Examples with solutions for Vertical Multiplication: Multiplying 2-Digit by 2-Digit Numbers

Exercise #1

7220x

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Identify the given numbers: 72 and 20.
  • Step 2: Use vertical multiplication to multiply these numbers.
  • Step 3: Break down the multiplication into simpler steps and perform the calculations.

Let's work through each step:

Step 1: The given numbers are 72 and 20.

Step 2: We'll perform vertical multiplication by breaking down the problem into parts. Start with:

72×20 72 \times 20

Step 3: Multiply 72 by each digit of 20 separately.

  • First, multiply 72 by 0 (the units digit of 20).
    72×0=0 72 \times 0 = 0 .
  • Next, multiply 72 by 2 (the tens digit of 20), noting it represents 20.
    72×2=144 72 \times 2 = 144 .
    Since this 2 is in the tens place, we write this as 1440 (i.e., 144 shifted one place to the left).

Now add the results:
- From 72×0 72 \times 0 : 0
- From 72×20 72 \times 20 : 1440

Adding these results gives:
0+1440=1440 0 + 1440 = 1440 .

Therefore, the solution to the problem is 1440 1440 .

Answer

1440 1440

Exercise #2

2916x

Video Solution

Step-by-Step Solution

To solve the multiplication problem 29×16 29 \times 16 , we'll follow these steps using the vertical multiplication method:

  • First, multiply the digit in the units place of 16 by 29: 6×29 6 \times 29 .
  • Then, multiply the digit in the tens place of 16 (1) by 29, and shift one position to the left (because it represents a ten): 10×29 10 \times 29 .
  • Add the two products to get the final product.

Let's work through each step:

Step 1: Calculate 6×29 6 \times 29 .
- 29×6=174 29 \times 6 = 174 .

Step 2: Calculate 10×29 10 \times 29 .
- 29×1=29 29 \times 1 = 29 , and then shift one position to the left to get 290 290 .

Step 3: Add both results.
- 174+290=464 174 + 290 = 464 .

Thus, the solution to 29×16 29 \times 16 is 464 464 .

Answer

464 464

Exercise #3

2513x

Video Solution

Step-by-Step Solution

To find the value of x x using vertical multiplication, follow these steps:

  • Write the two numbers vertically, with 25 on top and 13 below it:
    25× 13 \begin{array}{c} \ \ \ \ 25 \\ \times \ \text{13} \\ \hline \end{array}
  • Multiply the digit in the units place of 13 (which is 3) by each digit in 25:
    • 3 times 5 equals 15. Write 5 in the units place and carry over 1
    • 3 times 2 equals 6, plus the carried over 1 equals 7
        75 \begin{array}{c} \ \ \ \ 75 \end{array}
    • Next, multiply the digit in the tens place of 13 (which is 1) by each digit in 25. Remember to shift this product one place to the left:
      • Starting beneath the tens column, 1 times 5 equals 5
      • 1 times 2 equals 2
        250 \begin{array}{c} \ \ 250 \end{array}
    • Add the two partial products together to get the final product:
    •    75+ 250 325 \begin{array}{c} \ \ \ 75 \\ + \ 250 \\ \hline \ 325 \end{array}

      Therefore, the value of x x is 325 325 .

Answer

325 325

Exercise #4

6416x

Video Solution

Step-by-Step Solution

To solve this problem, we'll perform the following steps using column multiplication:

  • Step 1: Write the numbers in a column, with 64 on top and 16 beneath, ensuring proper alignment.
  • Step 2: Multiply the units digit (6) of the bottom number (16) by the entire top number (64).
  • Step 3: Multiply the tens digit (1) of the bottom number (16) by the entire top number (64) and shift the result one place to the left (equivalent to multiplying the result by 10).
  • Step 4: Add these two partial products to find the final result.

Let's work through this step-by-step:

Step 1: Set up the multiplication vertically.

+64×16 \begin{array}{c} \phantom{+}64 \\ \times 16 \\ \end{array}

Step 2: Multiply the units digit of the bottom number (6) by the entire top number (64):
6×64=384 6 \times 64 = 384 .

Step 3: Multiply the tens digit of the bottom number (1) by the entire top number (64) and remember to place a zero since this is in the tens place:
1×64=64 1 \times 64 = 64 , shift by one place to get 640 640 .

Step 4: Add the two partial products:
384+640=1024 384 + 640 = 1024 .

Therefore, the solution to the problem is 1024 1024 .

Answer

1024 1024

Exercise #5

7313x

Video Solution

Step-by-Step Solution

To solve this problem, we will perform vertical multiplication of the numbers 73 73 and 13 13 .

