What is meant by Place Value in math?
Place value is an important foundation of the number system. Under this system, the position of a digit in a particular number determines its value. Ten ones create one of the next larger units – tens. Ten of tens create one of the next larger units – hundreds. This pattern continues for greater values as well.
What is a Place Value Chart?
A place value chart ensures that the digits are in their proper places. It helps with comparing numbers, addition, and subtraction.
How can we use Place Value for Addition?
Place value is ideal for lessons in addition to second graders as it provides the basis for regrouping, multi-digit addition, and understanding other base systems.
For example, if we have to add 46 and 25, we will do it in the following steps:
46 \({\longrightarrow}\) 40 + 6
+ 25 \({\longrightarrow}\) 20 + 5
First, we use place value to break the addends into tens and ones.
Tens | Ones | |
|---|---|---|
40 | + | 6 |
20 | + | 5 |
Now, we add the tens and ones individually to find the whole sum.
Tens | Ones | |
|---|---|---|
40 | + | 6 |
20 | + | 5 |
60 | + | 11 |
Finally, on adding 60 and 11, we get 71 as the answer.
What is an Addition Equation?
An addition equation is an equation where two or more addends are added together to get the sum. For example, 5 + 2 is an addition equation.
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Solved Examples
- Using place value, find the sum of the following numbers: 34 and 52.
Solution: First, we will use place value to break apart the addends into tens and ones. That will give us,
Tens | Ones | |
|---|---|---|
30 | + | 4 |
50 | + | 2 |
Now, add the tens and add the ones separately.
Tens | Ones | |
|---|---|---|
30 | + | 4 |
50 | + | 2 |
80 | + | 6 |
Finally, on adding the tens and ones together, we get 80 + 6 = 86 as the answer.
2. You have 72 blocks to build a toy house. Your friend uses 15 blocks in the same toy house. How many blocks were used in total?
Solution:
In this word problem, let us first find the addition equation. As per the question, the addition equation is 72 + 15. As we learned before, we have to use place value to break apart the addends and then find the sum.
70 + 2
10 + 5
Now that the tens and ones are separated, adding them individually will give us 80 + 7.
The required sum is 87.
Hence, the answer is 87 blocks.
3. Find the sum of 22 and 36.
Solution: First, we will break up the addends and write them in place value columns.
Tens | Ones | |
|---|---|---|
20 | + | 2 |
30 | + | 6 |
Then, we will individually add the tens and ones.
Tens | Ones | |
|---|---|---|
20 | + | 2 |
30 | + | 6 |
50 | + | 8 |
The sum will be 50 + 8 = 58.
Hence, the answer is 58.
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Place value is given by the value of each digit that appears in a particular number. For example, in the number 372, 3 is 300 (hundreds), 7 is 70 (tens) and 2 is 2 (units or ones).