Examples with solutions for Vertical Multiplication: Multiplying 3-Digit by 1-Digit Numbers

Exercise #1

1522x

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Start by multiplying the number at the ones place of 152152 by 22.
  • Step 2: Move to the tens place of 152152 and multiply by 22.
  • Step 3: Finally, multiply the hundreds place of 152152 by 22.
  • Step 4: Sum these products, maintaining their respective place values to find the total product.

Let's perform the calculations:
Step 1: Multiply the ones digit:

2×2=42 \times 2 = 4

Step 2: Multiply the tens digit, and align it in the tens place:

5×2=105 \times 2 = 10.

Since 5×2=105 \times 2 = 10, we write 00 in the tens place and carry 11 over to the hundreds place.

Step 3: Multiply the hundreds digit, and include the carry-over:

1×2=21 \times 2 = 2

Add the carry-over from the previous step:

2+1=32 + 1 = 3

Combine these results to form the final product:

The hundreds place is 33, the tens place is 00, and the ones place is 44, resulting in:

152×2=304152 \times 2 = 304

Therefore, the correct answer is 304304. Looking at the options given, the correct choice is option 2.

Answer

304 304

Exercise #2

1633x

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Align 163 for vertical multiplication by 3.
  • Step 2: Multiply the units digit (3 from 163) by 3.
  • Step 3: Multiply the tens digit (6 from 163) by 3, adding any carry from step 2.
  • Step 4: Multiply the hundreds digit (1 from 163) by 3, adding any carry from step 3.

Now, let's work through each step:

Step 1: Multiply the units digit:
3×3=9 3 \times 3 = 9
Write 9 at the units place.
Carry over = 0 (since 9<10 9 < 10 ).

Step 2: Multiply the tens digit:
6×3=18 6 \times 3 = 18
Add the previous carry (0):
Total = 18.
Write 8 at the tens place and carry over 1.

Step 3: Multiply the hundreds digit:
1×3=3 1 \times 3 = 3
Add the previous carry (1):
Total = 4.
Write 4 at the hundreds place.

The result of 163×3 163 \times 3 is:

489 489

Therefore, the solution to the problem is 489 489 .

Answer

489 489

Exercise #3

1714x

Video Solution

Step-by-Step Solution

To solve this problem, let's perform the multiplication 171×4 171 \times 4 using the vertical multiplication method:

  • Step 1: Multiply the one's place: 4×1=4 4 \times 1 = 4 .
  • Step 2: Multiply the ten's place: 4×7=28 4 \times 7 = 28 . Write 8 under ten's column and carry over 2.
  • Step 3: Multiply the hundred's place: 4×1=4 4 \times 1 = 4 , then add the carry over: 4+2=6 4 + 2 = 6 .

Combine all parts to find the final result: The product is 684 684 .

Therefore, the solution to the problem is 684 684 .

Answer

684 684

Exercise #4

1754x

Video Solution

Step-by-Step Solution

To solve the problem of multiplying 175 by 4, we proceed as follows:

  • Step 1: Set up the numbers for vertical multiplication, writing 175 on top and 4 beneath.
  • Step 2: Multiply the rightmost digit of the top number, 5, by 4:
    • 5×4=20 5 \times 4 = 20 . Write 0 in the units place and carry over 2 to the next digit.
  • Step 3: Multiply the next digit, 7, by 4 and add the carry over:
    • 7×4=28 7 \times 4 = 28 . Add the carry of 2 to this, resulting in 30. Write 0 in the tens place and carry over 3.
  • Step 4: Multiply the leftmost digit, 1, by 4 and add the carry over:
    • 1×4=4 1 \times 4 = 4 . Add the carry of 3 to this, resulting in 7.
  • Step 5: Combine the results from each step to form the complete product: 700.

Thus, the product of 175×4 175 \times 4 is 700 700 .

Therefore, the correct answer is 700 700 , which corresponds to choice 3.

Answer

700 700

Exercise #5

4624x

Video Solution

Step-by-Step Solution

To solve the problem of multiplying 462 by 4, we will follow these steps:

  • Write the numbers 462 and 4 in a vertical format:

462
×     4
────

  • Step 1: Multiply the unit digit of 462 by 4.

2×4=82 \times 4 = 8.
Write 8 under the units column, as there is no carryover.

  • Step 2: Multiply the tens digit of 462 by 4.

6×4=246 \times 4 = 24.
Write 4 under the tens column, and carry over 2 to the hundreds column.

  • Step 3: Multiply the hundreds digit of 462 by 4.

4×4=164 \times 4 = 16.
Add the carryover 2: 16+2=1816 + 2 = 18.
Write 8 under the hundreds column and 1 in the thousands column.