First, write the numbers vertically:

73 73

× 13\times \ 13

Step 1: Multiply the units digit of 13 13 (which is 3 3 ) by each digit of 73 73 :

  • 3×3=9 3 \times 3 = 9
  • 3×7=21 3 \times 7 = 21

The partial result is 219 219 .

Step 2: Multiply the tens digit of 13 13 (which is 1 1 , but treat it as 10 10 ) by each digit of 73 73 :

  • 10×3=30 10 \times 3 = 30
  • 10×7=70 10 \times 7 = 70

The partial result is 730 730 because we start from the tens place.

Step 3: Add the results from Step 1 and Step 2:

   219+ 730 949\begin{array}{c} \ \ \ \,219\\ + \ 730\\ \hline \ 949\\ \end{array}

Therefore, the product of 73 73 and 13 13 is 949 949 .

The solution is 949\boxed{949}, which corresponds to choice 4 4 .

Answer

949 949

Exercise #6

3611x

Video Solution

Step-by-Step Solution

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

  • Step 1: Write the numbers vertically, aligning by place value.
  • Step 2: Multiply the digit in the units place of the lower number by the entire upper number.
  • Step 3: Multiply the digit in the tens place of the lower number by the entire upper number and shift one place to the left.
  • Step 4: Add the products obtained in Step 2 and Step 3.

Let's work through each step:
Step 1: Arrange the numbers:

  • ...... 36
  • x .... 11

Step 2: Multiply the upper number by the units digit of the lower number (1):

  • 36 (since 36×1=36 36 \times 1 = 36 )

Step 3: Multiply the upper number by the tens digit of the lower number (1) and remember to shift by one place (which represents multiplying by 10):

  • 360 (since 36×10=360 36 \times 10 = 360 )

Step 4: Add the results from Steps 2 and 3:

  • .......... 36
  • + ......360
  • -----------
  • ).......396

Therefore, the product of 36 and 11 is 396 396 , which corresponds to choice 2.

Answer

396 396

Exercise #7

2021x

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the numbers to be multiplied, which are 20 and 21.
  • Step 2: Multiply 20 by 21 using simple arithmetic rules for multiplication.
  • Step 3: Compare the result to the provided answer choices to confirm the correct one.

Now, let's work through each step:
Step 1: The numbers given are 20 and 21.
Step 2: We'll use the formula a×b=Product a \times b = \text{Product} , which becomes 20×21 20 \times 21 .
To simplify the multiplication:
- Multiply each digit: 20×20=400 20 \times 20 = 400 and 20×1=20 20 \times 1 = 20 .
- Add the products together: 400+20=420 400 + 20 = 420 .

Therefore, the solution to the problem is x=420 x = 420 .

Answer

420 420

Exercise #8

1611x

Video Solution

Step-by-Step Solution

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

  • Step 1: Set up the numbers in vertical format for multiplication.
  • Step 2: Multiply each digit of the number 16 by each digit of the number 11, starting with the rightmost digit.
  • Step 3: Sum the results, considering the appropriate place values.

Now, let's proceed with the steps in detail:

Step 1: Write the numbers vertically:
           16
×        11
--------------------

Step 2: Multiply as follows:
- Multiply 16 by 1 (the units place of the lower number):
              16

- Multiply 16 by 10 (the tens place of the lower number, written as 1 * 10):
          160   (shifted one place to the left)

Step 3: Add both results. Here, aligning by place values is crucial:

            16
+        160
--------------------
          176

Therefore, the product of 16 and 11 is 176 176 .

Answer

176 176

Exercise #9

3219x

Video Solution

Step-by-Step Solution

To solve this problem, we'll perform vertical multiplication:

  • First, multiply the ones digit of 19 by 32: 9×32 9 \times 32 .
    9×2=18 9 \times 2 = 18 (write 8, carry over 1).
    9×3=27 9 \times 3 = 27 . Add the carry over: 27+1=28 27 + 1 = 28 .
    This gives us the partial product 288.
  • Next, multiply the tens digit of 19 by 32, remembering to align correctly by adding a zero at the end: 1×32 1 \times 32 (shift result one position to the left).
    1×2=2 1 \times 2 = 2 and 1×3=3 1 \times 3 = 3 , thus giving 32.
    Write this as 320 (by placing a 0 after, to account for tens place).
  • Add these two partial products:
      288
    + 320
    -------
      608

Therefore, the product of 32 and 19 is 608 608 .

Answer

608 608

Exercise #10

3117x

Video Solution

Step-by-Step Solution

To find x x in this multiplication problem, we will multiply the numbers 31 and 17 step-by-step:

Write down the numbers as they would appear in vertical multiplication:

    31
  × 17
  -----

Step 1: Multiply the units digit of 17, which is 7, by the entire number 31.

