Vertical Multiplication Practice Problems & Worksheets

Master vertical multiplication with step-by-step practice problems. Learn multi-digit multiplication methods, improve accuracy, and build confidence with guided exercises.

📚What You'll Master in Vertical Multiplication Practice
  • Multiply 2-digit and 3-digit numbers using vertical alignment method
  • Apply proper place value positioning in multi-digit multiplication problems
  • Master carrying and regrouping techniques for accurate calculations
  • Solve real-world word problems using vertical multiplication strategies
  • Build speed and accuracy with timed multiplication practice exercises
  • Identify and correct common multiplication errors and misconceptions

Understanding Vertical Multiplication

Complete explanation with examples

Vertical Multiplication

Vertical multiplication is a method used to multiply numbers by aligning them vertically, with one number on top of the other. This layout makes it easier to multiply digits step by step, especially when dealing with multi-digit numbers.

Steps for Vertical Multiplication:

Solving Vertical Multiplication is easy when following these steps:

1. Write the Numbers Vertically Properly:
Place the larger number on top and the smaller number below it, aligning the digits by their place values (ones under ones, tens under tens, etc.) .

Vertical Multiplication - write the number

2. Multiply Each Digit Systematically:
Start by multiplying the bottom number’s rightmost digit (ones place) with each digit of the top number, working from right to left. Write the results below, ensuring they are aligned properly.

Vertical Multiplication - first digit

3. Add the Carry:
If the product of two digits exceeds 9, write down the ones place and carry the tens place to the next column.

Vertical Multiplication - add the carry

4. Shift for Place Value:
When moving to the next digit of the bottom number, shift the results one place to the left (to account for place value).

Vertical Multiplication - shift the place

5. Add the Results:
After multiplying with all digits of the bottom number, add the rows of partial products to find the final result.

Vertical Multiplication - add the results

Important rules to keep in mind

Learn the multiplication tables thoroughly and follow these rules:

First rule

Write down the exercise correctly:
The ones under the ones, the tens under the tens, and the hundreds under the hundreds.
The number with more digits will be written above the one with fewer digits.

Second rule

When the product is greater than 99 it is stored at the top left and must be remembered to add it to the next result.

Third rule

Before moving on to multiply the next digit, the "numbers stored" at the top left must be erased to avoid confusion.

Fourth rule

We will add a 00 below the result to indicate that we have moved to the next digit, each row of results will start one place to the left in relation to the previous row.

Detailed explanation

Practice Vertical Multiplication

Test your knowledge with 27 quizzes

646x

Examples with solutions for Vertical Multiplication

Step-by-step solutions included
Exercise #1

247x

Step-by-Step Solution

To solve this problem, we will multiply 24 by 7 using standard multiplication:

  • Step 1: Multiply the unit digit of 24 by 7:
    4×7=28 4 \times 7 = 28 . Write down 8 and carry over 2.
  • Step 2: Multiply the tens digit of 24 by 7, then add the carry over:
    2×7=14 2 \times 7 = 14 , and add the carried-over 2 to get 16.

The final result of these calculations is:
Since the unit's place is 8 and the ten's place is 16, our final answer is 168 168 .

Therefore, the solution to the problem is 168 168 .

Answer:

168 168

Video Solution
Exercise #2

773x

Step-by-Step Solution

To solve this problem, we'll follow these steps to multiply 7777 by 33:

First, set up the numbers for vertical multiplication:

77×  3\begin{array}{c} & 77 \\ \times & \,\,3 \\ \hline \end{array}

  • Step 1: Multiply the units:
  • 7×3=217 \times 3 = 21

    Write down 11 and carry over 22.

  • Step 2: Multiply the tens:
  • 7×3=217 \times 3 = 21

    Add the carry-over 22, resulting in 2323.

    Write down 2323 as there are no more digits to multiply.

Combining both steps, we find the product of 7777 and 33 is:

77×  3231\begin{array}{c} & 77 \\ \times & \,\,3 \\ \hline & 231 \\ \end{array}

Therefore, the solution to the problem is 231231.

Answer:

231 231

Video Solution
Exercise #3

624x

Step-by-Step Solution

To solve this problem, we'll employ vertical multiplication.

