Column Multiplication Worksheet - Solve 12 multi-digit multiplication equations.

The task involves solving column multiplication problems. Column multiplication is a method used to multiply large numbers by breaking the process into smaller, more manageable steps. Below, I will solve each problem step by step.

---

Problem 1: \( 97 \times 289 \)

#### Step-by-Step Solution:
1. Multiply \( 97 \) by the units digit of \( 289 \) (which is \( 9 \)):
\[
97 \times 9 = 873
\]
Write down \( 873 \).

2. Multiply \( 97 \) by the tens digit of \( 289 \) (which is \( 8 \)), and shift the result one place to the left:
\[
97 \times 8 = 776
\]
Shift \( 776 \) one place to the left: \( 7760 \).

3. Multiply \( 97 \) by the hundreds digit of \( 289 \) (which is \( 2 \)), and shift the result two places to the left:
\[
97 \times 2 = 194
\]
Shift \( 194 \) two places to the left: \( 19400 \).

4. Add all the results together:
\[
873 + 7760 + 19400 = 27033
\]

Answer:
\[
\boxed{27033}
\]

---

Problem 2: \( 88 \times 347 \)

#### Step-by-Step Solution:
1. Multiply \( 88 \) by the units digit of \( 347 \) (which is \( 7 \)):
\[
88 \times 7 = 616
\]
Write down \( 616 \).

2. Multiply \( 88 \) by the tens digit of \( 347 \) (which is \( 4 \)), and shift the result one place to the left:
\[
88 \times 4 = 352
\]
Shift \( 352 \) one place to the left: \( 3520 \).

3. Multiply \( 88 \) by the hundreds digit of \( 347 \) (which is \( 3 \)), and shift the result two places to the left:
\[
88 \times 3 = 264
\]
Shift \( 264 \) two places to the left: \( 26400 \).

4. Add all the results together:
\[
616 + 3520 + 26400 = 30536
\]

Answer:
\[
\boxed{30536}
\]

---

Problem 3: \( 67 \times 359 \)

#### Step-by-Step Solution:
1. Multiply \( 67 \) by the units digit of \( 359 \) (which is \( 9 \)):
\[
67 \times 9 = 603
\]
Write down \( 603 \).

2. Multiply \( 67 \) by the tens digit of \( 359 \) (which is \( 5 \)), and shift the result one place to the left:
\[
67 \times 5 = 335
\]
Shift \( 335 \) one place to the left: \( 3350 \).

3. Multiply \( 67 \) by the hundreds digit of \( 359 \) (which is \( 3 \)), and shift the result two places to the left:
\[
67 \times 3 = 201
\]
Shift \( 201 \) two places to the left: \( 20100 \).

4. Add all the results together:
\[
603 + 3350 + 20100 = 24053
\]

Answer:
\[
\boxed{24053}
\]

---

Problem 4: \( 27 \times 678 \)

#### Step-by-Step Solution:
1. Multiply \( 27 \) by the units digit of \( 678 \) (which is \( 8 \)):
\[
27 \times 8 = 216
\]
Write down \( 216 \).

2. Multiply \( 27 \) by the tens digit of \( 678 \) (which is \( 7 \)), and shift the result one place to the left:
\[
27 \times 7 = 189
\]
Shift \( 189 \) one place to the left: \( 1890 \).

3. Multiply \( 27 \) by the hundreds digit of \( 678 \) (which is \( 6 \)), and shift the result two places to the left:
\[
27 \times 6 = 162
\]
Shift \( 162 \) two places to the left: \( 16200 \).

4. Add all the results together:
\[
216 + 1890 + 16200 = 18306
\]

Answer:
\[
\boxed{18306}
\]

---

Problem 5: \( 49 \times 829 \)

#### Step-by-Step Solution:
1. Multiply \( 49 \) by the units digit of \( 829 \) (which is \( 9 \)):
\[
49 \times 9 = 441
\]
Write down \( 441 \).

2. Multiply \( 49 \) by the tens digit of \( 829 \) (which is \( 2 \)), and shift the result one place to the left:
\[
49 \times 2 = 98
\]
Shift \( 98 \) one place to the left: \( 980 \).

3. Multiply \( 49 \) by the hundreds digit of \( 829 \) (which is \( 8 \)), and shift the result two places to the left:
\[
49 \times 8 = 392
\]
Shift \( 392 \) two places to the left: \( 39200 \).

4. Add all the results together:
\[
441 + 980 + 39200 = 40621
\]

Answer:
\[
\boxed{40621}
\]

---

Problem 6: \( 36 \times 288 \)

#### Step-by-Step Solution:
1. Multiply \( 36 \) by the units digit of \( 288 \) (which is \( 8 \)):
\[
36 \times 8 = 288
\]
Write down \( 288 \).

2. Multiply \( 36 \) by the tens digit of \( 288 \) (which is \( 8 \)), and shift the result one place to the left:
\[
36 \times 8 = 288
\]
Shift \( 288 \) one place to the left: \( 2880 \).

3. Multiply \( 36 \) by the hundreds digit of \( 288 \) (which is \( 2 \)), and shift the result two places to the left:
\[
36 \times 2 = 72
\]
Shift \( 72 \) two places to the left: \( 7200 \).

