Subtraction

Subtraction is second fundamental operation in mathematics. It uses is minus sign (-) The or subtraction is derived from the Latin word ‘subtract here’ which is a compound word comprising ‘sub’ and ‘tra here’ ‘sub’ means ‘under’ and ‘tra here’ means ‘to full down’ or ‘ to take away’. 

           Of methods will be I will be discussing in this chapter first let me begin with the Austrian  Method.

Austrian Method of subtraction

The basic problem with subtraction is borrowing. In borrowing we need to regroup the by decreasing the preceding digit by 1, and the overall look of a subtract problem appears somewhat to be like.

I give a detailed description about some interesting method of subtract. I hope you enjoy learn very fast.

The Austrian method is neat ad easy to understand. How does it work? The basic difference between the general method of subtract being taught in and Austrian method is that here, instead of decreasing the digit in the next place on the top by 1, we increase the digit in the next place on the bottom by 1.

Subtraction  247 from 561

Solution :- 561-247

=  500+60+1-( 200+40+7 )                              = ( 500+60+10+1 ) – ( 200+40+10+7) {10 is added  in both groups }

= ( 500+60+11) – ( 200+50+7)

= ( 500-200) + (60-50)+(11-7)

= 300+10+4

= 314  

Lets Take one more example.

 Subtraction 1874 from 4003

Solution:-   4003- 1874

= ( 4000+3) – ( 1000+800+70+4) 

= ( 4000+1000+100+10+3) –                           (1000+1000+800+100+70+10+4)

= ( 4000+1000+100+13) -( 2000+900+80+4)

= ( 4000-2000)+(1000-900)+(100-80)+(13-4)

= 2000+100+20+9

= 2129

As you can see, subtract in the above example has done smoothly by adding a number of choice on both sides. While actually engaging in the process of subtracting, you need not write out so many steps as explained above; this is only for the purpose of understanding. Lets see the working of Austrian Method in short.

Subtraction is one of the fundamental arithmetic operations in mathematics. It involves finding the difference between two numbers or quantities. The result of a subtraction operation is called the “difference.”

The subtract operation is denoted by the “-” symbol or by writing the numbers with a minus sign between them. For example:

1. Using the “-” symbol: 10 – 5 = 5
2. Using a minus sign: 10 – 5 = 5

In the above examples, we are subtracting 5 from 10, which results in the difference of 5.

Subtract can be visualized as “taking away” or “removing” a certain quantity from another. For example:

10 – 5 = 5

This can be interpreted as starting with ten items and then removing five of them, leaving us with five items.

Here are some more examples of subtract:

8 – 3 = 5 15 – 7 = 8 20 – 10 = 10

Subtract is not commutative, which means changing the order of the numbers will affect the result:

10 – 5 = 5 5 – 10 = -5

In the second example, subtracting 10 from 5 results in a negative difference, indicating that we have to move in the opposite direction on the number line.

Subtract has various applications in everyday life, such as calculating change during transactions, determining time intervals, solving word problems, and finding differences in measurements. It is also an essential component of more advanced mathematical concepts like algebra and calculus.

To perform subtract, one must understand the concept of negative numbers, as it is possible to subtract a larger number from a smaller number, resulting in a negative difference. Understanding subtraction lays the groundwork for more complex mathematical operations and is a crucial skill for problem-solving and critical thinking. Moreover, subtraction is used extensively in disciplines such as physics, economics, engineering, and computer programming to analyze data, make comparisons, and identify trends or patterns. Mastery of subtraction is essential for building a solid mathematical foundation and is a key skill in a wide range of practical applications throughout life.