What does Decomposition of Numbers mean?
Decomposition of numbers means breaking down numbers into parts. The practice of decomposing numbers helps in developing number sense and understanding their place value. Decomposition also helps in understanding the different place values of different digits in a number.
What are Addends or Summands?
Addends are numbers or quantities that are added together. For example, 5 + 6 = 11. Here, 5 and 6 are the addends, while 11 is the sum. Addition problems can have more than two addends.
How is Addition done in the Decomposition method?
For basic mathematical operations such as addition, the decomposition method is done by breaking the numbers apart. The concept of place value is used for this method. For example, if we have to find the sum of 34 + 25 using the decomposition method, then this is how it should be done:
34 + 25 = ?
We break apart the second number, 25, using place value, into tens and ones. That will give us 20 + 5.
34 + 20 + 5 = ?
Now, we add the tens to the first addend, and then we add the ones.
34 + 20 = 54
54 + 5 = 59
So, 34 + 25 = 59
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Solved Examples
Example 1: Use place value to break apart an addend. Then find the sum for 71 + 11.
Solution: Let us first break apart the second addend into tens and ones.
After breaking the second addend, we get 1 ten and 1 one.
Now, first we add the tens to the first addend and then the ones.
So, the sum would be 82.
Example 2: Find: 32 + 47 = ?
Solution: First, break apart the second addend, 47, into tens and ones.
We get 4 tens and 7 ones after breaking the second addend. Now add the tens to the first addend. Then add the ones.
Hence, the answer is 79.
Example 3: There are 64 students in a class. 12 other students join in. How many students are there in total?
Solution: Here, the first addend is 64 and the second addend is 12. The addition equation is 64 + 12 = ?
Now, we will break apart the second addend, 12, into tens and ones. We get 1 ten and 2 ones.
Now, we add the first addend to the tens and then to the ones.
64 + 10 + 2
The sum will be 76.
Hence, the total number of students in a class is 76.
Example 4: Find: 28 + 61 = _____
Solution: As per the decomposition method, we will first break apart the second addend into tens and ones.
We get 6 tens and 1 one after breaking the second addend. Now add the tens to the first addend. Then add the ones.
28 + 60 + 1 = 89
That will give us 89 as the answer.
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It is important for kids to learn the decomposition method at a young age so that they find math problems and concepts easier . For example, by adding 8 + 7, a kid can easily decompose 7 into 5 and 2, and then add the 2 to the 8 to make it a 10 and then add 5 to it to arrive at the total of 15.
Decomposition of numbers by place value involves breaking down two, three and four-digit numbers according to their respective place values. This method is easier and helps in understanding what a number is made up of.