Answer :
We wish to find the quotient and remainder when dividing each dividend by its respective divisor. Below is a detailed step‐by‐step explanation for each long division.
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1. Division of
[tex]$$28497\div46$$[/tex]
Step 1. Examine the first part of the dividend. Notice that the number formed by the first few digits (in this example, the first three digits “284”) is the smallest block that is greater than or equal to the divisor 46.
• Determine how many times 46 goes into 284. Since
[tex]$$6\times46=276\quad\text{and}\quad7\times46=322,$$[/tex]
6 is the correct number.
• Subtract to find the remainder:
[tex]$$284-276=8.$$[/tex]
Step 2. Bring down the next digit. In the dividend, the next digit is 9, so we now have 89.
• Determine how many times 46 goes into 89. Since
[tex]$$1\times46=46\quad\text{and}\quad2\times46=92,$$[/tex]
the digit is 1.
• Subtract:
[tex]$$89-46=43.$$[/tex]
Step 3. Bring down the final digit, which is 7, giving us 437.
• Determine how many times 46 goes into 437. We have
[tex]$$9\times46=414\quad\text{and}\quad10\times46=460,$$[/tex]
so the digit is 9.
• Subtract:
[tex]$$437-414=23.$$[/tex]
Since there are no more digits to bring down, the quotient is
[tex]$$619$$[/tex]
and the remainder is
[tex]$$23.$$[/tex]
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2. Division of
[tex]$$76462\div19$$[/tex]
Step 1. Start with the leftmost digits. Notice that the first block “76” is divisible by 19.
• Since
[tex]$$4\times19=76,$$[/tex]
the first quotient digit is 4 with a remainder of 0.
Step 2. Bring down the next digit (which is 4). Now the number is 04 (or simply 4).
• 19 does not go into 4 (since [tex]$19>4$[/tex]), so write 0 in the quotient. The remainder remains 4.
Step 3. Bring down the next digit (which is 6), forming 46.
• Since
[tex]$$2\times19=38\quad\text{and}\quad3\times19=57,$$[/tex]
the correct digit is 2. Subtract:
[tex]$$46-38=8.$$[/tex]
Step 4. Bring down the last digit (which is 2), making the number 82.
• Since
[tex]$$4\times19=76\quad\text{and}\quad5\times19=95,$$[/tex]
the final digit in the quotient is 4. Subtract:
[tex]$$82-76=6.$$[/tex]
Thus, the quotient is
[tex]$$4024$$[/tex]
and the remainder is
[tex]$$6.$$[/tex]
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3. Division of
[tex]$$95760\div36$$[/tex]
Step 1. Consider the first group of digits. With dividend digits “9, 5, 7, 6, 0,” we begin with the leftmost part that is large enough.
• Looking at “95,” we notice that 36 goes into 95 twice because
[tex]$$2\times36=72\quad\text{and}\quad3\times36=108,$$[/tex]
so write 2 in the quotient. Subtract:
[tex]$$95-72=23.$$[/tex]
Step 2. Bring down the next digit (which is 7) to form 237.
• Determine how many times 36 fits into 237. We have
[tex]$$6\times36=216\quad\text{and}\quad7\times36=252,$$[/tex]
so the next digit is 6. Subtract:
[tex]$$237-216=21.$$[/tex]
Step 3. Bring down the next digit (which is 6) resulting in 216.
• Since
[tex]$$6\times36=216,$$[/tex]
the next digit is 6 and subtracting gives:
[tex]$$216-216=0.$$[/tex]
Step 4. Finally, bring down the last digit (which is 0). Since the current number is 0, the last digit of the quotient is 0.
Thus, the quotient is
[tex]$$2660$$[/tex]
and the remainder is
[tex]$$0.$$[/tex]
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Summary of the Results:
[tex]$$
\begin{array}{ccc}
\textbf{Division} & \textbf{Quotient} & \textbf{Remainder} \\
28497 \div 46 & 619 & 23 \\
76462 \div 19 & 4024 & 6 \\
95760 \div 36 & 2660 & 0 \\
\end{array}
$$[/tex]
This completes the detailed long division steps for each problem.
