Multiplying 3 Digit by 2 Digit Numbers for Daily Practice. 3 Digit ... - Free Printable

Problem Description:

The task involves solving a series of multiplication problems where a 3-digit number is multiplied by a 2-digit number. Each problem requires performing the multiplication step-by-step and providing the final product.

Solution Approach:

To solve each multiplication problem, we will use the standard algorithm for multiplication. Here are the steps for each problem:

1. Write down the numbers to be multiplied.
2. Multiply the 3-digit number by the units digit of the 2-digit number.
3. Multiply the 3-digit number by the tens digit of the 2-digit number, remembering to shift the result one place to the left (equivalent to multiplying by 10).
4. Add the two partial products to get the final result.

Let's solve each problem step-by-step.

---

Problem 1: \( 355 \times 95 \)

#### Step 1: Multiply by the units digit (5)
\[ 355 \times 5 = 1775 \]

#### Step 2: Multiply by the tens digit (9), shifted left
\[ 355 \times 9 = 3195 \]
Shift this result one place to the left: \( 31950 \)

#### Step 3: Add the partial products
\[ 1775 + 31950 = 33725 \]

Answer: \( 355 \times 95 = 33725 \)

---

Problem 2: \( 167 \times 36 \)

#### Step 1: Multiply by the units digit (6)
\[ 167 \times 6 = 1002 \]

#### Step 2: Multiply by the tens digit (3), shifted left
\[ 167 \times 3 = 501 \]
Shift this result one place to the left: \( 5010 \)

#### Step 3: Add the partial products
\[ 1002 + 5010 = 6012 \]

Answer: \( 167 \times 36 = 6012 \)

---

Problem 3: \( 190 \times 45 \)

#### Step 1: Multiply by the units digit (5)
\[ 190 \times 5 = 950 \]

#### Step 2: Multiply by the tens digit (4), shifted left
\[ 190 \times 4 = 760 \]
Shift this result one place to the left: \( 7600 \)

#### Step 3: Add the partial products
\[ 950 + 7600 = 8550 \]

Answer: \( 190 \times 45 = 8550 \)

---

Problem 4: \( 763 \times 40 \)

#### Step 1: Multiply by the units digit (0)
\[ 763 \times 0 = 0 \]

#### Step 2: Multiply by the tens digit (4), shifted left
\[ 763 \times 4 = 3052 \]
Shift this result one place to the left: \( 30520 \)

#### Step 3: Add the partial products
\[ 0 + 30520 = 30520 \]

Answer: \( 763 \times 40 = 30520 \)

---

Problem 5: \( 767 \times 12 \)

#### Step 1: Multiply by the units digit (2)
\[ 767 \times 2 = 1534 \]

#### Step 2: Multiply by the tens digit (1), shifted left
\[ 767 \times 1 = 767 \]
Shift this result one place to the left: \( 7670 \)

#### Step 3: Add the partial products
\[ 1534 + 7670 = 9204 \]

Answer: \( 767 \times 12 = 9204 \)

---

Problem 6: \( 643 \times 18 \)

#### Step 1: Multiply by the units digit (8)
\[ 643 \times 8 = 5144 \]

#### Step 2: Multiply by the tens digit (1), shifted left
\[ 643 \times 1 = 643 \]
Shift this result one place to the left: \( 6430 \)

#### Step 3: Add the partial products
\[ 5144 + 6430 = 11574 \]

Answer: \( 643 \times 18 = 11574 \)

---

Problem 7: \( 756 \times 18 \)

#### Step 1: Multiply by the units digit (8)
\[ 756 \times 8 = 6048 \]

#### Step 2: Multiply by the tens digit (1), shifted left
\[ 756 \times 1 = 756 \]
Shift this result one place to the left: \( 7560 \)

#### Step 3: Add the partial products
\[ 6048 + 7560 = 13608 \]

Answer: \( 756 \times 18 = 13608 \)

---

Problem 8: \( 642 \times 71 \)

#### Step 1: Multiply by the units digit (1)
\[ 642 \times 1 = 642 \]

#### Step 2: Multiply by the tens digit (7), shifted left
\[ 642 \times 7 = 4494 \]
Shift this result one place to the left: \( 44940 \)

#### Step 3: Add the partial products
\[ 642 + 44940 = 45582 \]

Answer: \( 642 \times 71 = 45582 \)

---

Problem 9: \( 438 \times 44 \)

#### Step 1: Multiply by the units digit (4)
\[ 438 \times 4 = 1752 \]

#### Step 2: Multiply by the tens digit (4), shifted left
\[ 438 \times 4 = 1752 \]
Shift this result one place to the left: \( 17520 \)

#### Step 3: Add the partial products
\[ 1752 + 17520 = 19272 \]

Answer: \( 438 \times 44 = 19272 \)

---

Problem 10: \( 477 \times 78 \)

#### Step 1: Multiply by the units digit (8)
\[ 477 \times 8 = 3816 \]

#### Step 2: Multiply by the tens digit (7), shifted left
\[ 477 \times 7 = 3339 \]
Shift this result one place to the left: \( 33390 \)

#### Step 3: Add the partial products
\[ 3816 + 33390 = 37206 \]

Answer: \( 477 \times 78 = 37206 \)

---

Problem 11: \( 467 \times 53 \)