Step 1: Set up the multiplication:
        62 62
×       4 4
      ---------

Step 2: Multiply each digit of 62 by 4. We start with the ones place, then the tens place.

  • Multiply the ones digit: 2×4=8 2 \times 4 = 8 .
  • Multiply the tens digit: 6×4=24 6 \times 4 = 24 .

Step 3: Consider the place value for each part of the calculation:
The result from multiplying the tens digit by 4 represents 240 240 because it is 24×10 24 \times 10 .

Step 4: Add the two partial results:
         8
+ 240
      ---------
      248

Therefore, the solution to the problem is 248 248 .

Answer:

248 248

Video Solution
Exercise #4

913x

Step-by-Step Solution

To solve this problem, we will multiply 91 91 by 3 3 using standard multiplication techniques:

  • Step 1: Multiply the unit digit of 91 91 by 3 3 :
    1×3=3 1 \times 3 = 3 .
  • Step 2: Multiply the tens digit of 91 91 by 3 3 :
    9×3=27 9 \times 3 = 27 .
  • Step 3: Place the result of 27 27 correctly one digit to the left (because it's actually 90×3 90 \times 3 ), which gives 270 270 .
  • Step 4: Add the results from Step 1 and Step 3:
    270+3=273 270 + 3 = 273 .

Therefore, the product of 91×3 91 \times 3 is 273 273 .

Answer:

273 273

Video Solution
Exercise #5

863x

Step-by-Step Solution

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

  • Step 1: Identify the given numbers: 8686 and 33.
  • Step 2: Perform the vertical multiplication of 8686 by 33.

Let's work through each step:

Step 1: We will multiply 8686 by 33. The multiplication can be broken down as follows:

  1. Multiply the units digit of 8686, which is 66, by 33:

6×3=186 \times 3 = 18

Write down 88 and carry over 11 to the next column (the tens place).

  1. Multiply the tens digit of 8686, which is 88, by 33:

8×3=248 \times 3 = 24

Add the carried over 11 to 2424:

24+1=2524 + 1 = 25

Write down 2525. Since we're only multiplying a two-digit number by a one-digit number, our result directly follows:

Therefore, the solution to the problem is 258 258 .

Answer:

258 258

Video Solution

Frequently Asked Questions

What is vertical multiplication and how does it work?

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Vertical multiplication is a method where numbers are aligned vertically (one above the other) to multiply multi-digit numbers systematically. You multiply each digit of the bottom number by each digit of the top number, starting from the rightmost digits, then add all partial products together.

How do you line up numbers for vertical multiplication?

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To line up numbers correctly: 1) Write the larger number on top, 2) Align the rightmost digits (ones place), 3) Ensure each digit is in its proper place value column, 4) Draw a line underneath the bottom number before starting multiplication.

What grade level learns vertical multiplication?

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Vertical multiplication is typically introduced in 3rd grade with 2-digit numbers and expanded in 4th-5th grade with 3-digit and 4-digit numbers. Students usually master this method by middle school for all multi-digit calculations.

Why is vertical multiplication better than other methods?

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Vertical multiplication offers several advantages: • Organizes work clearly and reduces errors • Handles large numbers efficiently • Builds understanding of place value • Provides a systematic approach that works for any size numbers • Easier to check work and identify mistakes

How do you handle zeros in vertical multiplication?

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When multiplying by zeros: If the top number has zeros, multiply normally (any number × 0 = 0). If the bottom number has zeros, skip that digit or write zeros as placeholders, then continue with the next digit position.

What are common mistakes in vertical multiplication?

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Common errors include: misaligning digits in wrong place value columns, forgetting to carry over when regrouping, adding partial products incorrectly, and not using proper placeholder zeros. Practice with grid paper helps avoid alignment issues.

How can I check if my vertical multiplication is correct?

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Verification methods include: 1) Estimate the answer first using rounding, 2) Use a calculator to verify, 3) Try the multiplication in reverse order, 4) Break down into smaller multiplication facts, 5) Use repeated addition for smaller numbers.

When should students use vertical multiplication vs mental math?

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Use vertical multiplication for: numbers with 3+ digits, when accuracy is crucial, complex word problems, and when mental math becomes too difficult. Use mental math for: simple 2-digit numbers, multiples of 10, and when speed is more important than showing work.

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