The result will be read as follows from top to bottom in the columns:
1848

Therefore, the product of 462 and 4 is 1848 1848 .

Answer

1848 1848

Exercise #6

3412x

Video Solution

Step-by-Step Solution

To solve the multiplication 341×2 341 \times 2 :

  • Step 1: Multiply the units digit.
    1×2=2 1 \times 2 = 2 . Write 2 in the units place.

  • Step 2: Multiply the tens digit.
    4×2=8 4 \times 2 = 8 . Write 8 in the tens place.

  • Step 3: Multiply the hundreds digit.
    3×2=6 3 \times 2 = 6 . Write 6 in the hundreds place.

Now, putting it all together, the product is 682 682 .

The solution to 341×2 341 \times 2 is 682 682 .

Answer

682 682

Exercise #7

1307x

Video Solution

Step-by-Step Solution

To solve the problem of multiplying the numbers 130130 and 77, we will perform vertical multiplication, focusing on each digit of the three-digit number:

  • Step 1: Multiply the unit digit of 130130 by 77.
    The unit digit of 130130 is 00.
    0×7=00 \times 7 = 0 (carryover is 0).

  • Step 2: Multiply the tens digit of 130130 by 77.
    The tens digit of 130130 is 33.
    3×7=213 \times 7 = 21 (write down 11 and carry 22 to the next column).

  • Step 3: Multiply the hundreds digit of 130130 by 77.
    The hundreds digit of 130130 is 11. Including the carried over 22, we calculate 1×7=71 \times 7 = 7 plus 22 equals 99 (no further carryover is required).

Thus, the final step includes combining results: the hundreds place has 99, tens place 11, and the units place 00, leading to the solution.

Therefore, the solution to the problem is 910 910 .

Answer

910 910

Exercise #8

2306x

Video Solution

Step-by-Step Solution

To solve this multiplication problem, we will use a step-by-step approach:

  • Step 1: Write down the numbers in vertical format, aligning by place values:
                   230 230
                × 6 6
  • Step 2: Start multiplying from the rightmost digit:

First, multiply the units digit, 0×6=00 \times 6 = 0.
Next, multiply the tens digit, 3×6=183 \times 6 = 18. Write 88 below the line in the tens place and carry over 11 to the hundreds place.
Then, multiply the hundreds digit, 2×6=122 \times 6 = 12. Add the carried 11, giving 1313.

Thus, the multiplications line up to give 13801380 as the final product.

Therefore, the solution to the multiplication is 1380 \boxed{1380} .

Answer

1380 1380

Exercise #9

1434x

Video Solution

Step-by-Step Solution

To solve the multiplication problem 143×4 143 \times 4 , we'll follow these steps:

  • Set up the numbers for vertical multiplication: write 143 and directly beneath it, write 4, followed by the multiplication line.
  • Multiply each digit of 143 by 4, starting from the units place.
  • Add any necessary carried numbers to the next multiplicative step.

Let's break down the multiplication:

  • Step 1: Multiply the units place: 3×4=12 3 \times 4 = 12 . Write 2 in the units column, carry over 1 to the tens column.
  • Step 2: Multiply the tens place: 4×4=16 4 \times 4 = 16 . Add the carried over 1, resulting in 17. Write 7 in the tens column and carry over 1 to the hundreds column.
  • Step 3: Multiply the hundreds place: 1×4=4 1 \times 4 = 4 . Add the carried over 1, resulting in 5. Write 5 in the hundreds column.

By combining these, the result of 143×4 143 \times 4 is 572 572 .

The choices provided are:

  • Choice 1: 570 570
  • Choice 2: 572 572
  • Choice 3: 573 573
  • Choice 4: 574 574

The correct answer corresponds to Choice 2: 572 572 .

Therefore, the solution to the problem is 572 572 .

Answer

572 572

Exercise #10

2317x

Video Solution

Step-by-Step Solution

To solve this multiplication problem, we'll follow these steps:

  • Step 1: Multiply each digit of 231 by 7.
  • Step 2: Handle carry-over carefully.
  • Step 3: Add results together to get the final product.

Let's execute the steps:
Step 1: Start from the rightmost digit of 231, which is the units place (1). Multiply it by 7:
1×7=7 1 \times 7 = 7

Step 2: Move to the tens digit, which is 3. Multiply it by 7 and add any carry-over. Since there was no carry from the first multiplication, we have:
3×7=21 3 \times 7 = 21
Write 1 in the tens place and carry over 2 to the hundreds place.

Step 3: Multiply the hundreds digit, which is 2. Multiply by 7 and add the carry-over of 2:
2×7=14 2 \times 7 = 14
Add the carry 2:
14+2=16 14 + 2 = 16

Write down the product from left to right: 16 (hundreds place), 1 (tens place), 7 (units place).
The full product is 1617 1617 .

