What is Subtraction?
Subtraction is one of the four basic arithmetic operations in mathematics. We can see subtraction in our daily lives also.
When we buy chocolates and pencils for $50 and we hand over a $100 bill to the shopkeeper, we get back $50. This is one example of subtraction.
As another example,, is when you give the shopkeeper $60 and you get back $10.. The shopkeeper has subtracted $50 from $60 and hands you $10.
In subtraction problems, a minus (-) symbol is used.
A subtraction problem includes the minuend, subtrahend, and the difference, which is the result of subtracting one number from the other.
What are Multi-Digit Numbers?
Any given number that has more than one digit is called a multi-digit number.
Example: 234, 56754
Subtracting Multi-Digit Numbers Using Place Value
Place value: The value of each digit in a number is called place value.
Example: The 7 in 4780 represents seven hundreds or 700.
Place Value
Every digit in a number has a place value in mathematics.
The value represented by a digit in a number based on its position in the number is known as place value. Here’s an example of the relationship between the place or position of the digits in a number and their place value.
The Method of Regrouping
What is “regrouping” in math?
Regrouping in math can be defined as the process of grouping numbers in tens while performing mathematical operations, such as addition and subtraction.
What is subtraction with regrouping?
The process of subtraction with regrouping is subtracting each place value individually, and eventually reaching the highest place. Regrouping is ideal for subtracting smaller numbers from larger numbers.
For example, while subtracting 78 from 96, we can apply the regrouping of places method.
First, write the equation in the column form, or vertical form.
As we can see 6 is less than 8, here we need to regroup(also called borrowing), so one tens will regroup with 6 to get 16.
Steps to Subtract Multi-Digit Numbers
Step 1: Firstly, arrange the numbers using place value.
Step 2: Start subtracting from right to left i.e., the ones, then the tens, then the hundreds and so on.
Example: Calculate the following: 78,935 – 4,589.
Line up the numbers using place value.
This can be written as:
Subtract ones, 5 – 9 is not possible, so we will regroup tens with 5 to get 15.
Now, subtracting tens, 2 is less than 8, So regroup 2 with hundreds to get 12.
Subtracting hundreds, thousands and ten thousand.
How do we Check the Result of Subtraction Problems
As we know that addition and subtraction are opposite operations. We subtract the subtrahend from the minuend and as a result we will get a difference.
By adding the difference and the subtrahend we will get the minuend.
Example: Calculate the difference between 7575 and 0342. Check the difference that is obtained.
Answer:
From the above equation, minuend = 7575, subtrahend = 342 and difference = 7233.
To check the difference, we add the subtrahend and the difference.
Here we will get, 7233 + 0342 = 7575.
Hence, minuend = difference + subtrahend.
Solved Examples
Example 1: Jessica wrote 1452 pages on Thursday, Friday and Saturday. She wrote 339 pages on Friday and Saturday. How many pages did Jessica write on Thursday?
Answer:
The total number of pages Jessica wrote = 1452
The number of pages she wrote on Friday and Saturday = 339
The number of pages she wrote on Thursday = Total numbers of pages that is written on Thursday, Friday and Saturday-The number of pages she wrote on Friday and Saturday
= 1452 – 339
First, write the equation in column form.
Subtract the numbers in the ones place, 2 – 9 is not possible, so regroup 5 tens with 2 ones.
Now, subtracting the tens, then the hundreds and so on.
Jessica wrote 1,113 pages on Thursday.
Example 2: Find the result of 4,632 – 4,539.
Answer:
Line up the numbers using place value.
Subtract the numbers in the ones place, 2 – 9 is not possible, so we will regroup 3 tens with 2 ones.
Now, subtracting tens, 2 is less than 3, regroup 2 tens with 6 hundreds.
Subtracting the hundreds and the thousands.
Example 3: Calculate the result of 7,801 – 539.
Answer:
Example 4: The cell phone was invented in the year 1973 and the flip phone was invented in the year 1989. How long did it take to invent the flip phone?
Answer:
The cell phone invented in the year = 1973
Flip phone was invented in the year = 1989
Time taken to invent the flip phone = year the flip phone was invented – year the cell phone was invented
= 1989 – 1973
= 16
Hence, the flip phone took 16 years to to be invented after the cell phone was invented.
Place value plays an important role for subtraction because we subtract ones from ones, tens from tens, and so on.
Addition and subtraction are called inverse operations. This is because one operation can undo the other. We can consider the opposite of 9 minus 2 leaving 7. Now, by adding 2 and 7 we get 9, which is why addition and subtraction are inverse operations.