Vertical Multiplication

🏆Practice cross multiplication

Vertical Multiplication

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.

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Vertical Multiplication

Vertical multiplication is a basic topic in mathematics that every student must know and be able to solve.
To solve vertical multiplication exercises, in a simple and practical way, you must master the multiplication tables and follow the rules meticulously.


First rule

Correct notation: Ones under ones, tens under tens, and hundreds under hundreds.

Observe the exercise 4×34=4\times 34=
To convert it into a vertical multiplication, we must write the numbers one under the other, ensuring that the ones are under the ones, the tens under the tens, and the hundreds under the hundreds.
Moreover, the longer number, the one that contains more digits, should be written at the top.

Solution:

First rule - image 1

Now we will multiply the ones digit 22 by the ones digit 44. We will write the result and continue.

multiplying the units digit - Vertical multiplication

Now we will multiply the ones digit 22 by the tens digit 33 and write the result as follows:

A3 - Vertical multiplication


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Second rule

When the result is greater than 99 it is stored at the top left and must be remembered to add it to the next result. In the result row, only the ones digit is noted.

Let's move on to a more complex exercise.
36×8=36\times 8=

Solution:
Let's write it in vertical form:

Second rule - Vertical multiplication

Let's multiply the ones digit 88
by the ones digit 66
We will get 4848
4848 is greater than 99.
Therefore, we will apply the second rule and note in the result row only the ones digit 88.
The 44 will be written at the top left and remembered to add it to the result of the next multiplication.
We store it above the 33.
Now let's multiply the ones digit 88 by the tens digit 33 and let's not forget to add 44 to the result.
3×8=243\times 8=24
24+4=2824+4=28
We will note 2828.

5 - Vertical multiplication


Third rule

Erase "the carried numbers" at the top left before moving on to multiply the next digit, this prevents confusion.


Do you know what the answer is?

Fourth rule

Add 00 below the result to indicate that you move to the next digit, each row of results starts one place to the left in relation to the previous row.

Now we will see the multiplication of a two-digit number by another two or three-digit number, so we can apply the third and fourth rules.
Observe the exercise:  358×38=358\times 38=
Solution:

Fourth rule - Vertical multiplication

Let's write it in vertical form according to rule 11.
Multiply the ones digit 88,
by each of the digits according to rule 22.

8×8=648\times 8=64
8×5=408\times 5=40
40+6=4640+6=46
8×3=248\times 3=24
24+4=2824+4=28
Now, according to rule 33 let's erase the "carried numbers" on the top left to avoid confusion.
Furthermore, according to rule 44 we will add 00 below the answer to indicate that we have moved to the next digit and we will start writing the row of results one step to the left from the previous row.

That is:

8 - Vertical multiplication

After erasing and moving one step to the left, we can move to the tens digit 33 and continue multiplying it with the ones, tens, and hundreds, just as we have done so far.
Notice that, the result will be written to the left of the 00 we added in the following way: 
Make sure to write the digits correctly, each digit below the corresponding one.

3×8=343\times 8=34
We will keep the 22 and continue.
3×5=153\times 5=15
15+2=1715+2=17
We will keep the 11 and continue.
3×3=93\times 3=9
9+1=109+1=10

9 - Vertical multiplication

At this point, all we have left to do is, add all the solutions obtained, in the same way we solve a common addition exercise in vertical form.

10 - Vertical multiplication

Attention: if it were a multiplication of a three-digit number by another three-digit number, when moving to the third digit, we should reserve another place with the 00. That is, 22 places and then the answer would be written 22 steps to the left.


Check your understanding

examples with solutions for cross multiplication

Exercise #1

Darío eats 3 cookies per minute.

How many cookies does Darío eat in an hour?

Video Solution

Step-by-Step Solution

Answer

180 180

Exercise #2

304x

Video Solution

Answer

120 120

Exercise #3

196x

Video Solution

Answer

114 114

Exercise #4

285x

Video Solution

Answer

140 140

Exercise #5

247x

Video Solution

Answer

168 168

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