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Subtraction

 

Subtraction 

 

Subtraction is a fundamental arithmetic operation that involves finding the difference between two numbers. It is one of the four basic mathematical operations, the others being addition, multiplication, and division. Subtraction is often denoted by the “-” symbol.

In subtraction, you start with a minuend (the larger number) and subtract a subtrahend (the smaller number) from it to find the difference, also known as the result. The process can be visualized as “taking away” or “removing” a certain quantity from another.

Here’s an example:

Minuend: 10 Subtrahend: 4

Subtraction: 10 – 4 = 6

In this example, the minuend is 10, the subtrahend is 4, and the result (difference) is 6.

Subtraction can be performed using various methods, such as the traditional algorithm (borrowing and carrying over digits), number line representation, or mental math techniques. It is widely used in everyday life for various purposes, such as calculating change, measuring distances, and solving various mathematical and scientific problems.

 

 

Subtraction table

– 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
0 0                                      
1 1 0                                    
2 2 1 0                                  
3 3 2 1 0                                
4 4 3 2 1 0                              
5 5 4 3 2 1 0                            
6 6 5 4 3 2 1 0                          
7 7 6 5 4 3 2 1 0                        
8 8 7 6 5 4 3 2 1 0                      
9 9 8 7 6 5 4 3 2 1 0                    
10 10 9 8 7 6 5 4 3 2 1 0                  
11 11 10 9 8 7 6 5 4 3 2 1 0                
12 12 11 10 9 8 7 6 5 4 3 2 1 0              
13 13 12 11 10 9 8 7 6 5 4 3 2 1 0            
14 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0          
15 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0        
16 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0      
17 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0    
18 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0  
19 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

Subtraction table

1 Table 2 Table 3 Table 4 Table
2 – 1 = 1 3 – 2 = 1 4 – 3 = 1 5 – 4 = 1
3 – 1 = 2 4 – 2 = 2 5 – 3 = 2 6 – 4 = 2
4 – 1 = 3 5 – 2 = 3 6 – 3 = 3 7 – 4 = 3
5 – 1 = 4 6 – 2 = 4 7 – 3 = 4 8 – 4 = 4
6 – 1 = 5 7 – 2 = 5 8 – 3 = 5 9 – 4 = 5
7 – 1 = 6 8 – 2 = 6 9 – 3 = 6 10 – 4 = 6
8 – 1 = 7 9 – 2 = 7 10 – 3 = 7 11 – 4 = 7
9 – 1 = 8 10 – 2 = 8 11 – 3 = 8 12 – 4 = 8
10 – 1 = 9 11 – 2 = 9 12 – 3 = 9 13 – 4 = 9
11 – 1 = 10 12 – 2 = 10 13 – 3 = 10 14 – 4 = 10
12 – 1 = 11 13 – 2 = 11 14 – 3 = 11 15 – 4 = 11
13 – 1 = 12 14 – 2 = 12 15 – 3 = 12 16 – 4 = 12

Subtraction table

5 Table 6 Table 7 Table 8 Table
6 – 5 = 1 7 – 6 = 1 8 – 7 = 1 9 – 8 = 1
7 – 5 = 2 8 – 6 = 2 9 – 7 = 2 10 – 8 = 2
8 – 5 = 3 9 – 6 = 3 10 – 7 = 3 11 – 8 = 3
9 – 5 = 4 10 – 6 = 4 11 – 7 = 4 12 – 8 = 4
10 – 5 = 5 11 – 6 = 5 12 – 7 = 5 13 – 8 = 5
11 – 5 = 6 12 – 6 = 6 13 – 7 = 6 14 – 8 = 6
12 – 5 = 7 13 – 6 = 7 14 – 7 = 7 15 – 8 = 7
13 – 5 = 8 14 – 6 = 8 15 – 7 = 8 16 – 8 = 8
14 – 5 = 9 15 – 6 = 9 16 – 7 = 9 17 – 8 = 9
15 – 5 = 10 16 – 6 = 10 17 – 7 = 10 18 – 8 = 10
16 – 5 = 11 17 – 6 = 11 18 – 7 = 11 19 – 8 = 11
17 – 5 = 12 18 – 6 = 12 19 – 7 = 12 20 – 8 = 12

Subtraction table

9 Table 10 Table 11 Table 12 Table
10 – 9 = 1 11 – 10 = 1 12 – 11 = 1 13 – 12 = 1
11 – 9 = 2 12 – 10 = 2 13 – 11 = 2 14 – 12 = 2
12 – 9 = 3 13 – 10 = 3 14 – 11 = 3 15 – 12 = 3
13 – 9 = 4 14 – 10 = 4 15 – 11 = 4 16 – 12 = 4
14 – 9 = 5 15 – 10 = 5 16 – 11 = 5 17 – 12 = 5
15 – 9 = 6 16 – 10 = 6 17 – 11 = 6 18 – 12 = 6
16 – 9 = 7 17 – 10 = 7 18 – 11 = 7 19 – 12 = 7
17 – 9 = 8 18 – 10 = 8 19 – 11 = 8 20 – 12 = 8
18 – 9 = 9 19 – 10 = 9 20 – 11 = 9 21 – 12 = 9
19 – 9 = 10 20 – 10 = 10 21 – 11 = 10 22 – 12 = 10
20 – 9 = 11 21 – 10 = 11 22 – 11 = 11 23 – 12 = 11
21 – 9 = 12 22 – 10 = 12 23 – 11 = 12 24 – 12 = 12

