How to Add Numbers Easily with the Expanded Form Method
Ever wondered how a huge number can be broken down into small parts? This concept in mathematics is called the Expanded form. If you are unaware of this, you don’t need to worry. Because in this article, we will discuss everything about the expanded form and how we can add using expanded form. We will learn how to express the digits using addition in expanded form and expanded form sums from scratch, along with solved examples. Moreover, we will focus on how to add using the expanded form.
What is an Expanded Form?
Expanded form is a way to write a number by adding the value of its digits. Use a place value chart to get a clear idea about the value of a number's digits.
In an expanded form, a number is broken according to its place value and expanded to show the value of each digit. When we add using the expanded form, it makes it easy to understand, and by solving expanded form sums, we can develop a better understanding of it. For example, 943 can be written in expanded form, as given below.
The expanded form of 943 is given by 9 hundred 4 tens 3 ones.
expanded form: 900 + 40 + 3.
An Example of an Expanded Form
Place Value
Each number has a place value. The value of that digit is determined according to its position in the number. As we move from left to right, the value of a digit in a number increases. The place value of the digits on the left is lesser than those on the right.
By using the position of the number, the value for each number is computed. On starting from right to left, we can understand the notations used in the place value using an example.
Place Value of a Number
Thus, the expanded form of the number 254 is 200 + 50 + 4.
How to Find an Expanded Form?
Steps to write a number in the expanded form are given below.
Ones: $1 \times 4=4$
Tens: $7 \times 10=70$
Hundred: $3 \times 100=300$
Thousand: $8 \times 1000=8000$
$8000+300+70+4=8374$
Write the number in its most basic form.
Use the place value table to determine its place values.
Let the place value of the number be Multiplied by the number.
The number is multiplied by the number’s place value.
Display it as a digit place value.
Each digit should be represented as the product of the digit and its place value.
Expanded Form with Decimals
The extended form of a number with a decimal point or fraction is written with a base 10 denominator represented by a power of 10. For example, the number 3.482 in the expanded form is written as:
3.482 = 3 + 0.4 + 0.08 + 0.002.
How to Write in Expanded Form?
Suppose we want to expand 1.234. At first, we have one place, i.e. 1. Then, we have the first decimal place, the tenths. We take 2 and multiply it by a fraction $\dfrac{1}{10}$
$1+\left(2 \times \dfrac{1}{10}\right)$
Then, we have the hundredth place. Now move to a higher multiple of 10 for the denominator. In simple words, add another 0.
$1+\left(2 \times \dfrac{1}{10}\right)+\left(3 \times \dfrac{1}{100}\right)$
Finally, we have the thousandth place. Add another 0 in the denominator.
$1+\left(2 \times \dfrac{1}{10}\right)+\left(3 \times \dfrac{1}{100}\right)+\left(4 \times \dfrac{1}{1000}\right)$
Hence, the expanded form of $1.234$ is $1+0.2+0.03+0.004$.
Addition in Expanded Form
With the help of an example, we will learn about addition in expanded form.
1. Add 32 and 25
32= 30 + 2 (An expanded form of the number)
25= 20 + 5
Now, 32+25=30+2+20+5
= 50 + 7
= 57
The numbers are written in expanded form as 32 = 30 + 2 and 25 = 20 + 5.
Now digits of one’s place are added, i.e., 2 + 5 = 7.
Again numbers of ten’s place are added, i.e., 30 + 20 = 50
Total sum = 50 + 7 = 57
Thus the required total sum is 57.
Solved Expanded Form Sums
1. Add 361 and 527 by arranging the numbers in expanded form.
361 = 300 + 60 +1
527 = 500 + 20 +7
Sum = 800 + 80 + 8
= 888
Thus the required sum is 888.
2. Add using the expanded form: 231, 402, and 355
Adding ones = 1 + 2 + 5 = 8
Adding tens = 3 + 0 + 5 = 8
Adding hundred = 2 + 4 + 3 = 9
Therefore, the addition sum is 988.
Practice Questions
1. 31 + 42 =
Ans. 73
Q2. 43 + 44 =
Ans. 87
Q3. 23 + 25 =
Ans. 48
Summary
In this article, we learned that the expanded form is nothing more than a technique for rewriting a number by including the values of the digits. With the help of some solved expanded form sums, we tried to understand how numbers are arranged in the expanded form before adding.
By solving more and more expanded form sums, students can learn about expanded forms. We have also got some useful information about the expanded form. We have also learned about place value, its expanded form, how it is found, and the steps for addition in expanded form.
FAQs on Add Using Expanded Form: Explained for Students
1. What does it mean to write a number in expanded form?
Writing a number in expanded form means breaking it down into the sum of the place values of each of its digits. For example, the number 345 is made up of 3 hundreds, 4 tens, and 5 ones. So, its expanded form is 300 + 40 + 5. This method helps in understanding the value of each digit within a number.
2. How do you add two numbers using the expanded form method?
To add two numbers using the expanded form, you follow these steps:
- First, write both numbers in their expanded form based on place values (hundreds, tens, ones).
- Next, add the values for each place value category together (add all the hundreds, all the tens, and all the ones).
- Finally, add the sums of each place value to get the final answer.
3. Can you provide an example of adding 2-digit numbers using the expanded form?
Certainly. Let's add 27 + 41.
- Step 1: Expand both numbers.
27 = 20 + 7
41 = 40 + 1 - Step 2: Group and add the place values.
Add the tens: 20 + 40 = 60
Add the ones: 7 + 1 = 8 - Step 3: Add the results together.
60 + 8 = 68.
So, 27 + 41 = 68.
4. Why is learning to add with the expanded form useful?
Learning to add with the expanded form is very useful because it builds a strong foundation in understanding place value. Instead of just memorising a column-based addition method, this technique shows *why* that method works. It makes it easier to handle more complex maths concepts later, like regrouping (carrying over), and improves mental maths skills.
5. What is the difference between expanded form and expanded notation?
While similar, there is a key difference. The expanded form shows a number as the sum of its place values (e.g., 425 is 400 + 20 + 5). The expanded notation shows it as the sum of its digits multiplied by their place value (e.g., 425 is (4 × 100) + (2 × 10) + (5 × 1)). Expanded form is a simpler representation often taught first to build understanding.
6. How does the expanded form method work for addition with regrouping (carrying over)?
Yes, the expanded form method is excellent for understanding regrouping. For example, to add 48 + 35:
- Expand the numbers: (40 + 8) + (30 + 5).
- Add the tens: 40 + 30 = 70.
- Add the ones: 8 + 5 = 13.
- Here, 13 is regrouped into 10 + 3. You add this back: 70 + (10 + 3).
- The final sum is 70 + 10 + 3 = 83. This clearly shows how the 'carry over 1' is actually a '10' being moved to the tens place.
7. Can the expanded form method be used for subtraction?
Yes, the expanded form method can also be adapted for subtraction, where it is especially helpful for understanding the concept of borrowing or regrouping. You expand both numbers and then subtract the corresponding place values. For example, for 56 - 24, you would calculate (50 - 20) + (6 - 4), which equals 30 + 2 = 32. This makes the subtraction process more visual.
