How to Use Partial Products for Easier Multiplication
What does Partial Product Mean?
In Mathematics, partial products mean multiplying each digit of a number with each digit of another number where each digit maintains its place value. For example, the place value of 4 in 43 would be 40.
Partial products are generally used to multiply larger numbers. With this, you can split the given number into pieces to make the multiplication process easier. Then you add those pieces back together to get the product or result.
Look at the example to understand better.
Let’s try it with 3154.
3154=1003+101+15=300+10+5 (Expanded Form)
=3004+104+54=1200+40+20 Partial Products
= 1200 + 40 + 20 (Adding partial products)
= 1260 Product
Read the steps below to understand partial products in a better way.
How Partial Products are Used to Multiply One-Digit Number?
The steps given below show how partial products can be multiplied with one-digit number:
Let’s try it with 5264.
Step 1: First write 526 in expanded form.
To write 526 in expanded form, we will look at the value of each digit in 526.
Here,
The value of 5 in 526 is 5 hundreds, which is 5100=500.
The value of 2 in 526 is 2 tens, which is 210=20.
The value of 5 in 526 is 6 ones, which is 61=6.
Therefore, 526 in the expanded form will be
526 = 500 + 20 + 6.
Step 2: Multiply each of these expanded numbers with 4. This will give you partial products.
5004=2000
204=80
64=24
Step 3: Now, add the partial products. This will give you the final product.
2000 + 80 + 24 = 2104
Therefore, 5264=2104
How Partial Products are Used to Multiply Two-Digit Numbers?
The steps given below show how partial products can be multiplied with two-digit numbers:
Let’s try it with 5425.
Step 1: First write 54 and 25 in expanded form.
To write 54 in expanded form, we will look at the value of each digit in 54.
Here,
The value of 5 in 54 is 5 tens, which is 510=50.
The value of 4 in 54 is 4 ones, which is 41=4.
Therefore, 54 in the expanded form will be
54 = 50 + 4
Similarly, we will find the expanded form of 25.
The expanded form of 25=210+51
=20+5
Hence, the expanded form of 54 and 25 is:
54 = 50 + 4
25 = 20 + 5
Step 2: Now we are left with four numbers, i.e., 50, 4, 20, and 5. In this step, multiply each part of 54 by each part of 25 as shown below. This will give you partial products.
5020=1000
505=250
420=80
45=20
Step 3: Now, add the partial products. This will give you the final product.
1000 + 250 + 80 + 20 = 1350
Therefore, 5425=1350.
Similarly, you can use partial products to multiply three-digit numbers, four-digit numbers, and so on.
In short, a partial product is a three-step process of multiplying large numbers. It is a method that splits the factors in a multiplication problem down its parts on the basis of their place value enabling the readers to understand what exactly has been multiplied rather than following the step-by-step process as performed in standard logarithm.
FAQs on What Are Partial Products in Maths?
1. What are partial products in Maths?
In Maths, the partial products method is a strategy used to multiply numbers, especially multi-digit numbers. It involves breaking down numbers into their place values (e.g., 45 becomes 40 + 5), multiplying each of these parts separately, and then adding all the resulting 'partial' products together to get the final answer. This method makes multiplication easier to understand by focusing on the value of each digit.
2. How do you find the product of 58 x 6 using the partial products method? Provide an example.
To multiply 58 x 6 using the partial products method, you follow these steps:
- Step 1: Break down the number 58 into its expanded form based on place value: 50 (tens) + 8 (ones).
- Step 2: Multiply each part by 6 separately. These are your partial products.
- Multiply the tens: 50 × 6 = 300
- Multiply the ones: 8 × 6 = 48
- Step 3: Add the partial products together to find the final product.
- 300 + 48 = 348
3. How is the partial products method different from the standard multiplication method?
The main difference lies in how place value is handled. In the partial products method, you multiply the actual value of each digit (e.g., '5' in 58 is treated as 50) and write down each product separately before adding them. In the standard multiplication method, you multiply digit by digit from right to left and use 'carrying over' for values greater than 9. The partial products method makes the role of place value more visible, while the standard method is a more compact and faster shortcut.
4. What is the main benefit of learning the partial products method for a student?
The primary benefit is that it builds a strong and intuitive understanding of place value in multiplication. By breaking numbers apart and multiplying their true values, students can see exactly how each part contributes to the final answer. This method also forms a foundation for understanding the distributive property (e.g., 6 x (50 + 8) = (6 x 50) + (6 x 8)), which is a critical concept in algebra and higher mathematics as per the CBSE curriculum.
5. Can you use the partial products method to multiply two double-digit numbers, for instance, 34 x 25?
Yes, the method works perfectly for multiplying two double-digit numbers. It will result in four partial products.
- Step 1: Break down both numbers: 34 becomes 30 + 4, and 25 becomes 20 + 5.
- Step 2: Multiply each part of the first number by each part of the second number:
- 30 × 20 = 600
- 30 × 5 = 150
- 4 × 20 = 80
- 4 × 5 = 20
- Step 3: Add all four partial products: 600 + 150 + 80 + 20 = 850.
6. Why is it important to find each partial product before adding them up?
Finding each partial product separately is the core of the method. It ensures that you are systematically accounting for the multiplication of each place value component (ones, tens, hundreds, etc.) against the other number. This prevents errors and breaks a complex problem into simpler, manageable calculations. Adding them at the end is the final step that combines these individual parts to reconstruct the total product accurately.