 

Here are some examples of subtraction:

 

Basic Subtraction: Minuend: 15 Subtrahend: 7 Difference: 15 – 7 = 8

Calculating Change: You buy an item for $20 and pay with a $50 bill. Change = Amount Paid – Cost of Item Change = $50 – $20 = $30

Measuring Distances: You have two points on a number line: Point A at 25 and Point B at 12. Distance = Position of Point A – Position of Point B Distance = 25 – 12 = 13 units

Time Difference: If it’s currently 3:30 PM and an event starts at 5:45 PM. Time Difference = Event Time – Current Time Time Difference = 5:45 PM – 3:30 PM = 2 hours and 15 minutes

Removing Items: You have 28 candies, and you give away 14 of them. Remaining candies = Initial candies – Given away candies Remaining candies = 28 – 14 = 14 candies

Temperature Change: If the temperature drops from 78°F to 63°F. Temperature Change = Initial Temperature – Final Temperature Temperature Change = 78°F – 63°F = 15°F

Financial Transactions: Your bank account has $500, and you withdraw $100. Remaining balance = Initial balance – Withdrawal amount Remaining balance = $500 – $100 = $400

Data Analysis: You have a dataset with values: 42, 17, 28, and 9. The sum of values = 42 + 17 + 28 + 9 = 96 If you subtract the value 28 from the sum: New sum = 96 – 28 = 68

These examples demonstrate various scenarios in which subtraction is used to find differences or calculate changes between quantities. Subtraction is a versatile mathematical concept that applies to a wide range of everyday situations and academic disciplines.

Subtraction Properties

 Like addition, Subtraction has several important properties that help us manipulate and understand numbers. Here are some key subtraction properties:

Closure Property: Subtraction is closed under real numbers. When you subtract two real numbers, the result is also a real number.

Commutative Property: The order of subtraction doesn’t affect the result. In other words, for any real numbers a and b, a – b = b – a.

Associative Property: The grouping of numbers in a subtraction does not affect the result. For any real numbers a, b, and c, (a – b) – c = a – (b + c).

Identity Property: There is no direct identity element for subtraction. Unlike addition, there is no single number you can subtract from another number to get the original number.

Inverse Property: Every real number “a” has an additive inverse (also called a negative) -a, such that a + (-a) = 0. In subtraction, this property is used to convert subtraction into addition by adding the additive inverse of the subtrahend.

Addition and Subtraction Relationship: Subtraction can be seen as the inverse operation of addition. Adding a negative is equivalent to subtracting the positive. For example, a – b is the same as a + (-b).

Distributive Property: Subtraction distributes over addition. For any real numbers a, b, and c, a * (b – c) = a * b – a * c.

Subtraction with Zero: Subtracting zero from any number does not change the value of that number. a – 0 = a.

Subtraction by Itself: Subtracting a number by itself results in zero. a – a = 0.

These properties provide a foundation for performing mathematical operations involving subtraction, manipulating expressions, and understanding the behavior of numbers under subtraction. They are crucial for solving equations, simplifying expressions, and working with real-world problems that involve subtraction.

 

Here are some subtraction word problems along with their solutions:

Problem 1:

Samantha had 15 marbles. She gave away 8 marbles to her friend. How many marbles does Samantha have now?

Solution:

Initial marbles = 15

Marbles given away = 8

Remaining marbles = Initial marbles – Marbles given away,  Remaining marbles = 15 – 8 = 7

Samantha has 7 marbles now.

Problem 2:

A bakery had 68 cupcakes. During a sale, they sold 42 cupcakes. How many cupcakes are left?

Solution:

Initial cupcakes = 68

Cupcakes sold = 42

Cupcakes left = Initial cupcakes – Cupcakes sold,  Cupcakes left = 68 – 42 = 26

There are 26 cupcakes left.

Problem 3:

John has saved $350. He spent $125 on a new bicycle. How much money does John have left?

Solution:

Initial savings = $350

Money spent = $125

Money left = Initial savings – Money spent , Money left = $350 – $125 = $225

John has $225 left.

Problem 4:

A farmer harvested 256 apples from his orchard. After giving away 112 apples to his neighbors, how many apples does he have left?

Solution:

Initial apples = 256

Apples given away = 112

Apples left = Initial apples – Apples given away , Apples left = 256 – 112 = 144

The farmer has 144 apples left.

Problem 5:

A train traveled a distance of 580 kilometers. It stopped for maintenance after covering 273 kilometers. How much farther does the train need to travel to reach its destination?

Solution:

Total distance = 580 km

Distance covered before maintenance = 273 km

Distance remaining = Total distance – Distance covered,  Distance remaining = 580 km – 273 km = 307 km

The train needs to travel 307 kilometers more to reach its destination.

These word problems showcase real-life scenarios where subtraction is used to find differences or calculate remaining quantities. They require translating the given information into subtraction expressions and then solving for the desired result.

 

Subtraction Worksheet:

  1. 25 – 9 = 
  2. 76 – 42 = 
  3. 135 – 87 = 
  4. 308 – 165 = 
  5. 572 – 289 = 
  6. 423 – 189 = 
  7. 760 – 381 = 
  8. 943 – 525 = 
  9. 624 – 412 = 
  10. 879 – 754 = 

Answers:

  1. 16
  2. 34
  3. 48
  4. 143
  5. 283
  6. 234
  7. 379
  8. 418
  9. 212
  10. 125

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