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1. Division of
[tex]$$28497\div46$$[/tex]
Step 1. Examine the first part of the dividend. Notice that the number formed by the first few digits (in this example, the first three digits “284”) is the smallest block that is greater than or equal to the divisor 46.
• Determine how many times 46 goes into 284. Since
[tex]$$6\times46=276\quad\text{and}\quad7\times46=322,$$[/tex]
6 is the correct number.
• Subtract to find the remainder:
[tex]$$284-276=8.$$[/tex]
Step 2. Bring down the next digit. In the dividend, the next digit is 9, so we now have 89.
• Determine how many times 46 goes into 89. Since
[tex]$$1\times46=46\quad\text{and}\quad2\times46=92,$$[/tex]
the digit is 1.
• Subtract:
[tex]$$89-46=43.$$[/tex]
Step 3. Bring down the final digit, which is 7, giving us 437.
• Determine how many times 46 goes into 437. We have
[tex]$$9\times46=414\quad\text{and}\quad10\times46=460,$$[/tex]
so the digit is 9.
• Subtract:
[tex]$$437-414=23.$$[/tex]
Since there are no more digits to bring down, the quotient is
[tex]$$619$$[/tex]
and the remainder is
[tex]$$23.$$[/tex]
──────────────────────────────
2. Division of
[tex]$$76462\div19$$[/tex]
Step 1. Start with the leftmost digits. Notice that the first block “76” is divisible by 19.
• Since
[tex]$$4\times19=76,$$[/tex]
the first quotient digit is 4 with a remainder of 0.
Step 2. Bring down the next digit (which is 4). Now the number is 04 (or simply 4).
• 19 does not go into 4 (since [tex]$19>4$[/tex]), so write 0 in the quotient. The remainder remains 4.
Step 3. Bring down the next digit (which is 6), forming 46.
• Since
[tex]$$2\times19=38\quad\text{and}\quad3\times19=57,$$[/tex]
the correct digit is 2. Subtract:
[tex]$$46-38=8.$$[/tex]
Step 4. Bring down the last digit (which is 2), making the number 82.
• Since
[tex]$$4\times19=76\quad\text{and}\quad5\times19=95,$$[/tex]
the final digit in the quotient is 4. Subtract:
[tex]$$82-76=6.$$[/tex]
Thus, the quotient is
[tex]$$4024$$[/tex]
and the remainder is
[tex]$$6.$$[/tex]
──────────────────────────────
3. Division of
[tex]$$95760\div36$$[/tex]
Step 1. Consider the first group of digits. With dividend digits “9, 5, 7, 6, 0,” we begin with the leftmost part that is large enough.
• Looking at “95,” we notice that 36 goes into 95 twice because
[tex]$$2\times36=72\quad\text{and}\quad3\times36=108,$$[/tex]
so write 2 in the quotient. Subtract:
[tex]$$95-72=23.$$[/tex]
Step 2. Bring down the next digit (which is 7) to form 237.
• Determine how many times 36 fits into 237. We have
[tex]$$6\times36=216\quad\text{and}\quad7\times36=252,$$[/tex]
so the next digit is 6. Subtract:
[tex]$$237-216=21.$$[/tex]
Step 3. Bring down the next digit (which is 6) resulting in 216.
• Since
[tex]$$6\times36=216,$$[/tex]
the next digit is 6 and subtracting gives:
[tex]$$216-216=0.$$[/tex]
Step 4. Finally, bring down the last digit (which is 0). Since the current number is 0, the last digit of the quotient is 0.
Thus, the quotient is
[tex]$$2660$$[/tex]
and the remainder is
[tex]$$0.$$[/tex]
──────────────────────────────
Summary of the Results:
[tex]$$
\begin{array}{ccc}
\textbf{Division} & \textbf{Quotient} & \textbf{Remainder} \\
28497 \div 46 & 619 & 23 \\
76462 \div 19 & 4024 & 6 \\
95760 \div 36 & 2660 & 0 \\
\end{array}
$$[/tex]
This completes the detailed long division steps for each problem.
