2-Digit Multiplication

2-digit multiplication or double-digit multiplication is done by arranging the numbers in a way such that the given numbers are placed one below the other. A 2-digit number can be multiplied with a single digit, with another 2-digit number, a 3-digit number, and so on. Let us learn more about 2-digit multiplication, the steps for multiplication, and solve a few examples to understand the concept better.

2-digit multiplication is the method of multiplying 2-digit numbers arranged in two place values, i.e., ones and tens. The method of multiplying numbers is the same as multiplying single digits. However, in double digits, we multiply each digit one by one by the multiplier. This means the multiplier is first multiplied with the ones digit of the multiplicand and then it is multiplied with the tens digit of the multiplicand. Let us learn about 2-digit by 1-digit multiplication and 2-digit by 2-digit multiplication in the following sections.

2-Digit by 1-Digit Multiplication

Multiplying 2-digit numbers with 1-digit numbers is quite simple. Let us understand this using the following steps and example.

Example: Multiply 23 × 2

• Step 1: Place the one-digit number below the 2-digit number. This makes the one-digit number the multiplier. Multiply the one-digit number (the multiplier) with the ones digit of the multiplicand. Here, 2 is the multiplier and the ones digit of the multiplicand is 3. So, 2 × 3 = 6. This partial product (6) will be placed under the ones column.
• Step 2: Now, multiply the multiplier with the tens digit of the multiplicand. Here, 2 is the multiplier and the tens digit of the multiplicand is 2. This means 2 × 2 = 4. This partial product (4) will be placed in the tens column. Therefore, 23 × 2 = 46

Now, let us learn how to multiply 2-digit numbers with 2-digit numbers.

2-digit by 2-digit multiplication means when both the numbers that are to be multiplied are of two digits. The multiplication starts with the ones place first and then moves on to the tens place. The numbers are placed one below the other. Although any of the two numbers can be placed on top or below, it is preferable to place the smaller number below because that makes multiplication easier. Let us understand this multiplication with the help of the following example. Let us multiply 34 × 12. In this case let us consider 34 to be the multiplicand and 12 as the multiplier.

• Step 1: Place the multiplicand (34) on top and the multiplier (12) below it as shown in the figure given above. Multiply the ones digit of the multiplier with the multiplicand. Here, 34 is the multiplicand and the ones digit of 12 is 2. This will give 34 × 2 = 68. This is the first partial product that will be placed in one line.
• Step 2: Multiply the multiplicand with the tens digit of the multiplier. Here, 34 is the multiplicand and the tens digit of the multiplier is 1. This will be 34 × 1 = 34. It should be noted that we need to place a zero below the ones digit of the partial product and then write the second partial product. (This 0 is placed here because we are actually multiplying 34 by 10 in this step). So we get 340 here.
• Step 3: Add both the partial products to get the final product. This will be 68 + 340 = 408.

Now, let us learn about 2-digit multiplication in which we have carry-overs.

2-digit multiplication with regrouping or carrying over happens when a number is carried forward. Let us understand this with the following example and steps. Let us multiply 45 × 6.

• Step 1: Multiply the multiplier with the ones digit of the multiplicand. Here, the multiplicand is 45 and the ones digit in 45 is 5, and the multiplier is 6. So, this will be 6 × 5 = 30.
• Step 2: Since the product obtained in step 1 is 30, we will carry over 3 to the preceding tens column and write 0 below the ones column as the partial product.
• Step 3: Now, we will multiply the multiplier with the tens digit of the multiplicand. Here, the tens digit of the multiplicand is 4 and the multiplier is 6. So, this will be 6 × 4 = 24. At this point, we need to add the number that was carried over in the previous step. This means 24 + 3 = 27. Therefore, the final product is 270.

2-digit multiplication with decimals is quite similar to the regular multiplication using a few rules of decimal numbers. Let us learn more about it in the following section.

2-Digit Multiplication With Decimals

2-digit multiplication with decimals is done in the same manner as the usual multiplication of double-digits keeping in mind the rules of decimal numbers. While multiplying such numbers we can ignore the decimal point until we have obtained the final result. Once the final result is obtained, we count the number of decimal places in both the numbers, add them and place the decimal point according to that. Let us understand this with an example and multiply 2.5 × 1.1

• Step 1: Arrange the numbers vertically according to the place value. Do not align the numbers based on the decimal point.
• Step 2: Multiply the ones digit of the multiplier with the multiplicand. Here, it is 25 × 1 = 25.
• Step 3: Place a zero below the ones digit of the partial product.
• Step 4: Multiply the tens digit of the multiplier with the multiplicand. This will be 25. Place this next to the 0 below the partial product.
• Step 5: Add the two products to get the final product. Here, 25 + 250 = 275.
• Step 6: Place the decimal point after 2 places from the right in the final product. Since the multiplicand and the multiplier have 1 decimal place each, this makes it 1 + 1 = 2 decimal places. Therefore, we place the decimal point after 2 places from the right and we get 2.5 × 1.1 = 2.75

☛ Related Topics

• 2-Digit Subtraction
• 2-Digit Addition
• 3-Digit Addition
• 3-Digit Subtraction
• 3-Digit Multiplication
• 4-Digit Addition
• 4-Digit Subtraction
• Multiplication and Division of Integers

What is 2-Digit Multiplication?

