Long Division – Two-Digit Divisor

706

Explanation

\[ \require{enclose} \begin{array}{r} 7 \enspace 0 \enspace 6 \\[-3pt] 48 \enclose{longdiv}{3 \enspace 3 \enspace 8 \enspace 8 \enspace 8} \\[-3pt] \underline{-3 \enspace 3 \enspace 6} \phantom{8 \enspace 8} \\[-3pt] 2 \enspace 8 \phantom{8 \enspace 8} \\[-3pt] \underline{-\phantom{2} \enspace 0} \phantom{8 \enspace 8} \\[-3pt] 2 \enspace 8 \enspace 8 \\[-3pt] \underline{-2 \enspace 8 \enspace 8} \\[-3pt] 0 \end{array} \]

Step 1: The First Division
Look at the first two digits of 33888 (since 48 is larger than one digit). That is 33. Since 33 < 48, we take the first three digits: 338.

Action: How many times does 48 go into 338? Estimate: \(48 \times 7 = 336\), which fits.

\[ \require{enclose} \begin{array}{r} \mathbf{7} \phantom{0 \enspace 6} \\[-3pt] 48 \enclose{longdiv}{3 \enspace 3 \enspace 8 \enspace 8 \enspace 8} \\[-3pt] \underline{-3 \enspace 3 \enspace 6} \phantom{8 \enspace 8} \\[-3pt] 2 \phantom{8 \enspace 8 \enspace 8} \end{array} \]

• Divide: \(338 \div 48 \approx 7\)
• Multiply: \(48 \times 7 = 336\)
• Subtract: \(338 - 336 = 2\)
• Placement: The 7 goes above the last digit of 338.

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Step 2: Bring Down and the "Zero Trap"
Bring down the next digit (8) → now we have 28.

Action: How many times does 48 go into 28? Zero times.

\[ \require{enclose} \begin{array}{r} 7 \enspace \mathbf{0} \phantom{6} \\[-3pt] 48 \enclose{longdiv}{3 \enspace 3 \enspace 8 \enspace 8 \enspace 8} \\[-3pt] \underline{-3 \enspace 3 \enspace 6} \phantom{8 \enspace 8} \\[-3pt] 2 \enspace 8 \phantom{8 \enspace 8} \\[-3pt] \underline{-\phantom{2} \enspace 0} \phantom{8 \enspace 8} \\[-3pt] 2 \enspace 8 \phantom{8 \enspace 8} \end{array} \]

• Bring down: The next 8 comes down → 28.
• Divide: \(28 \div 48 = 0\) → put 0 on top.
• Multiply/Subtract: \(48 \times 0 = 0\), then \(28 - 0 = 28\).

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Step 3: The Final Digit
Bring down the last digit (8) → now we have 288.

Action: How many times does 48 go into 288? \(48 \times 6 = 288\), exactly.

\[ \require{enclose} \begin{array}{r} 7 \enspace 0 \enspace \mathbf{6} \\[-3pt] 48 \enclose{longdiv}{3 \enspace 3 \enspace 8 \enspace 8 \enspace 8} \\[-3pt] \underline{-3 \enspace 3 \enspace 6} \phantom{8 \enspace 8} \\[-3pt] 2 \enspace 8 \phantom{8 \enspace 8} \\[-3pt] \underline{-\phantom{2} \enspace 0} \phantom{8 \enspace 8} \\[-3pt] 2 \enspace 8 \enspace 8 \\[-3pt] \underline{-2 \enspace 8 \enspace 8} \\[-3pt] 0 \end{array} \]

• Bring down: Last 8 comes down → 288.
• Divide: \(288 \div 48 = 6\)
• Multiply: \(48 \times 6 = 288\)
• Subtract: \(288 - 288 = 0\)

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Final Result
The quotient on top is 706.

\(33888 \div 48 = 706\)

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Why This Works
By keeping digits in their columns, you've actually broken it into:

\(33600 \div 48 = 700\)
\(288 \div 48 = 6\)
\(700 + 6 = 706\)

Long division organizes those partial quotients cleanly.

\(33{,}888 \div 48 = 706\). The interior 0 appears because 48 does not divide into 28 (after bringing down), so 0 is placed in that column. Check: \(706 \times 48 = 33{,}888\) ✓