Use of Place Value to Divide
Division is an arithmetic operation with which we can distribute a group of objects into equal parts. It is mostly denoted by the symbol “÷”. There are two ways to represent a division equation.
Division equations can be written or represented in a sentence form or in a long division format as shown.
Any division equation will have three main parts – a dividend, a divisor and the quotient.
The dividend is the larger number that is divided into equal parts.
The divisor is the number of groups that divides the dividend. The quotient is the answer after the division is done.
There are a number of methods to perform division operations. One of such methods includes the use of place value. Here we will discuss this method in detail along with solved examples.
What is the Place Value of a Number?
The place value of a number is the value of a digit in a number as per its position in the number.
Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
3 | 7 | 1 |
In the above example, we have used the number 371, and placed it in the place value chart to observe the place value of its digits.
If we begin from the right of the place value chart, the digit 1 is placed in the ones place, the digit 7 is placed in the tens place, and the digit 3 is in the hundreds place.
Hence, the place value of the digits 3, 7 and 1 are hundreds, tens and ones respectively.
The concept of place value of the digits in a number can be used to solve division problems.
How to Use Place Value for Division?
Using place value along with division facts in a division equation, helps in dividing larger numbers easily. Place value counters and tape diagrams are often used to represent division using place value.
In the below examples, we will see the method to divide tens, hundreds, and thousands, using place value and division facts.
In the first equation, the digits are 4 and 2. We can write it as 4 ones ÷ 2 ones = 2 ones (using the division fact).
Now we will use the same digits to divide, but for tens.
For the second equation, the digits are the same, but a zero has been added after 4, and the quotient thus has one zero at the end. So, we can write it as 4 tens ÷ 2 ones = 2 tens (using place value and the division fact).
Similarly, for the third division equation, the same digits are present, but the number of zeros has increased. We are dividing 4 hundreds ÷ 2 ones = 2 hundreds (using place value and the division fact).
While dividing thousands, here is how the division looks like. 4 thousands ÷ 2 ones = 2 thousands (using place value and the division fact).
There is a pattern as you can see from the above examples – every time the dividend is multiplied by 10, the quotient is multiplied by 10 as well.
Solved Examples Using Place Value to Divide
Example 1: Find 3400 ÷ 2.
Answer: Here, we can consider 3400 as 34 x 100. So, we can take it to be, 34 ÷ 2 = 17 (division fact)
Hence, 3400 ÷ 2 = 34 hundreds ÷ 2 (using place value)
= 17 hundreds (divide)
= 1700
So, 3400 ÷ 2 = 1700
Example 2: Find the quotient of 390 ÷ 3.
Answer: Let us consider 39 ÷ 3, which will give us 13.
Now, have a look at the tape diagram to understand the division method using place value.
<——————39——————>
So, 39 ÷ 3 = 13 (division fact)
390 ÷ 3 = 13 tens ÷ 3 (using place value)
= 13 tens (divide)
= 130
<—————–390——————>
The quotient of 390 ÷ 3 is 130.
Example 3: There are 660 books in a library that needs to be stacked on shelves. Each shelf can hold 3 books. How many shelves are needed to hold all the books?
Answer: We will divide 660 by 3 to find the number of shelves.
Let us draw a model to understand the problem.
<——————660-—————->
The ? represents the number of shelves needed to hold the books.
As we know, 66 ÷ 3 = 22 (division fact)
Now, 660 ÷ 3 = 22 tens ÷ 3 (using place value)
= 220 (divide)
Thus, 220 shelves are needed for 660 books to be stacked.
Example 4: Find the missing number: 200 ÷ ____ = 50
Answer: Here, the dividend is 200 and the quotient is 50. We have to find the divisor.
Just as we use addition to check for subtraction, we can use multiplication to check the division. To find the divisor, we can confirm the result by multiplying the divisor with the quotient.
We know,
5 x 4 = 20
So, 5 tens x 4 = 20 tens
That is, 50 x 4 = 200
Hence, 200 ÷ 4 = 50
Hence, the missing number is 4.
Example 5: Find the quotient in this equation: 6300 ÷ 7
Answer: Let us consider 6300 as 63 x 100. We can think of it as 63 ÷ 7, which will give us 9 (division fact).
So, 6300 ÷ 7 = 63 hundreds ÷ 7 (using place value)
= 9 hundreds (divide)
= 900
Thus, 6300 ÷ 7 has a quotient of 900.
Example 6: 260 students are visiting a science fair. The students are divided into groups of 2 students each to explore the fair. How many groups are created?
Answer: To find the number of groups, we have to divide 260 by 2. We can write it as 26 ÷ 2.
So, 26 ÷ 2 = 13 (division fact)
260 ÷ 2 = 26 tens ÷ 2 (using place value)
= 13 tens (divide)
= 130
Thus, there were 130 groups of children in the science fair.
For division using the partial quotient method, we break the dividend into smaller parts to make the division simple. These smaller parts are multiples of the divisor, and are subtracted from the dividend until the remainder is less than the divisor. The factors that are multiplied by the divisor are known as the partial quotients. These partial quotients are then added to get the final quotient.
Multiplication and division are inversely related. Division is the inverse operation of multiplication.
For example, if we have a multiplication equation 4 x 5 = 20, then, its inverse relation in the form of division will be 20 ÷ 5 = 4 or 20 ÷ 4 = 5. As you can see, for both the operations, the same set of numbers are being used.
When we multiply two numbers, we get a product, and when we divide the same product by one of the factors, we get the other factor as the answer.