#### Step 1: Multiply by the units digit (3)
\[ 467 \times 3 = 1401 \]

#### Step 2: Multiply by the tens digit (5), shifted left
\[ 467 \times 5 = 2335 \]
Shift this result one place to the left: \( 23350 \)

#### Step 3: Add the partial products
\[ 1401 + 23350 = 24751 \]

Answer: \( 467 \times 53 = 24751 \)

---

Problem 12: \( 209 \times 78 \)

#### Step 1: Multiply by the units digit (8)
\[ 209 \times 8 = 1672 \]

#### Step 2: Multiply by the tens digit (7), shifted left
\[ 209 \times 7 = 1463 \]
Shift this result one place to the left: \( 14630 \)

#### Step 3: Add the partial products
\[ 1672 + 14630 = 16302 \]

Answer: \( 209 \times 78 = 16302 \)

---

Problem 13: \( 967 \times 15 \)

#### Step 1: Multiply by the units digit (5)
\[ 967 \times 5 = 4835 \]

#### Step 2: Multiply by the tens digit (1), shifted left
\[ 967 \times 1 = 967 \]
Shift this result one place to the left: \( 9670 \)

#### Step 3: Add the partial products
\[ 4835 + 9670 = 14505 \]

Answer: \( 967 \times 15 = 14505 \)

---

Problem 14: \( 992 \times 73 \)

#### Step 1: Multiply by the units digit (3)
\[ 992 \times 3 = 2976 \]

#### Step 2: Multiply by the tens digit (7), shifted left
\[ 992 \times 7 = 6944 \]
Shift this result one place to the left: \( 69440 \)

#### Step 3: Add the partial products
\[ 2976 + 69440 = 72416 \]

Answer: \( 992 \times 73 = 72416 \)

---

Problem 15: \( 396 \times 76 \)

#### Step 1: Multiply by the units digit (6)
\[ 396 \times 6 = 2376 \]

#### Step 2: Multiply by the tens digit (7), shifted left
\[ 396 \times 7 = 2772 \]
Shift this result one place to the left: \( 27720 \)

#### Step 3: Add the partial products
\[ 2376 + 27720 = 30096 \]

Answer: \( 396 \times 76 = 30096 \)

---

Problem 16: \( 356 \times 63 \)

#### Step 1: Multiply by the units digit (3)
\[ 356 \times 3 = 1068 \]

#### Step 2: Multiply by the tens digit (6), shifted left
\[ 356 \times 6 = 2136 \]
Shift this result one place to the left: \( 21360 \)

#### Step 3: Add the partial products
\[ 1068 + 21360 = 22428 \]

Answer: \( 356 \times 63 = 22428 \)

---

Problem 17: \( 575 \times 87 \)

#### Step 1: Multiply by the units digit (7)
\[ 575 \times 7 = 4025 \]

#### Step 2: Multiply by the tens digit (8), shifted left
\[ 575 \times 8 = 4600 \]
Shift this result one place to the left: \( 46000 \)

#### Step 3: Add the partial products
\[ 4025 + 46000 = 50025 \]

Answer: \( 575 \times 87 = 50025 \)

---

Problem 18: \( 362 \times 64 \)

#### Step 1: Multiply by the units digit (4)
\[ 362 \times 4 = 1448 \]

#### Step 2: Multiply by the tens digit (6), shifted left
\[ 362 \times 6 = 2172 \]
Shift this result one place to the left: \( 21720 \)

#### Step 3: Add the partial products
\[ 1448 + 21720 = 23168 \]

Answer: \( 362 \times 64 = 23168 \)

---

Problem 19: \( 986 \times 45 \)

#### Step 1: Multiply by the units digit (5)
\[ 986 \times 5 = 4930 \]

#### Step 2: Multiply by the tens digit (4), shifted left
\[ 986 \times 4 = 3944 \]
Shift this result one place to the left: \( 39440 \)

#### Step 3: Add the partial products
\[ 4930 + 39440 = 44370 \]

Answer: \( 986 \times 45 = 44370 \)

---

Problem 20: \( 299 \times 59 \)

#### Step 1: Multiply by the units digit (9)
\[ 299 \times 9 = 2691 \]

#### Step 2: Multiply by the tens digit (5), shifted left
\[ 299 \times 5 = 1495 \]
Shift this result one place to the left: \( 14950 \)

#### Step 3: Add the partial products
\[ 2691 + 14950 = 17641 \]

Answer: \( 299 \times 59 = 17641 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
&355 \times 95 = 33725 \\
&167 \times 36 = 6012 \\
&190 \times 45 = 8550 \\
&763 \times 40 = 30520 \\
&767 \times 12 = 9204 \\
&643 \times 18 = 11574 \\
&756 \times 18 = 13608 \\
&642 \times 71 = 45582 \\
&438 \times 44 = 19272 \\
&477 \times 78 = 37206 \\
&467 \times 53 = 24751 \\
&209 \times 78 = 16302 \\
&967 \times 15 = 14505 \\
&992 \times 73 = 72416 \\
&396 \times 76 = 30096 \\
&356 \times 63 = 22428 \\
&575 \times 87 = 50025 \\
&362 \times 64 = 23168 \\
&986 \times 45 = 44370 \\
&299 \times 59 = 17641 \\
\end{aligned}
}
\]