  • 31×7=217 31 \times 7 = 217

Write this partial product below the line:

    31
  × 17
  -----
   217

Step 2: Multiply the tens digit of 17, which is 1, by the entire number 31, remembering this is actually multiplying by 10, so we add a zero at the end.

  • 31×1=31 31 \times 1 = 31 . Since we are multiplying by 10, it becomes 310 310 .

Write this partial product, shifted one position to the left (adding a zero):

    31
  × 17
  -----
   217
+ 310
  -----

Step 3: Add the two partial products together to get the final product.

  • Adding 217 217 and 310 310 gives us 527 527 .

Thus, the product of 31 and 17, which is the value of x x , is 527 527 .

Answer

527 527

Exercise #11

2613x

Video Solution

Step-by-Step Solution

To solve this problem, we'll perform vertical multiplication between the numbers 26 and 13. Here are the steps:

  • Step 1: Multiply the digits in the units place.
  • Step 2: Multiply the units place digit of the second number by the first number:
  • 3×263 \times 26

    Calculate 6×3=186 \times 3 = 18. Write down 8, carry over 1.

    Then 2×3=62 \times 3 = 6 plus the carry over 1 gives 7.

    Result: 78.

  • Step 3: Multiply the digit in the tens place of the second number by the first number.
  • 1×26=261 \times 26 = 26. Since this is tens place, write down 260 (shift one place to the left).

  • Step 4: Add the two results.
  • 78+260=33878 + 260 = 338

Therefore, the product of 26 and 13 is 338\textbf{338}.

Answer

338 338

Exercise #12

2721x

Video Solution

Step-by-Step Solution

To solve this problem, we'll employ the vertical multiplication method to compute 27×2127 \times 21.

  • First, multiply 2727 by the units digit of 2121 (which is 11):
    27×1=2727 \times 1 = 27
  • Next, multiply 2727 by the tens digit of 2121 (which is 22) and shift the result one place to the left:
    27×2=5427 \times 2 = 54. Because this represents tens, it becomes 540540.
  • Sum the two products obtained above:
    27+540=56727 + 540 = 567

Therefore, the solution to the problem is 567567.

Answer

567 567

Exercise #13

2115x

Video Solution

Step-by-Step Solution

To solve this problem, we'll multiply the two-digit numbers 21 and 15 using vertical multiplication:

  • Step 1: Multiply the ones digit of 15 (5) by each digit of 21.

    - 5×1=5 5 \times 1 = 5
    - 5×2=10 5 \times 2 = 10

    So, we write this partial product as 105, ensuring that we account for place value.

  • Step 2: Multiply the tens digit of 15 (1, which is actually 10) by each digit of 21, adding one zero beforehand for the tens place.

    - 1×1=1 1 \times 1 = 1 (Since 1 is actually 10, consider this as 10×1=10 10 \times 1 = 10 )
    - 1×2=2 1 \times 2 = 2 (Since 1 is actually 10, consider this as 10×2=20 10 \times 2 = 20 )

    Write this second partial product as 210, remembering the zero addition for the tens place.

  • Step 3: Add the partial products from Step 1 and Step 2.

    105+210=315 105 + 210 = 315

So, the final product of 21 and 15 is 315 315 .

We can confirm that the correct choice among the provided options is 315 315 .

Answer

315 315

Exercise #14

2515x

Video Solution

Step-by-Step Solution

To solve the problem of finding x x , we will calculate the area of a rectangle with sides 25 and 15. This requires multiplying these two lengths:

Here is a step-by-step breakdown of the multiplication process using the column method:

  • Step 1: Multiply the unit value of 15 by 25:
    5×25=125 5 \times 25 = 125
  • Step 2: Multiply the tens value of 15 (which is 10) by 25:
    10×25=250 10 \times 25 = 250
  • Step 3: Add the results of step 1 and step 2:
    125+250=375 125 + 250 = 375

Therefore, the value of x x is the area of the rectangle, which equals 375 375 .

The correct choice corresponding to this result is option 2.

Thus, the solution to the problem is x=375 x = 375 .

Answer

375 375

Exercise #15

9210x

Video Solution

Step-by-Step Solution

To solve this problem, we will multiply the numbers 92 and 10. Here's how:

  • Step 1: Write the problem vertically with 92 on top and 10 below it because 10 is a simpler number to multiply.
  • Step 2: Start by multiplying 92 by 0, which gives 0.
  • Step 3: Next, multiply 92 by 1 (from 10) but remember this is in the tens place, so it actually represents multiplying 92 by 10, resulting in 920.

Multiplication Breakdown:
92
× 10
------
920

Therefore, 92 multiplied by 10 equals 920 920 .

Thus, the solution to the problem is 920 920 .