4. Add all the results together:
\[
288 + 2880 + 7200 = 10368
\]

Answer:
\[
\boxed{10368}
\]

---

Problem 7: \( 29 \times 674 \)

#### Step-by-Step Solution:
1. Multiply \( 29 \) by the units digit of \( 674 \) (which is \( 4 \)):
\[
29 \times 4 = 116
\]
Write down \( 116 \).

2. Multiply \( 29 \) by the tens digit of \( 674 \) (which is \( 7 \)), and shift the result one place to the left:
\[
29 \times 7 = 203
\]
Shift \( 203 \) one place to the left: \( 2030 \).

3. Multiply \( 29 \) by the hundreds digit of \( 674 \) (which is \( 6 \)), and shift the result two places to the left:
\[
29 \times 6 = 174
\]
Shift \( 174 \) two places to the left: \( 17400 \).

4. Add all the results together:
\[
116 + 2030 + 17400 = 19546
\]

Answer:
\[
\boxed{19546}
\]

---

Problem 8: \( 86 \times 249 \)

#### Step-by-Step Solution:
1. Multiply \( 86 \) by the units digit of \( 249 \) (which is \( 9 \)):
\[
86 \times 9 = 774
\]
Write down \( 774 \).

2. Multiply \( 86 \) by the tens digit of \( 249 \) (which is \( 4 \)), and shift the result one place to the left:
\[
86 \times 4 = 344
\]
Shift \( 344 \) one place to the left: \( 3440 \).

3. Multiply \( 86 \) by the hundreds digit of \( 249 \) (which is \( 2 \)), and shift the result two places to the left:
\[
86 \times 2 = 172
\]
Shift \( 172 \) two places to the left: \( 17200 \).

4. Add all the results together:
\[
774 + 3440 + 17200 = 21414
\]

Answer:
\[
\boxed{21414}
\]

---

Problem 9: \( 85 \times 648 \)

#### Step-by-Step Solution:
1. Multiply \( 85 \) by the units digit of \( 648 \) (which is \( 8 \)):
\[
85 \times 8 = 680
\]
Write down \( 680 \).

2. Multiply \( 85 \) by the tens digit of \( 648 \) (which is \( 4 \)), and shift the result one place to the left:
\[
85 \times 4 = 340
\]
Shift \( 340 \) one place to the left: \( 3400 \).

3. Multiply \( 85 \) by the hundreds digit of \( 648 \) (which is \( 6 \)), and shift the result two places to the left:
\[
85 \times 6 = 510
\]
Shift \( 510 \) two places to the left: \( 51000 \).

4. Add all the results together:
\[
680 + 3400 + 51000 = 55080
\]

Answer:
\[
\boxed{55080}
\]

---

Problem 10: \( 76 \times 867 \)

#### Step-by-Step Solution:
1. Multiply \( 76 \) by the units digit of \( 867 \) (which is \( 7 \)):
\[
76 \times 7 = 532
\]
Write down \( 532 \).

2. Multiply \( 76 \) by the tens digit of \( 867 \) (which is \( 6 \)), and shift the result one place to the left:
\[
76 \times 6 = 456
\]
Shift \( 456 \) one place to the left: \( 4560 \).

3. Multiply \( 76 \) by the hundreds digit of \( 867 \) (which is \( 8 \)), and shift the result two places to the left:
\[
76 \times 8 = 608
\]
Shift \( 608 \) two places to the left: \( 60800 \).

4. Add all the results together:
\[
532 + 4560 + 60800 = 65892
\]

Answer:
\[
\boxed{65892}
\]

---

Problem 11: \( 93 \times 419 \)

#### Step-by-Step Solution:
1. Multiply \( 93 \) by the units digit of \( 419 \) (which is \( 9 \)):
\[
93 \times 9 = 837
\]
Write down \( 837 \).

2. Multiply \( 93 \) by the tens digit of \( 419 \) (which is \( 1 \)), and shift the result one place to the left:
\[
93 \times 1 = 93
\]
Shift \( 93 \) one place to the left: \( 930 \).

3. Multiply \( 93 \) by the hundreds digit of \( 419 \) (which is \( 4 \)), and shift the result two places to the left:
\[
93 \times 4 = 372
\]
Shift \( 372 \) two places to the left: \( 37200 \).

4. Add all the results together:
\[
837 + 930 + 37200 = 38967
\]

Answer:
\[
\boxed{38967}
\]

---

Problem 12: \( 68 \times 159 \)

#### Step-by-Step Solution:
1. Multiply \( 68 \) by the units digit of \( 159 \) (which is \( 9 \)):
\[
68 \times 9 = 612
\]
Write down \( 612 \).

2. Multiply \( 68 \) by the tens digit of \( 159 \) (which is \( 5 \)), and shift the result one place to the left:
\[
68 \times 5 = 340
\]
Shift \( 340 \) one place to the left: \( 3400 \).

3. Multiply \( 68 \) by the hundreds digit of \( 159 \) (which is \( 1 \)), and shift the result two places to the left:
\[
68 \times 1 = 68
\]
Shift \( 68 \) two places to the left: \( 6800 \).

4. Add all the results together:
\[
612 + 3400 + 6800 = 10812
\]

Answer:
\[
\boxed{10812}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{cccc}
1. & 27033 & 2. & 30536 \\
3. & 24053 & 4. & 18306 \\
5. & 40621 & 6. & 10368 \\
7. & 19546 & 8. & 21414 \\
9. & 55080 & 10. & 65892 \\
11. & 38967 & 12. & 10812 \\
\end{array}
}
\]