Vertical Multiplication - Examples, Exercises and Solutions

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

• Step 1: Multiply the ones digit of the two-digit number by the single-digit number.
• Step 2: Multiply the tens digit of the two-digit number by the single-digit number.
• Step 3: Add the two products from the above steps to find the final result.

Now, let's work through each step:
Step 1: Multiply $5 \times 9$. This results in $45$, which includes the 5 in the ones place, and we carry over 4.
Step 2: Next, multiply $2 \times 9$ (from the tens place), which equals $18$. Add the carried-over 4 to get $18 + 4 = 22$. This 22 represents 220 when taking place value into account.
Step 3: Combining steps 1 and 2, we put the $5$ from step 1 in the ones digit and the result from step 2 as tens (which corresponds to $220 + 5 = 225$).

Therefore, the solution to the problem is $x = 225$, aligning with choice 4.

We will solve the problem using direct multiplication of the two numbers, 30 and 4.

Steps:

• First, multiply the one's place of 30 by 4:
  $0 \times 4 = 0$

• Second, multiply the ten's place of 30 by 4:
  $3 \times 4 = 12$

• The result from the tens multiplication is over the magnitude of the number 30 (since it's in the tens place), so we already account for place by multiplying 3 by 4 directly forming a product 12, no tens digit carries from one's digit.

• Combine these results to get the total product:
  $0 + 120 = 120$

Therefore, the product of $30$ and $4$ is $\mathbf{120}$.

By referencing the multiple-choice options provided, the correct choice matches the calculation we performed and is choice 3: $120$.

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

• Step 1: Identify the given information
• Step 2: Perform the multiplication of 36 by 5
• Step 3: Verify the product against the provided answer choices

Now, let's work through each step:
Step 1: We are given the numbers 36 (a two-digit number) and 5 (a single-digit number).
Step 2: Perform direct multiplication:
Multiply the units digit of 36 by 5: $6 \times 5 = 30$. Write down the 0 and carry over the 3.
Multiply the tens digit of 36 by 5: $3 \times 5 = 15$. Add the carry-over 3 to get 18.
Combine these results to form the full product: 180.
Step 3: The calculated product is 180. Comparing this with the provided answer choices, the correct choice is $180$.

Therefore, the solution to the problem is $180$.

To solve this problem, we'll use long multiplication. Here's how to proceed step-by-step:

• Step 1: Begin with the multiplication of the units digit of 28, which is 8, by 5.
• Step 1 Calculation: $8 \times 5 = 40$. We write 0 in the units place and carry over 4.
• Step 2: Multiply the tens digit of 28, which is 2, by 5.
• Step 2 Calculation: $20 \times 5 = 100$.
• Step 3: Add the products from Step 1 and Step 2.
• Addition: $100 + 40 = 140$.

Therefore, the product of 28 and 5 is $140$.

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

• Step 1: Identify the numbers to be multiplied: $15$ and $2$.
• Step 2: Calculate the product of these two numbers.

Now, let's work through each step:
Step 1: We are given the numbers $15$ and $2$.
Step 2: We will multiply these numbers together: $15 \times 2$ = $30$.

Therefore, the solution to the problem is $30$.

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

• Step 1: Write down the multiplication in the vertical form:
         $96$
  $\times$     $3$
  $\_\_\_\_\_\_\_\_$
• Step 2: Multiply the one's digit of the bottom number (3) by the one's digit of the top number:\
  3 \times 6 = 18. Write 8 in the one's place and carry over 1 to the next place.
• Step 3: Multiply the tens digit of the top number (9) by 3:
  3 \times 9 = 27. Add the carryover 1, getting 28. Write 28 in the tens and hundreds places.
• Step 4: Write down the results:
       $288$

Therefore, the product of $96 \times 3$ is $288$.

Hence, the correct answer is choice $288$.

To solve this multiplication problem, follow these clear steps:

• Step 1: Align the numbers vertically (place 26 above 6), ensuring the digits are properly arranged by place value.
• Step 2: Begin multiplication with the unit digit of the bottom number (6). Multiply 6 by each digit in 26, starting from the right.

Now, let's perform the calculations:

Step 1: Multiply the units digit of 6 with the number 26:
- $6 \times 6 = 36$. Write 6 in the units place of the answer, and carry over the 3.
- Next, multiply $6 \times 2 = 12$. Then, add the carryover (3) to 12, resulting in 15.

Step 2: Write 15 next to the 6 in the result. Thus, the complete multiplication gives 156.

Therefore, the solution to the problem is $\boxed{156}$.

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

• Step 1: Identify the given numbers. We have $45$ and $8$.
• Step 2: Perform vertical multiplication of $45 \times 8$.

Now, let's work through each step:

• Multiply the units digit of 45 by 8:
  $5 \times 8 = 40$.
  Write 0 in the units place and carry over 4 to the tens.
• Multiply the tens digit of 45 by 8, and add the carry-over:
  $4 \times 8 = 32$.
  Add the carry-over 4: $32 + 4 = 36$.
• Write 36 in the tens and hundreds place, giving us the final product:

Combining these, the final result of the multiplication is $360$.

