Subtraction is defined as the process of the inverse of addition. In other words, it is also defined as removing one number from the other to get a difference. The greater number from which the lesser number is subtracted is known as minuend and the number that is subtracted from the minuend is known as subtrahend and the result of the subtraction is known as difference.
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Representation of Subtraction
Subtraction is written by using a mathematical operator minus “ – “, which is used to subtract and the equal symbol is notated as “ = “ gives the difference.
Example: 9 – 5 = 4
Nine minus five equals four, where 9 and 5 are known as minuend and subtrahend.
Properties of Subtraction of Whole Numbers
Property 1: Closure Property
Closure property states that when one whole number is subtracted from the other, the difference is not always a whole number.
Let us consider a and b are two whole numbers and a – b = c, then c is not a whole number.
Example : let a = 7, b = 2 and 7 – 2 = 5, it is a whole number
2 -7 = -5, it is not a whole number.
Property 2: Commutative Property
The commutative property states that the order of subtraction will change the value of the difference.
This means the subtraction of two whole numbers is not commutative.
Let us consider a and b are two whole numbers then a − b ≠b – a.
Example : let a = 7 , b = 5
7 – 5 = 2 ≠5 – 7 = -2
Property 3: Associative Property
The associative property states that we cannot group two whole numbers and subtract them first. The order of subtraction is an important factor.
Let us consider a, b and c are three whole numbers then a − (b − c) ≠(a − b) – c.
Example : let a = 8, b= 6 and c = 4
8 – (6 – 4) = 6 ≠(8 – 6) – 4 = -2
Property 4: Subtractive Property of Zero
This property states that when we subtract zero from any whole number, the value of the whole number remains the same. Let us consider w as a whole number, w – 0 = w.
Example : let w = 8
8 – 0 = 8, it is a whole number
How do you Subtract Whole Numbers?
Follow the simple and easy steps listed below for Subtracting Whole Numbers and they are along the lines
- Write the numbers in vertical columns
- Subtract the digits in each place value starting from right to left, if the digit on top is less than the digit below, borrow as needed.
- Continue subtracting each place value from right to left, borrow if needed.
- Check by adding.
Examples on Subtraction of Whole Numbers
Example 1:
Subtract 78 – 56?
Solution:
Step 1: Write the given numbers in vertical columns and subtract values in one’s place.
i.e 8 – 6 = 2
Step 2: Subtract the numbers in the tens place
i.e 7 – 5 = 2
Therefore the difference is 22.
Example 2:
Subtract 385 – 250.
Solution:
Step 1: Write the given numbers in vertical columns and subtract values in ones place.
i.e 5 – 0 = 5
Step 2: Subtract the values in the tens place
8 – 5 = 3
Step 3: Subtract the values in the hundreds place
3 – 2 = 1
Therefore the difference is 135.
Example 3:
Subtract 1148 – 978.
Solution:
Step 1: Write the values in vertical columns and subtract the values in ones place.
i.e 8 – 8 = 0
Step 2: Subtract the values in the tens place. We cannot subtract 7 from 4, so we borrow 1 hundred. This makes 14 tens and 0 hundred.
i.e 14 – 7 = 7
Step 3: Now, Subtract the values in the hundreds place
i.e 10 – 9 = 1
Therefore, the difference is 170.
Example 4:
Dany has 1245 beads. Out of them 650 are red and the rest of them are blue. How many blue beads does he have?
Solution:
Given
Total number of beads = 1245
Number of red beads = 650
Number of blue beads = total number of beads – number of red beads
= 1245 – 650
= 595 beads
Therefore, the number of blue beads dany have are 595 beads
Example 5:
There are 280 students in a class. Out of them 146 are boys and how many of them are girls in a class?
Solution:
Given
Total number of students = 280
Number of boys = 146
Number of girls = total number of students – number of boys
= 280 – 146
=134
Therefore the number of girls = 134
Example 6:
Veronica has 65 shirts and Diana has 42 shirts. How many fewer shirts does Diana have than veronica?
Solution:
Number of shirts with veronica = 65
Number of shirts with Diana = 42
Number of shirts that Diana less than veronica = Number of shirts with veronica- Number of shirts with Diana
= 65 – 42
= 23
Example 7:
The sum of the two numbers is 1067. If one number is 650, find the other number?
Solution:
Sum of two numbers = 1067
One of the number = 650
Second number = 1067 – 650
= 417
Therefore, the other number is 417.