Therefore, the solution to the problem is 1617 1617 .

Answer

1617 1617

Exercise #11

9213x

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these detailed steps:

  • Step 1: Arrange the numbers for multiplication: write 921 on top and 3 below it with equal alignment.
  • Step 2: Multiply the digit in the ones place of 921, which is 1, by 3.
  • Step 3: Multiply the digit in the tens place of 921, which is 2, by 3.
  • Step 4: Multiply the digit in the hundreds place of 921, which is 9, by 3.
  • Step 5: Place each resulting product in the corresponding position in the final sum.
  • Step 6: Sum all the individual results to get the final product.

Let's perform the calculations:

  • Step 1: Multiply 1 by 3 giving us 33 (put in the ones place).
  • Step 2: Multiply 2 by 3 giving us 66 (put in the tens place as 60).
  • Step 3: Multiply 9 by 3 giving us 2727 (put in the hundreds place as 2700).
  • Step 4: Sum up these results: 2700+60+3=27632700 + 60 + 3 = 2763.

Therefore, the solution to the problem is 2763 2763 .

Answer

2763 2763

Exercise #12

3416x

Video Solution

Step-by-Step Solution

To solve this multiplication problem, we will use the vertical (long) multiplication method:

  • Step 1: Multiply the units digit of 341341 by 66.
    The units digit is 11, so 1×6=61 \times 6 = 6.
  • Step 2: Multiply the tens digit of 341341 by 66.
    The tens digit is 44, so 4×6=244 \times 6 = 24.
    As 2424 is a two-digit number, place 44 in the tens column and carry over 22 to the hundreds column.
  • Step 3: Multiply the hundreds digit of 341341 by 66.
    The hundreds digit is 33, so 3×6=183 \times 6 = 18.
    Add the carried-over 22 from the previous step to get 18+2=2018 + 2 = 20.

Finally, combining all the partial products, we get 20462046:

  • Units column: 66
  • Tens column: 44
  • Hundreds column: 00
  • Thousands column (result of any carried-over sums): 22

Therefore, the multiplication of 341341 by 66 gives us the product 2046 2046 .

Answer

2046 2046

Exercise #13

5315x

Video Solution

Step-by-Step Solution

To solve the multiplication problem 531×5 531 \times 5 , we will perform vertical multiplication, carefully managing place values and carries.

Let's break down the process:

  • Step 1: Multiply the units digit (1) by 5:
    1×5=5 1 \times 5 = 5 . Since this is a single-digit number, no carry is involved. The units place in the product is 5 5 .
  • Step 2: Multiply the tens digit (3) by 5:
    3×5=15 3 \times 5 = 15 . We place 5 in the tens place of the product and carry over 1 to the hundreds place.
  • Step 3: Multiply the hundreds digit (5) by 5:
    5×5=25 5 \times 5 = 25 . Add the carry of 1 from the previous step: 25+1=26 25 + 1 = 26 . We put the entire value 26 into the hundreds place and the thousands place as no more carries need to propagate beyond this point.

Constructing the final product from right to left, we have the value 2655 2655 .

Therefore, the final solution to the multiplication problem 531×5 531 \times 5 is 2655 2655 .

Answer

2655 2655

Exercise #14

4514x

Video Solution

Step-by-Step Solution

To solve the problem of multiplying a three-digit number 451451 by a one-digit number 44, let's use the vertical multiplication method.

Here are the steps:

  • Step 1: Multiply the ones digit of 451451, which is 11, by 44.
    This gives us 1×4=41 \times 4 = 4.
  • Step 2: Multiply the tens digit of 451451, which is 55, by 44.
    Calculating 5×4=205 \times 4 = 20.
    Remember to place this value one position to the left (as it represents tens, not units).
  • Step 3: Multiply the hundreds digit of 451451 which is 44, by 44.
    This gives 4×4=164 \times 4 = 16.
    This value represents hundreds, so its place value is shifted two positions to the left.

Now, let's put together these individual calculations for the final sum:
- For units: 44
- For tens: 2020, but considered as 200200 in terms of place value.
- For hundreds: 16001600
The total sum is 1600+200+4=18041600 + 200 + 4 = 1804.

Thus, the product of 451×4451 \times 4 is 1804\mathbf{1804}.

Answer

1804 1804

Exercise #15

5306x

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Align the given numbers for multiplication.
  • Step 2: Perform the multiplication digit by digit.
  • Step 3: Sum the partial results.

Now, let's work through each step:
Step 1: The problem asks us to multiply 530530 by 66. Set the numbers up such that 530530 is the multiplicand and 66 is the multiplier.

