Divide 4-Digit Numbers by 2-Digit Numbers with Remainder ... - Free Printable

The task involves solving division problems where 4-digit numbers are divided by 2-digit numbers, and the quotient and remainder are to be determined. Below is the step-by-step solution for each problem:

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1. \( 7523 \div 28 \)

#### Step 1: Divide
- How many times does 28 go into 75?
\( 28 \times 2 = 56 \) (fits), \( 28 \times 3 = 84 \) (too large).
So, \( 28 \) goes into \( 75 \) 2 times.

#### Step 2: Multiply and Subtract
- \( 28 \times 2 = 56 \)
- \( 75 - 56 = 19 \)

#### Step 3: Bring Down Next Digit
- Bring down the next digit (2): \( 192 \).

#### Step 4: Repeat Division
- How many times does 28 go into 192?
\( 28 \times 6 = 168 \) (fits), \( 28 \times 7 = 196 \) (too large).
So, \( 28 \) goes into \( 192 \) 6 times.

#### Step 5: Multiply and Subtract
- \( 28 \times 6 = 168 \)
- \( 192 - 168 = 24 \)

#### Step 6: Bring Down Next Digit
- Bring down the next digit (3): \( 243 \).

#### Step 7: Repeat Division
- How many times does 28 go into 243?
\( 28 \times 8 = 224 \) (fits), \( 28 \times 9 = 252 \) (too large).
So, \( 28 \) goes into \( 243 \) 8 times.

#### Step 8: Multiply and Subtract
- \( 28 \times 8 = 224 \)
- \( 243 - 224 = 19 \)

#### Final Answer:
- Quotient: \( 268 \)
- Remainder: \( 19 \)

Result: \( 7523 \div 28 = 268 \) R \( 19 \)

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2. \( 1954 \div 47 \)

#### Step 1: Divide
- How many times does 47 go into 195?
\( 47 \times 4 = 188 \) (fits), \( 47 \times 5 = 235 \) (too large).
So, \( 47 \) goes into \( 195 \) 4 times.

#### Step 2: Multiply and Subtract
- \( 47 \times 4 = 188 \)
- \( 195 - 188 = 7 \)

#### Step 3: Bring Down Next Digit
- Bring down the next digit (4): \( 74 \).

#### Step 4: Repeat Division
- How many times does 47 go into 74?
\( 47 \times 1 = 47 \) (fits), \( 47 \times 2 = 94 \) (too large).
So, \( 47 \) goes into \( 74 \) 1 time.

#### Step 5: Multiply and Subtract
- \( 47 \times 1 = 47 \)
- \( 74 - 47 = 27 \)

#### Final Answer:
- Quotient: \( 41 \)
- Remainder: \( 27 \)

Result: \( 1954 \div 47 = 41 \) R \( 27 \)

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3. \( 9573 \div 17 \)

#### Step 1: Divide
- How many times does 17 go into 95?
\( 17 \times 5 = 85 \) (fits), \( 17 \times 6 = 102 \) (too large).
So, \( 17 \) goes into \( 95 \) 5 times.

#### Step 2: Multiply and Subtract
- \( 17 \times 5 = 85 \)
- \( 95 - 85 = 10 \)

#### Step 3: Bring Down Next Digit
- Bring down the next digit (7): \( 107 \).

#### Step 4: Repeat Division
- How many times does 17 go into 107?
\( 17 \times 6 = 102 \) (fits), \( 17 \times 7 = 119 \) (too large).
So, \( 17 \) goes into \( 107 \) 6 times.

#### Step 5: Multiply and Subtract
- \( 17 \times 6 = 102 \)
- \( 107 - 102 = 5 \)

#### Step 6: Bring Down Next Digit
- Bring down the next digit (3): \( 53 \).

#### Step 7: Repeat Division
- How many times does 17 go into 53?
\( 17 \times 3 = 51 \) (fits), \( 17 \times 4 = 68 \) (too large).
So, \( 17 \) goes into \( 53 \) 3 times.

#### Step 8: Multiply and Subtract
- \( 17 \times 3 = 51 \)
- \( 53 - 51 = 2 \)

#### Final Answer:
- Quotient: \( 563 \)
- Remainder: \( 2 \)

Result: \( 9573 \div 17 = 563 \) R \( 2 \)

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4. \( 4942 \div 65 \)

#### Step 1: Divide
- How many times does 65 go into 494?
\( 65 \times 7 = 455 \) (fits), \( 65 \times 8 = 520 \) (too large).
So, \( 65 \) goes into \( 494 \) 7 times.

#### Step 2: Multiply and Subtract
- \( 65 \times 7 = 455 \)
- \( 494 - 455 = 39 \)

#### Step 3: Bring Down Next Digit
- Bring down the next digit (2): \( 392 \).

#### Step 4: Repeat Division
- How many times does 65 go into 392?
\( 65 \times 5 = 325 \) (fits), \( 65 \times 6 = 390 \) (fits), \( 65 \times 7 = 455 \) (too large).
So, \( 65 \) goes into \( 392 \) 6 times.

#### Step 5: Multiply and Subtract
- \( 65 \times 6 = 390 \)
- \( 392 - 390 = 2 \)

#### Final Answer:
- Quotient: \( 76 \)
- Remainder: \( 2 \)

Result: \( 4942 \div 65 = 76 \) R \( 2 \)

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5. \( 8386 \div 92 \)

#### Step 1: Divide
- How many times does 92 go into 838?
\( 92 \times 9 = 828 \) (fits), \( 92 \times 10 = 920 \) (too large).
So, \( 92 \) goes into \( 838 \) 9 times.

