2-Digit Multiplication

Two-digit multiplication is when you multiply a number that has two digits (like 12, 25, or 47) by another number. This other number can be a 1-digit number (like 4) or another 2-digit number (like 36).To make it easier, we align the numbers one below the other for easier multiplication. It’s just like regular multiplication, but with a little more work because there are more digits.

Multiplying 2-digit numbers with 1-digit numbers is a simple math operation. Let's learn more about this by using the following example:    

23 × 4 = ?

We can do this calculation by following these steps:

Multiply the ones place: 4 × 3 = 12

Write down the 2, and carry over the 1.

Multiply the tens place:

4 × 2 = 8, then add the carried-over

So, 23 × 4 = 92.

Here, two 2-digit numbers are multiplied. This process requires breaking the numbers down into tens and ones and performing multiplication step by step.

Let's learn this step by step with an example:

Example: Multiply 34 × 56 (two 2-digit numbers)

Write down the problem,

34 × 56

Distribute the numbers into place values; break down each number into tens and ones

34 = 30 + 4

56 = 50 + 6

Multiply the numbers that have been broken down

Step 1: multiply 30 by 50:

30 × 50 = 1500

Step 2: multiply 30 by 6:

30 × 6 = 180

Step 3: Multiply

4 × 50 = 200

4 × 6 = 24

Now add the results

1500 + 180 + 200 + 24 = 1904

So, 34 × 56 = 1904.

2-digit multiplication with regrouping, also called carrying or carrying over, is a procedure used when the intermediate results of multiplication exceed 9. This requires “regrouping” or “carrying” the tens to the next column. Sometimes, we use a method called long multiplication to help us multiply bigger numbers. In this method, we do the multiplication step by step, starting with the one's place and then moving to the tens. We make sure to add the numbers carefully, and if a number is too big, we carry over the extra to the next column, just like in addition.

Let's learn 2-digit multiplication with regrouping step by step:

Example: Multiply 35 by 6

Step 1: Write the numbers as you would in a column format for long multiplication:

 35
×  6
_____

Step 2:  Multiply the ones place of the first number by the second number

Start by multiplying the one digit of the first number (5) by the second number (6).

Multiply 5 × 6:

5 × 6 = 30  

Write down the 0 in the one's place of the result.

Carry over the 3 (the tens part) to the next column.

Step 3: Multiply the tens place of the first number by the second number

Next, multiply the tens’ digit of the first number (3) by the second number (6).

Multiply 3 × 6:

3 × 6 = 18 + 3 (carry over) = 21

Write down 21 since there are no hundreds of places to carry over.

Therefore, the final answer is 210.

When we multiply 2-digit numbers with decimals, we use the same steps as regular 2-digit multiplication. But there’s one extra step: after you multiply the numbers like usual, you need to put the decimal point in the right place in your answer. To do that, just count how many decimal places are in the numbers you started with, and then move the decimal point to that many places in your final answer. 

Let’s go through this process step-by-step.

Example: Multiply 24.5 by 3.6

Step 1: We need to ignore the decimal points and carry on with the multiplication process. The multiplication is done as if we are multiplying whole numbers, and the decimal point will be added in the final answer. 

So, 24.5 becomes 245 and 3.6 becomes 36

Now, we multiply 245 by 36 as if they were whole numbers.

Step 2: Perform the multiplication as if the numbers were whole numbers

 We’ll now follow the standard method of multiplying 245 by 36.

a. 6 × 5 = 30, write down 0, carry over 3.

b. 6 × 4 = 24, plus the carry-over 3:
   24 + 3 = 27, write down 7, carry over 2.

c. 6 × 2 = 12, plus the carry-over 2:
   12 + 2 = 14. This gives us 1470.

Step 3: Multiply the tens place of the second number by the first number

Now, multiply the tens digit of 36 (which is 3) by each digit of 245. Since we're multiplying by 30 (not just 3), we need to add a zero at the end of this row.

3 × 5 = 15
Write down 5, and carry over 1.

3 × 4 = 12, plus the carry-over 1:
12 + 1 = 13

Write down 3, carry over 1.

3 × 2 = 6, plus the carry-over 1:
 6 + 1 = 7

Write down 7. This gives us 7350

Now we must add 1470 and 7350

Therefore, 1470 + 7350 = 8820

Step 4: Add the results and place the decimal point

Now we need to determine the place value of the decimal point. For that, we must look at the decimals that we multiplied. Here, we multiplied 24.5 by 3.6. In these two decimal numbers, the decimal point is placed two places from the right. So, if we count the total number of decimal places, we get 2. Therefore, in the answer 8820, we should add two decimal places.

The final result after adding the decimal point is 88.20

When shopping, you might buy several items that cost two-digit amounts, and you need to multiply to find the total cost. It’s also useful in planning events, calculating travel distances, or figuring out pay over several days or weeks. Here are some real-life applications of 2-digit multiplication:

 1. Shopping

When we buy many items that cost the same, we multiply the number of items by the price of one item to find the total cost.
For example, if one notebook costs ₹25, and we buy 12, we do 25 × 12 to find the total amount to pay.

2. Party Planning

If we are giving the same number of gifts or snacks to each person at a party, we can use multiplication to find out how many we need in total.
For example, if there are 20 guests and each one gets 3 chocolates, we do 20 times 3 to find out we need 60 chocolates for everyone.

 3. School and Classroom

Teachers use multiplication to find out how many supplies are needed for all students.
If each student requires 2 pencils and there are 30 students, we multiply 30 × 2 = 60 pencils.

4. Home and Construction

We use multiplication when measuring space. To find out how much carpet or how many tiles we require for a room, we multiply the length by the width of the room.
For example, if a room is 12 feet wide and 15 feet long, we multiply 12 × 15 to get the total area in square feet.

5. Packing and Organizing

When packing boxes, we multiply the number of boxes by how many items go in each box to find the total number of items.
If there are 24 boxes with 20 books in each, we do 24 × 20 = 480 books to know how many books there are altogether.