Step 2: Let's multiply 66 by each digit of 530530, from right to left:

  • 6×0=06 \times 0 = 0 (units place)
  • 6×3=186 \times 3 = 18. Write 88 in the tens place and carry over 11 to the hundreds place.
  • 6×5=306 \times 5 = 30. Adding the carried over 11 gives 3131.

Step 3: Write down the resulting multiplication: 31803180.

Therefore, the solution to the multiplication problem is 3180 3180 .

Answer

3180 3180

Exercise #16

1467x

Video Solution

Step-by-Step Solution

We will perform the multiplication of the numbers 146 and 7 using the vertical multiplication method:

  • Step 1: Write the numbers vertically aligning the digits by place value:

999146 \phantom{999}146
×997 \times \phantom{99}7
999999999\underline{\phantom{999999999}}

  • Step 2: Multiply 7 by each digit of 146 starting from the right:

Multiply 7 by 6 (units place):

7×6=42 7 \times 6 = 42

  • Write 2 in the units place and carry over 4 to the tens place.

Multiply 7 by 4 (tens place), add the carry over:

7×4=28 7 \times 4 = 28
28+4=32 28 + 4 = 32

  • Write 2 in the tens place and carry over 3 to the hundreds place.

Multiply 7 by 1 (hundreds place), add the carry over:

7×1=7 7 \times 1 = 7
7+3=10 7 + 3 = 10

  • Write 0 in the hundreds place and 1 in the thousands place.

Combine these to write out the full product:

1022 1022

Therefore, the solution to the problem is 1022 1022 .

Answer

1022 1022

Exercise #17

2399x

Video Solution

Step-by-Step Solution

Let us now perform the multiplication step-by-step:

  • Step 1: Multiply the ones digit: 9×9=819 \times 9 = 81. Write down 11 and carry over 88.
  • Step 2: Multiply the tens digit: 3×9=273 \times 9 = 27, then add the carryover 8=358 = 35. Write down 55 and carry over 33.
  • Step 3: Multiply the hundreds digit: 2×9=182 \times 9 = 18, then add the carryover 3=213 = 21. Write down 2121.
  • Final Product: Arrange the results to form the number: 21512151.

Therefore, the product of 239239 and 99 is 21512151.

Thus, the correct answer is 2151 2151 .

Answer

2151 2151

Exercise #18

6316x

Video Solution

Step-by-Step Solution

To solve the multiplication problem 631×6 631 \times 6 using vertical multiplication, follow these steps:

  • Step 1: Begin with the rightmost digit of 631, which is 1.
  • Multiply 1×6=6 1 \times 6 = 6 . Write 6 under the line.
  • Step 2: Move to the next digit to the left, which is 3.
  • Multiply 3×6=18 3 \times 6 = 18 . Write 8 below and carry over 1 to the next column.
  • Step 3: Multiply the leftmost digit 6 by 6.
  • Multiply 6×6=36 6 \times 6 = 36 . Add the carry-over 1 to get 37.
  • Write down 37 on the left side.

The sum of these values is 3786.

Thus, the product of 631 631 and 6 6 is 3786\textbf{3786}.

The correct answer, as per the answer choices, is 3786.

Answer

3786 3786

Exercise #19

7206x

Video Solution

Step-by-Step Solution

To solve this problem, we will perform the multiplication step by step:

  • Step 1: Multiply the units digit of 720 by 6, which is 0×6=00 \times 6 = 0.
  • Step 2: Multiply the tens digit of 720 by 6 and add any carryovers. So, 2×6=122 \times 6 = 12. Write down 2 and carry over 1.
  • Step 3: Multiply the hundreds digit of 720 by 6 and add any carryovers. So, 7×6=427 \times 6 = 42, and add the 1 carried over, resulting in 43.

Combining these results gives us 4320. Thus, the product of 720 and 6 is 4320 4320 .

Therefore, the solution to the problem is 4320 4320 .

Answer

4320 4320

Exercise #20

7615x

Video Solution

Step-by-Step Solution

To solve this multiplication problem, we will use the vertical multiplication method:

  • Step 1: Multiply the units digit of 761 by 5. This is 1×5=51 \times 5 = 5.
  • Step 2: Multiply the tens digit of 761 by 5. This is 6×5=306 \times 5 = 30. Write the 0 below and carry over the 3.
  • Step 3: Multiply the hundreds digit of 761 by 5. This is 7×5=357 \times 5 = 35. Add the carry-over 3 to get 38.

Write down the results from each multiplication:
From the units place, we have 5.
From the tens place, considering the carry, we have 0 (as 3030 is written as 0 with carry 3).
From the hundreds place, we have 3838.

Combining these, starting from the hundreds, tens, and units positions, gives us the final result of the multiplication: 3805.

Therefore, the product of 761 and 5 is 3805 3805 .

Answer

3805 3805