#### Step 2: Multiply and Subtract
- \( 92 \times 9 = 828 \)
- \( 838 - 828 = 10 \)

#### Step 3: Bring Down Next Digit
- Bring down the next digit (6): \( 106 \).

#### Step 4: Repeat Division
- How many times does 92 go into 106?
\( 92 \times 1 = 92 \) (fits), \( 92 \times 2 = 184 \) (too large).
So, \( 92 \) goes into \( 106 \) 1 time.

#### Step 5: Multiply and Subtract
- \( 92 \times 1 = 92 \)
- \( 106 - 92 = 14 \)

#### Final Answer:
- Quotient: \( 91 \)
- Remainder: \( 14 \)

Result: \( 8386 \div 92 = 91 \) R \( 14 \)

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6. \( 6091 \div 54 \)

#### Step 1: Divide
- How many times does 54 go into 609?
\( 54 \times 11 = 594 \) (fits), \( 54 \times 12 = 648 \) (too large).
So, \( 54 \) goes into \( 609 \) 11 times.

#### Step 2: Multiply and Subtract
- \( 54 \times 11 = 594 \)
- \( 609 - 594 = 15 \)

#### Step 3: Bring Down Next Digit
- Bring down the next digit (1): \( 151 \).

#### Step 4: Repeat Division
- How many times does 54 go into 151?
\( 54 \times 2 = 108 \) (fits), \( 54 \times 3 = 162 \) (too large).
So, \( 54 \) goes into \( 151 \) 2 times.

#### Step 5: Multiply and Subtract
- \( 54 \times 2 = 108 \)
- \( 151 - 108 = 43 \)

#### Final Answer:
- Quotient: \( 112 \)
- Remainder: \( 43 \)

Result: \( 6091 \div 54 = 112 \) R \( 43 \)

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7. \( 7527 \div 98 \)

#### Step 1: Divide
- How many times does 98 go into 752?
\( 98 \times 7 = 686 \) (fits), \( 98 \times 8 = 784 \) (too large).
So, \( 98 \) goes into \( 752 \) 7 times.

#### Step 2: Multiply and Subtract
- \( 98 \times 7 = 686 \)
- \( 752 - 686 = 66 \)

#### Step 3: Bring Down Next Digit
- Bring down the next digit (7): \( 667 \).

#### Step 4: Repeat Division
- How many times does 98 go into 667?
\( 98 \times 6 = 588 \) (fits), \( 98 \times 7 = 686 \) (fits), \( 98 \times 8 = 784 \) (too large).
So, \( 98 \) goes into \( 667 \) 7 times.

#### Step 5: Multiply and Subtract
- \( 98 \times 7 = 686 \)
- \( 667 - 686 = -19 \) (This is incorrect; recheck: \( 98 \times 6 = 588 \))

#### Correct Step:
- \( 98 \times 6 = 588 \)
- \( 667 - 588 = 79 \)

#### Final Answer:
- Quotient: \( 76 \)
- Remainder: \( 79 \)

Result: \( 7527 \div 98 = 76 \) R \( 79 \)

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8. \( 7659 \div 38 \)

#### Step 1: Divide
- How many times does 38 go into 765?
\( 38 \times 20 = 760 \) (fits), \( 38 \times 21 = 798 \) (too large).
So, \( 38 \) goes into \( 765 \) 20 times.

#### Step 2: Multiply and Subtract
- \( 38 \times 20 = 760 \)
- \( 765 - 760 = 5 \)

#### Step 3: Bring Down Next Digit
- Bring down the next digit (9): \( 59 \).

#### Step 4: Repeat Division
- How many times does 38 go into 59?
\( 38 \times 1 = 38 \) (fits), \( 38 \times 2 = 76 \) (too large).
So, \( 38 \) goes into \( 59 \) 1 time.

#### Step 5: Multiply and Subtract
- \( 38 \times 1 = 38 \)
- \( 59 - 38 = 21 \)

#### Final Answer:
- Quotient: \( 201 \)
- Remainder: \( 21 \)

Result: \( 7659 \div 38 = 201 \) R \( 21 \)

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Final Answers:

1. \( 7523 \div 28 = 268 \) R \( 19 \)
2. \( 1954 \div 47 = 41 \) R \( 27 \)
3. \( 9573 \div 17 = 563 \) R \( 2 \)
4. \( 4942 \div 65 = 76 \) R \( 2 \)
5. \( 8386 \div 92 = 91 \) R \( 14 \)
6. \( 6091 \div 54 = 112 \) R \( 43 \)
7. \( 7527 \div 98 = 76 \) R \( 79 \)
8. \( 7659 \div 38 = 201 \) R \( 21 \)

\[
\boxed{
\begin{aligned}
&7523 \div 28 = 268 \text{ R } 19 \\
&1954 \div 47 = 41 \text{ R } 27 \\
&9573 \div 17 = 563 \text{ R } 2 \\
&4942 \div 65 = 76 \text{ R } 2 \\
&8386 \div 92 = 91 \text{ R } 14 \\
&6091 \div 54 = 112 \text{ R } 43 \\
&7527 \div 98 = 76 \text{ R } 79 \\
&7659 \div 38 = 201 \text{ R } 21 \\
\end{aligned}
}
\]