Answer

920 920

Exercise #16

1612x

Video Solution

Step-by-Step Solution

To solve the problem of multiplying 16 by 12 using vertical multiplication, follow these steps:

  • Step 1: Multiply the units digit of 12 (2) by 16.
  • Step 2: 2×6=12 2 \times 6 = 12 . Write 2, carry 1.
  • Step 3: 2×1+1=3 2 \times 1 + 1 = 3 . So, the result is 32.
  • Step 4: Multiply the tens digit of 12 (1) by 16.
  • Step 5: 1×16=16 1 \times 16 = 16 . Shift this result one place to the left (add a trailing zero).
  • Step 6: Add the partial products: 32 + 160 = 192.

Therefore, the product of 16×12 16 \times 12 is 192 192 .

Answer

192 192

Exercise #17

3317x

Video Solution

Step-by-Step Solution

To solve this problem, we will multiply 33 by 17 using vertical multiplication:

  • Step 1: Multiply 33 by the unit digit of 17, which is 7.
  • Step 2: Multiply 33 by the tens digit of 17, which is 1, and remember to position its result correctly as it's equivalent to multiplying by 10.
  • Step 3: Sum the results obtained in the above steps to get the final product.

Let's perform the calculations:

Step 1: 33×7=231 33 \times 7 = 231

Step 2: 33×10=330 33 \times 10 = 330 (since the tens digit of 17 is 1, effectively 33×1×10 33 \times 1 \times 10 )

Step 3: Add these two results:

231+330=561 231 + 330 = 561

Therefore, the solution to this problem is 561 561 .

Answer

561 561

Exercise #18

2611x

Video Solution

Step-by-Step Solution

To solve the vertical multiplication problem of 26×1126 \times 11, we proceed as follows:

  • First, write 26 and 11 as a vertical multiplication setup.
  • Step 1: Multiply 26 by the digit in the units place of 11, which is 1:
  • 26×1=26 26 \times 1 = 26
  • Step 2: Multiply 26 by the digit in the tens place of 11 (when thinking about multiplication, consider it 10):
  • 26×10=260 26 \times 10 = 260
  • Ensure to shift the result by one place to the left since we are multiplying by the tens place;
  • Add the two results together:
  • 26+260=286 26 + 260 = 286

Therefore, the product of 26×1126 \times 11 is 286286.

Answer

286 286

Exercise #19

2516x

Video Solution

Step-by-Step Solution

To solve this problem, we will multiply the two numbers 25 and 16 using the standard method of vertical multiplication. Let's break this down step-by-step:

First, multiply the smallest place value:

  • Multiply the units digit of the second number (6) by the first number (25):
    25×6 25 \times 6 :
  • Multiply: 6×5=30 6 \times 5 = 30 , write 0 and carry over 3.
  • Multiply: 6×2=12 6 \times 2 = 12 , add the carryover 3 to get 15.
    This gives us 150.

Next, multiply the tens digit of the second number (1) by the first number (25), remembering to shift this result one place to the left (equivalent to multiplying by 10):

  • 25×10=250 25 \times 10 = 250
  • The multiplication by 1 here doesn't change the product, only the shift does.

Now, add the partial products obtained from the above steps:

  • Add: 150+250 150 + 250
  • Result: 400 400

Therefore, the solution to the problem is 400 400 .

Answer

400 400

Exercise #20

8230x

Video Solution

Step-by-Step Solution

To solve this problem, we will use vertical multiplication to find the product of 82 and 30. Begin with these steps:

  • Step 1: Write the numbers in vertical format:

        82
      x 30
      ----
      
  • Step 2: Start by multiplying the 2 in the unit's place of 82 by each digit of 30. Since 30 is composed of 0 and 3 (which represents 30 because it’s in the tens place), the small segments of multiplication become:

    • 82×0=082 \times 0 = 0

    • Record this result beneath the line, shifted to match the units place. Since this is multiplication by zero, this line remains:

              0
           
  • Step 3: Now multiply the next digit in the number 30: Since it is 3×82, and it is in the tens place, it actually represents 30×82.\text{Since it is } 3 \times 82,\text{ and it is in the tens place, it actually represents } 30 \times 82.

    • First, multiply 82×3=24682 \times 3 = 246

    • Then multiply 246 by 10 (since 3 is actually 30):

           2460
           
  • Step 4: Add the two results (noting the multipliers from each digit of 30 already included their place value):

        82
      x 30
      ----
        0   (from 82 x 0)
      2460  (from 82 x 30)
      ----
      2460
      
  • Therefore, the product of 82×3082 \times 30 is 2460\mathbf{2460}.

Therefore, the correct answer to the problem is 2460 2460 , which corresponds to choice (1).

Answer

2460 2460