide
[tex]$$8940 \div 3.$$[/tex]
Let's work through the steps:
1. Divide the first digit:
Divide the first digit, [tex]$8$[/tex], by [tex]$3$[/tex]. Since
[tex]$$3 \times 2 = 6 \quad \text{and} \quad 3 \times 3 = 9,$$[/tex]
the largest multiple not exceeding [tex]$8$[/tex] is [tex]$6$[/tex]. Thus, [tex]$3$[/tex] goes into [tex]$8$[/tex] a total of [tex]$2$[/tex] times.
The remainder from this step is:
[tex]$$8 - 6 = 2.$$[/tex]
2. Bring down the next digit:
Next, bring down the [tex]$9$[/tex] (the second digit of [tex]$8940$[/tex]) next to the remainder [tex]$2$[/tex], forming [tex]$29$[/tex].
Now, divide [tex]$29$[/tex] by [tex]$3$[/tex]. Since
[tex]$$3 \times 9 = 27 \quad \text{and} \quad 3 \times 10 = 30,$$[/tex]
the number [tex]$3$[/tex] goes into [tex]$29$[/tex] a total of [tex]$9$[/tex] times.
The remainder now is:
[tex]$$29 - 27 = 2.$$[/tex]
3. Bring down the next digit:
Bring down the [tex]$4$[/tex] (the third digit) to the remainder [tex]$2$[/tex], which gives [tex]$24$[/tex].
Divide [tex]$24$[/tex] by [tex]$3$[/tex]. We have:
[tex]$$3 \times 8 = 24,$$[/tex]
so [tex]$3$[/tex] goes into [tex]$24$[/tex] exactly [tex]$8$[/tex] times.
The remainder here is:
[tex]$$24 - 24 = 0.$$[/tex]
4. Bring down the last digit:
Finally, bring down the [tex]$0$[/tex] (the last digit). Since we have a [tex]$0$[/tex], dividing gives:
[tex]$$3 \times 0 = 0,$$[/tex]
so [tex]$3$[/tex] goes into [tex]$0$[/tex] exactly [tex]$0$[/tex] times, with a remainder of [tex]$0$[/tex].
Now, collecting the quotient digits from each step, we get:
[tex]$$\text{Quotient} = 2980.$$[/tex]
Since the final remainder is [tex]$0$[/tex], our answer is:
[tex]$$\boxed{2980 \text{ with remainder } 0.}$$[/tex]
[tex]$$8940 \div 3.$$[/tex]
Let's work through the steps:
1. Divide the first digit:
Divide the first digit, [tex]$8$[/tex], by [tex]$3$[/tex]. Since
[tex]$$3 \times 2 = 6 \quad \text{and} \quad 3 \times 3 = 9,$$[/tex]
the largest multiple not exceeding [tex]$8$[/tex] is [tex]$6$[/tex]. Thus, [tex]$3$[/tex] goes into [tex]$8$[/tex] a total of [tex]$2$[/tex] times.
The remainder from this step is:
[tex]$$8 - 6 = 2.$$[/tex]
2. Bring down the next digit:
Next, bring down the [tex]$9$[/tex] (the second digit of [tex]$8940$[/tex]) next to the remainder [tex]$2$[/tex], forming [tex]$29$[/tex].
Now, divide [tex]$29$[/tex] by [tex]$3$[/tex]. Since
[tex]$$3 \times 9 = 27 \quad \text{and} \quad 3 \times 10 = 30,$$[/tex]
the number [tex]$3$[/tex] goes into [tex]$29$[/tex] a total of [tex]$9$[/tex] times.
The remainder now is:
[tex]$$29 - 27 = 2.$$[/tex]
3. Bring down the next digit:
Bring down the [tex]$4$[/tex] (the third digit) to the remainder [tex]$2$[/tex], which gives [tex]$24$[/tex].
Divide [tex]$24$[/tex] by [tex]$3$[/tex]. We have:
[tex]$$3 \times 8 = 24,$$[/tex]
so [tex]$3$[/tex] goes into [tex]$24$[/tex] exactly [tex]$8$[/tex] times.
The remainder here is:
[tex]$$24 - 24 = 0.$$[/tex]
4. Bring down the last digit:
Finally, bring down the [tex]$0$[/tex] (the last digit). Since we have a [tex]$0$[/tex], dividing gives:
[tex]$$3 \times 0 = 0,$$[/tex]
so [tex]$3$[/tex] goes into [tex]$0$[/tex] exactly [tex]$0$[/tex] times, with a remainder of [tex]$0$[/tex].
Now, collecting the quotient digits from each step, we get:
[tex]$$\text{Quotient} = 2980.$$[/tex]
Since the final remainder is [tex]$0$[/tex], our answer is:
[tex]$$\boxed{2980 \text{ with remainder } 0.}$$[/tex]
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