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Subtraction of natural numbers

subtraction

Subtraction is one of the four basic arithmetic operations (the others being: addition, multiplication and division). It probably evolved around the same time as addition and it continued to develop at pretty much the same pace as addition. That makes it one of the oldest mathematical operations in existence. In fact, it’s easy (and a lot of fun) to try to imagine early, prehistoric humans trying to wrap their heads around the concept of different quantities getting larger or smaller and the reasons behind that. The development of these basic operations allowed them to make plans, manage resources and slowly build the foundations of the civilizations we live in today.

subtraction in the history

Also, subtraction occupies the same place in the order of operations and, with the use of negative numbers, it can be considered as a form of addition. But, unless some negative numbers are in the picture…

The basic concept of subtraction

…subtraction is, in fact, the opposite of addition. In addition you add (objects) members to a group, while in subtraction you take them away. And by doing that, you’re making the starting group of objects smaller. For example, let’s say you have five candies to start with. If you eat two of them, you are left with three uneaten candies.

subtraction

Elements of subtraction

The number that’s being subtracted from is called the “minuend”, while the number subtracted from the minuend is the “subtrahend”. The result of the subtraction is called the difference and the sign for subtraction is “-“. The basic principle behind subtraction is this:

subtraction elements

How to subtract?

Performing subtraction is simple enough. The most popular method of performing subtraction with multiple digit numbers relies on doing several subtractions using the more manageable, single digit numbers that form the multiple digit numbers in question.

You begin by subtracting the digit with smallest positional value (the one on the far right) of the subtrahend from the digit with the same positional value (again, the one on the far right) of the minuend. The number you got as a result from that subtraction (the difference) will have the same positional value as the minuend and subtrahend did. Then you move to the digits with the next greatest positional value (one digit to the left) and repeat. You do that until you run out of digits. Like this:

subtraction parts

Now, we are going to look at subtraction of two three-digit numbers:

subtraction of two numbers

The subtraction in the previous example should look like this:
-> 7 is lower than 8, so we can’t subtract. Borrow the 1 from the tens digit. Now we have 17 and we can subtract. 17 minus 8 equals 9. Write down 9.
-> We borrowed 1 from the ‘tens’ digit so it is now 8 instead of 9. 8 minus 8 equals 0. Write down 0.
-> 2 minus 1 equals 1.
-> The final result is 109.

Now, we are going to look at subtraction of three three-digit numbers:

\ 948 - 652 - 121 = 296 - 121 = 175

subtract three numbers

The process of subtracting three three-digit numbers can be divided into two subtractions of two three digit numbers. In our example the process of subtracting should look like this:
-> 8 minus 2 equals 6.
-> 4 is lower than 5 so we can’t subtract. Borrow the 1 from the ‘hundreds’ digit. Now we have 14 and we can subtract. 14 minus 5 equals 9. Write down 9.
-> Now the hundreds digit is 8 because we borrowed 1 for the previous subtraction. 8 minus 6 equals 2. Write down 2.
-> Now we need to subtract 296 with 121. 6 minus 1 equals 5. Write down 5.
-> 9 minus 2 equals 7. Write down 7.
-> 2 minus 1 equals 1. Write down 1.
-> The final result is 175.

Now we are going to look at subtraction of fractions. Fractions are used to describe division of one “whole” in “parts”.
They are composed of two numbers. One is called the numerator and it’s the top number in a fraction.
The other one is called the denominator and it’s the bottom number in a fraction.

Let’s look at an example of subtraction of two fractions for better understanding:

subtraction of fractions

We start by finding the common denominator for the two fractions.
Then we divide the common denominator with the denominator of the first fraction and multiply by its numerator.
We do the same for the second fraction and subtract the results.

-> The common denominator for these two fractions is 15. Write 15 on the bottom of the resulting fraction.
-> 15 divided by 5 is 3. 4 times 3 is 12. Write down 12 on the top of the resulting fraction.
-> 15 divided by 15 is 1. 8 times 1 is 8. Write down 8 on the top of the resulting fraction.
-> The numerator of the resulting fraction is now 12 minus 8, and that equals 4.
-> The resulting fraction is 4/15.

When we need to subtract three fractions, we first need to find the common denominator.

subtract three fractions

The process of subtracting three fractions should look like this:
-> Find the common denominator. It’s 18. We write 18 on the bottom of the resulting fraction.
-> 18 divided by 9 is 2. 2 times 7 equals 14. Write down 14.
-> 18 divided by 6 is 3. 3 times 1 equals 3. Write down 3 in the resulting fraction.
-> 18 divided by 2 is 9. 9 times 1 equals 9. Write “9” in the resulting fraction.
-> The numerator of the resulting fraction is 14 minus 3 minus 9. It’s 2. The resulting fraction is 2/18.
-> The fraction can also be simplified. We can divide the numerator and denominator with 2.
-> The resulting fraction is 1/9.

Now we are going to talk about the subtraction of decimal numbers. Decimal numbers can be written as a fraction. Look at this example:

subtraction of decimals

-> 7 minus 2 equals 5. Write down 5.
-> 2 is lower than 8. Borrow 1. 12 minus 8 is 4. Write down 4.
-> 2 minus 1 that we borrowed is 1. 1 minus 1 is down 0.
-> 2 is lower than 5. Borrow 1. 12 minus 5 is 7. Write down 7.
-> 9 minus 1 that we borrowed is 8. 8 minus 5 equals 3. Write down 3.
-> 3 minus 1 equals 2. Write down 2.
-> The result is 237.045.

 

Subtraction of natural numbers worksheets

Integers

  Two positive integers (78.9 KiB, 408 hits)

  Three positive integers (88.3 KiB, 382 hits)

  Four positive integers (94.2 KiB, 373 hits)

  Two integers (104.1 KiB, 339 hits)

  Three integers (121.2 KiB, 358 hits)

  Four integers (141.0 KiB, 368 hits)

Decimals

  Two positive decimals (84.6 KiB, 386 hits)

  Three positive decimals (97.7 KiB, 348 hits)

  Four positive decimals (105.8 KiB, 353 hits)

  Two decimals (109.5 KiB, 393 hits)

  Three decimals (130.8 KiB, 351 hits)

  Four decimals (152.6 KiB, 369 hits)

Fractions

  Two positive fractions (168.5 KiB, 356 hits)

  Three positive fractions (275.3 KiB, 364 hits)

  Four positive fractions (238.2 KiB, 349 hits)

  Two fractions (193.0 KiB, 360 hits)

  Three fractions (238.9 KiB, 355 hits)

  Four fractions (282.3 KiB, 378 hits)

Improper fractions

  Two positive improper fractions (155.2 KiB, 347 hits)

  Three positive improper fractions (181.5 KiB, 405 hits)

  Four positive improper fractions (206.5 KiB, 327 hits)

  Two improper fractions (367.1 KiB, 153 hits)

  Three improper fractions (230.6 KiB, 371 hits)

  Four improper fractions (270.8 KiB, 351 hits)

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