Therefore, the solution to the problem is $360$, which corresponds to choice number 3.

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

• Step 1: Multiply the unit digits.
• Step 2: Multiply the tens digits.
• Step 3: Add the results from Steps 1 and 2.

Let's execute these steps:
Step 1: Multiply the unit digit of 53, which is 3, by 3:
$3 \times 3 = 9$.

Step 2: Multiply the tens digit of 53, which is 5 (standing for 50), by 3:
$50 \times 3 = 150$.

Step 3: Add the results of Step 1 and Step 2:
$150 + 9 = 159$.

Therefore, the solution to the problem is $159$.

To solve this problem, we'll multiply $42$ by $7$ using vertical multiplication.

• Step 1: Break down $42$ as $40 + 2$.
• Step 2: Multiply each part by $7$.

Let's perform the calculations:

• Multiply $2 \times 7$ makes $14$.
• Multiply $40 \times 7$ equals $280$.
• Add the two products: $280 + 14 = 294$.

Therefore, the solution to the multiplication problem is $\boxed{294}$.

Upon reviewing the provided choices, the correct choice is option $3$ with result $294$.

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

• Step 1: Multiply the units digit of 73 by 8.
• Step 2: Multiply the tens digit of 73 by 8.
• Step 3: Add the results of these two multiplications.

Now, let's work through each step:

Step 1: Multiply the units digit of 73 (which is 3) by 8:
$3 \times 8 = 24$
We'll write 4 in the ones place of the result and carry over 2 to the tens place.

Step 2: Multiply the tens digit of 73 (which is 7) by 8 and add the carried over 2:
$7 \times 8 = 56$
Adding the carried over 2 gives us:
$56 + 2 = 58$

Step 3: Write the result from the tens multiplication in the tens and hundreds place:
Combining our results, we get:
$73 \times 8 = 584$

Therefore, the solution to the problem is $584$.

To solve this problem, we'll perform vertical multiplication of $82$ by $2$:

• Step 1: Multiply the ones place. Multiply $2$ (from 82) by $2$:

$2 \times 2 = 4$
This gives us $4$ in the ones place.

• Step 2: Multiply the tens place. Multiply $8$ (in the tens place of 82) by $2$:

$8 \times 2 = 16$
Since the result is $16$, we place $6$ in the tens place and carry over $1$ to the next higher place (hundreds place).

• Step 3: Add up the intermediate results.

The ones place has $4$, and the tens place has $6$ plus $1$ (carry-over), totaling to $7$ in the tens place. Thus, the full number now reads:

$164$

Therefore, the solution to the problem is $164$.

To solve the multiplication problem $64 \times 6$, we'll perform the following steps:

• Step 1: Break down $64$ into tens and units. So, $64$ can be written as $60 + 4$.
• Step 2: Multiply each component separately by $6$.
• Step 3: Calculate $60 \times 6$ and $4 \times 6$ separately.
• Step 4: Sum the results of the above calculations to find the total product.

Now, let's execute these steps specifically:

Step 1: Represent $64$ as $60 + 4$. This simplifies the multiplication process.

Step 2: Multiply the tens: $60 \times 6 = 360$.

Step 3: Multiply the units: $4 \times 6 = 24$.

Step 4: Now, add the two results: $360 + 24 = 384$.

Therefore, the product of $64 \times 6$ is $384$.

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

• Step 1: Breakdown the multiplication into tens and units.
• Step 2: Multiply each digit by the single-digit multiplier.
• Step 3: Sum the partial results to get the final product.

Let's work through each step:

Step 1: We need to multiply each digit of the number 16 by 5.
- The tens digit of 16 is 1 (representing 10), and the units digit is 6.

Step 2: Perform the multiplication:
- Multiply the tens digit: $10 \times 5 = 50$
- Multiply the units digit: $6 \times 5 = 30$

Step 3: Add the results from these multiplications:
- Total: $50 + 30 = 80$

Therefore, the solution to the problem is $80$.

To solve this problem, we'll multiply the numbers directly:

• Step 1: Identify the numbers to multiply: $32$ and $8$.
• Step 2: Use the vertical multiplication method to calculate the product.
• Step 3: Verify the calculation by using the distributive property as a secondary method.

Now, let's work through each step:
Step 1: We have the multiplicand $32$ and the multiplier $8$.
Step 2: Multiply $32$ by $8$. To do this, break it down as follows:
- $32 = 30 + 2$
- Multiply each part by 8: $30 \times 8 = 240$ and $2 \times 8 = 16$.
- Add the two products together: $240 + 16 = 256$.

Step 3: Verify this by rechecking the arithmetic or using properties of multiplication.

Therefore, the solution to the problem is $256$.