What are place values ?
The place value of any digit in a given number is the value of that individual digit in the given number.
Example:
Let’s consider a 3-digit number, 241.
The digit “1” is at the ones place and its place value is, 1 × 1 = 1
The number “4″ is at the tens place and its place value is, 4 × 10 = 40
Finally, the number “2″ is at the hundreds place and its value is 2 × 100 = 200.
What is regrouping ?
In math, regrouping is the process of making groups of tens when carrying out addition and subtraction operations on numbers that have multiple digits.
For instance, regrouping in subtraction of 3 digit numbers is the process of exchanging 1 ten with 10 ones, or 1 hundred with 10 tens.
It is generally used when the minuend is smaller than subtrahend.
For example: 123 – 116
In the above diagram, we can see that in the one’s place, 3 is smaller than 6, so we borrow 1 ten from the ten’s place and bring it to the one’s place. We will then have 1 + 10 = 13 ones, so 13 – 6 = 7
Similarly, in the tens place 2 ten becomes 1 ten as 1 ten has been borrowed from it.
So 1 – 1 = 0 tens.
In the hundred’s place 1 – 1 = 0 hundreds.
Hence the difference is 7.
What is an open number line?
An open number line is a straight line with no numbers marked on it.
To solve a problem,numbers can be marked on an open number line and the operation can be carried out.
It helps in simplifying some mathematical calculations.
What is compensation ?
Compensation is a method of adding or taking away numbers, which will make the mathematical problems easily solvable.
It is basically a method in which if some numbers are taken away we compensate that number in later steps by adding the same number.
Similarly, if some numbers are added then we compensate for the same number by taking away the added number later on.
For example:
11 + 119
= (10 + 1) + 119 (11 can be written as 10 + 1)
= 10 + (1 + 119)
= 10 + 120
= 130
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Solved 3 Digit Subtraction Method Examples:
Example 1:
Using models subtract
(i) 112 – 10 = ___________
(ii) 112 – 100 = ________
Solution:
(i)
We know that 112 has 1 hundred, 1 ten and 2 ones and we need to subtract 1 ten from 112, let’s use models to represent this: in the above diagram, 112 is shown with a cubic block of 100 blocks representing 1 hundred, 1 block of vertical blocks consisting of 10 cubes representing 1 ten and 2 cubes representing 2 ones.
To subtract 10 from 112 using models we need to remove 1 group of ten blocks from 112.Upon carrying out the subtraction, one of the tens get canceled leaving 1 hundred cubic block and 2 single blocks as the difference which is 102.
(ii)
We know that 112 has 1 hundred, 1 ten and 2 ones and we need to subtract 1 hundred from 112, let’s use models to represent this: in the above diagram, 112 is shown with a cubic block of 100 blocks representing 1 hundred, 1 block of vertical blocks consisting of 10 cubes representing 1 ten and 2 cubes representing 2 ones.
To subtract 100 from 112 using models we need to remove 1 group of hundreds blocks from 112.Upon carrying out the subtraction, one of the hundreds gets canceled leaving 1 ten vertical cubic block and 2 single blocks as the difference which is 12.
Example 2:
Solve the following problem using an open number line.
(i) 122 – 10
(ii) 122 – 100
Solution:
122 – 10 = 112
To subtract 10 from 122, we first mark 122 on an open number line then we count back by 1 ten and we reach 112.
And,
122 – 100 = 22
To subtract 100 from 122, we first mark 122 on an open number line then we count back by 1 hundred and we reach 22.
Example 3:
Solve the following problem using an open number line.
251 – 130 =__________?
Solution:
In the above model, first of all we marked 251 (the minuend) on an open number line.
130 is 1 hundred and 3 tens
Then from 251 we count back by 130, so we first count back by 1 hundred at 151, then from 151 we count back 3 tens or 30 to reach 121.
251 – 100 = 151 (Count back 100 from 251)
151 – 10 = 141 (Count back 10 from 151)
141 – 10 = 131 (Count back 10 from 141)
131 – 10 = 121 (Count back 10 from 131)
Hence the required difference is 121.
Example 4:
Subtract 28 from 153 using compensation.
Solution:
153 – 28
= 153 – (28 + 2) (We change 28 to 30 which is a compatible number so the subtraction becomes easier)
= 153 – 30
= 123
As we have added 2 to the subtrahend we need to add 2 to the difference to get the final answer
= 123 + 2
= 125
Example 5:
Use model to solve 318 – 121
Solution:
In the model shown below,
318 is 3 hundreds, 1 tens and 8 ones.
It is represented as 3 squares in the hundreds column, 1 bar in the tens column and 8 dots in the ones column.
318 – 121
To subtract 1 from 8 we need to remove 1 dot at one’s place.
8 – 1 = 7 ones (7 dots at one’s column)
To subtract 2 tens from 1 tens we borrow 1 hundred from hundreds place. Since 1 hundred is 10 tens, now we have 10 + 1 = 11 tens
11 – 2 = 9 tens
In the resulting model, in the tens column 9 bars are left after removing 2 bars from 11 bars.
At the hundreds place 3 becomes 2 as we had borrowed 1 hundred from it earlier.
2 – 1 = 1 hundred
In the model, 1 square is left after subtraction.
Hence the difference is 197.
Example 6:
A vendor has 218 sunglasses and 321 handkerchiefs. If he sells 112 sunglasses, how many sunglasses and handkerchieves are left?
Solution:
Since the vendor has only sold sunglasses, the number of handkerchiefs remains the same, which is 321.
Number of sunglasses: 218 – 112 = 106
106 Sunglasses are left.
Example 7:
Solve the following subtraction problem.
200
-106
________
Solution:
Since the digit at one’s place is 0 < 6, borrow a tens from the digit just left of it but it is also 0. So we Borrow a hundred from the digit to its left.
As 1 hundred is borrowed from digit at 100’s place to the digit at tens place which was initially 0 but now becomes 10 tens. For the ones place, we borrow a ten from the ten’s place. Therefore the digit at one’s place becomes 10 and the digit at tens place becomes 9.
Now the subtraction can be carried as:
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1. Using an open number line
2. Using models
3. Using compensation
4. Using regrouping
Regrouping is used in subtraction when the minuend is smaller than the subtrahend.
0 is the number if subtracted from any number gives the number itself as the difference.