1000+ Printable Math Worksheets PDF | Free Download - Free Printable

The task involves solving six 3-digit by 3-digit multiplication problems. Below, I will solve each problem step by step.

---

Problem 1: \( 427 \times 945 \)

#### Step 1: Multiply \( 427 \) by \( 5 \)
\[
427 \times 5 = 2135
\]

#### Step 2: Multiply \( 427 \) by \( 40 \) (i.e., \( 4 \times 427 \))
\[
427 \times 4 = 1708 \quad \text{(shift one place to the left)} \quad \Rightarrow \quad 17080
\]

#### Step 3: Multiply \( 427 \) by \( 900 \) (i.e., \( 9 \times 427 \))
\[
427 \times 9 = 3843 \quad \text{(shift two places to the left)} \quad \Rightarrow \quad 384300
\]

#### Step 4: Add the results
\[
2135 + 17080 + 384300 = 403515
\]

Answer:
\[
\boxed{403515}
\]

---

Problem 2: \( 768 \times 460 \)

#### Step 1: Multiply \( 768 \) by \( 0 \)
\[
768 \times 0 = 0
\]

#### Step 2: Multiply \( 768 \) by \( 60 \) (i.e., \( 6 \times 768 \))
\[
768 \times 6 = 4608 \quad \text{(shift one place to the left)} \quad \Rightarrow \quad 46080
\]

#### Step 3: Multiply \( 768 \) by \( 400 \) (i.e., \( 4 \times 768 \))
\[
768 \times 4 = 3072 \quad \text{(shift two places to the left)} \quad \Rightarrow \quad 307200
\]

#### Step 4: Add the results
\[
0 + 46080 + 307200 = 353280
\]

Answer:
\[
\boxed{353280}
\]

---

Problem 3: \( 279 \times 177 \)

#### Step 1: Multiply \( 279 \) by \( 7 \)
\[
279 \times 7 = 1953
\]

#### Step 2: Multiply \( 279 \) by \( 70 \) (i.e., \( 7 \times 279 \))
\[
279 \times 7 = 1953 \quad \text{(shift one place to the left)} \quad \Rightarrow \quad 19530
\]

#### Step 3: Multiply \( 279 \) by \( 100 \) (i.e., \( 1 \times 279 \))
\[
279 \times 1 = 279 \quad \text{(shift two places to the left)} \quad \Rightarrow \quad 27900
\]

#### Step 4: Add the results
\[
1953 + 19530 + 27900 = 49383
\]

Answer:
\[
\boxed{49383}
\]

---

Problem 4: \( 329 \times 990 \)

#### Step 1: Multiply \( 329 \) by \( 0 \)
\[
329 \times 0 = 0
\]

#### Step 2: Multiply \( 329 \) by \( 90 \) (i.e., \( 9 \times 329 \))
\[
329 \times 9 = 2961 \quad \text{(shift one place to the left)} \quad \Rightarrow \quad 29610
\]

#### Step 3: Multiply \( 329 \) by \( 900 \) (i.e., \( 9 \times 329 \))
\[
329 \times 9 = 2961 \quad \text{(shift two places to the left)} \quad \Rightarrow \quad 296100
\]

#### Step 4: Add the results
\[
0 + 29610 + 296100 = 325710
\]

Answer:
\[
\boxed{325710}
\]

---

Problem 5: \( 115 \times 610 \)

#### Step 1: Multiply \( 115 \) by \( 0 \)
\[
115 \times 0 = 0
\]

#### Step 2: Multiply \( 115 \) by \( 10 \) (i.e., \( 1 \times 115 \))
\[
115 \times 1 = 115 \quad \text{(shift one place to the left)} \quad \Rightarrow \quad 1150
\]

#### Step 3: Multiply \( 115 \) by \( 600 \) (i.e., \( 6 \times 115 \))
\[
115 \times 6 = 690 \quad \text{(shift two places to the left)} \quad \Rightarrow \quad 69000
\]

#### Step 4: Add the results
\[
0 + 1150 + 69000 = 70150
\]

Answer:
\[
\boxed{70150}
\]

---

Problem 6: \( 504 \times 960 \)

#### Step 1: Multiply \( 504 \) by \( 0 \)
\[
504 \times 0 = 0
\]

#### Step 2: Multiply \( 504 \) by \( 60 \) (i.e., \( 6 \times 504 \))
\[
504 \times 6 = 3024 \quad \text{(shift one place to the left)} \quad \Rightarrow \quad 30240
\]

#### Step 3: Multiply \( 504 \) by \( 900 \) (i.e., \( 9 \times 504 \))
\[
504 \times 9 = 4536 \quad \text{(shift two places to the left)} \quad \Rightarrow \quad 453600
\]

#### Step 4: Add the results
\[
0 + 30240 + 453600 = 483840
\]

Answer:
\[
\boxed{483840}
\]

---

Problem 7: \( 414 \times 487 \)

#### Step 1: Multiply \( 414 \) by \( 7 \)
\[
414 \times 7 = 2898
\]

#### Step 2: Multiply \( 414 \) by \( 80 \) (i.e., \( 8 \times 414 \))
\[
414 \times 8 = 3312 \quad \text{(shift one place to the left)} \quad \Rightarrow \quad 33120
\]

#### Step 3: Multiply \( 414 \) by \( 400 \) (i.e., \( 4 \times 414 \))
\[
414 \times 4 = 1656 \quad \text{(shift two places to the left)} \quad \Rightarrow \quad 165600
\]

#### Step 4: Add the results
\[
2898 + 33120 + 165600 = 201618
\]

Answer:
\[
\boxed{201618}
\]

---

Problem 8: \( 236 \times 638 \)

#### Step 1: Multiply \( 236 \) by \( 8 \)
\[
236 \times 8 = 1888
\]

#### Step 2: Multiply \( 236 \) by \( 30 \) (i.e., \( 3 \times 236 \))
\[
236 \times 3 = 708 \quad \text{(shift one place to the left)} \quad \Rightarrow \quad 7080
\]

#### Step 3: Multiply \( 236 \) by \( 600 \) (i.e., \( 6 \times 236 \))
\[
236 \times 6 = 1416 \quad \text{(shift two places to the left)} \quad \Rightarrow \quad 141600
\]

#### Step 4: Add the results
\[
1888 + 7080 + 141600 = 149568
\]

Answer:
\[
\boxed{149568}
\]

---

Problem 9: \( 337 \times 461 \)

#### Step 1: Multiply \( 337 \) by \( 1 \)
\[
337 \times 1 = 337
\]

#### Step 2: Multiply \( 337 \) by \( 60 \) (i.e., \( 6 \times 337 \))
\[
337 \times 6 = 2022 \quad \text{(shift one place to the left)} \quad \Rightarrow \quad 20220
\]

#### Step 3: Multiply \( 337 \) by \( 400 \) (i.e., \( 4 \times 337 \))
\[
337 \times 4 = 1348 \quad \text{(shift two places to the left)} \quad \Rightarrow \quad 134800
\]

#### Step 4: Add the results
\[
337 + 20220 + 134800 = 155357
\]

Answer:
\[
\boxed{155357}
\]

---

Final Answers:

\[
\boxed{403515, 353280, 49383, 325710, 70150, 483840, 201618, 149568, 155357}
\]