2-digit multiplication is a method of multiplying a 2-digit number with another number. The numbers are placed one below the other to perform multiplication. The number written on top is known as the multiplicand and the number written below is the multiplier. 2-digit numbers can be multiplied with 1-digit numbers, 2-digit numbers, and so on.

How to do 2-Digit Multiplication?

The following steps explain the process of 2-digit multiplication. For example, let us multiply 42 × 3

• Arrange the numbers one below the other such that the bigger number (42) is on top and the smaller one (3) is below it. So, 3 becomes the multiplier while 42 becomes the multiplicand.
• Start multiplying the multiplier with the ones digit of the multiplicand. Here, 3 will be multiplied with 2 which will give 3 × 2 = 6. This 6 will be written as the partial product.
• Then, multiply 3 with the tens digit of the multiplicand, that is 4, which will be 3 × 4 = 12. Now, writing both the products together, the final product will be 42 × 3 = 126

How to do Two-Digit Multiplication with Carrying?

Two-digit multiplication with carrying is done when the product of one column is more than 9. The extra digit is carried over to the next column and added to that particular product. For example, let us multiply 45 × 7.

• Place 45 on top and 7 below it so that 45 becomes the multiplicand and 5 becomes the multiplier.
• Multiply 7 with 5 and it will give 7 × 5 = 35. Since the product is a two-digit number 35, we will carry over 3 to the tens column and write 5 below the ones column as the partial product.
• Now, multiply the multiplier with the tens digit of the multiplicand. Here, the tens digit of the multiplicand is 4 and the multiplier is 7. So, this will be 7 × 4 = 28. At this point, we need to add the number that was carried over in the previous step. This means 28 + 3 = 31. Therefore, the final product is 315.

How to do 2-Digit by 1-Digit Multiplication?

2-digit by 1-digit multiplication is done in the same way as single-digit multiplication. For example, let us multiply 13 × 2.

• The double-digit (13) is written on top and the single digit (2) is written below, so 13 becomes the multiplicand and 2 becomes the multiplier.
• We start multiplying the bottom digit (multiplier) with the ones digit of the multiplicand. Here, we will multiply 2 with 3 which will be 2 × 3 = 6. We will note down this 6.
• Then we move on and multiply the bottom digit (multiplier) with the tens digit of the multiplicand. Here, 2 × 1 = 2. This will also be written along with with the product obtained in the previous step. So, this will give the product as, 13 × 2 = 26.

How to do 2-Digit by 2-Digit Multiplication?

2-digit by 2-digit multiplication is the process of multiplication where a 2-digit number is multiplied with another 2-digit number. For example, let us multiply 23 × 14.

• Place 23 on top and 14 below it so that 23 becomes the multiplicand and 14 becomes the multiplier.
• Multiply the ones digit of the multiplier with the multiplicand. Here, 23 is the multiplicand and the ones digit of 14 is 4. After multiplying 23 with 4 we get 23 × 4 = 92. This is the first partial product that will be placed in one line.
• Multiply the multiplicand with the tens digit of the multiplier. This means we will multiply 23 with 1 and it will be 23 × 1 = 23. It should be noted that we need to place a zero below the ones digit of the partial product and then write the second partial product next to it. (This 0 is placed here because we are actually multiplying 23 by 10 in this step.) So we get 230 here.
• Now we will add both the partial products to get the final product. This will be 92 + 230 = 322.
• Therefore, the final product is 23 × 14 = 322.

How to do 3-Digit by 2-Digit Multiplication?

3-digit by 2-digit multiplication means we multiply a 3-digit number with a 2-digit number. The rules that are followed for the multiplication of a 2-digit number with the other digit numbers apply to this multiplication as well. For example, let us multiply 243 × 45.

• We place the 3-digit number (243) on top and the 2-digit number (45) below it, so 243 becomes the multiplicand and 45 becomes the multiplier.
• Multiply the ones digit of the multiplier with the multiplicand. Here, 243 is the multiplicand and the ones digit of 45 is 5. After multiplying 243 with 5 we get 243 × 5 = 1215. This is the first partial product that will be placed in one line.
• Now, multiply the multiplicand with the tens digit of the multiplier. This means we will multiply 243 with 4 and it will be 243 × 4 = 972. We need to place a zero below the ones digit of the partial product and then write the second partial product next to it. So we get 9720 here.
• Now we will add both the partial products to get the final product. This will be 1215 + 9720 = 10935
• Therefore, the final product is 243 × 45 = 10935.