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Integer Calculator

Integer Calculator

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Operation:

a + b = ?

a:

b:

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Let this free integer calculator go for adding and subtracting integers and display the final answer on your device screen. Moreover, you can also perform basic arithmetic operations on integers and get to know when to change signs while doing integers subtraction by using this negative calculator.

What about moving ahead and discussing a little bit more about integers theory?

Let’s go ahead

What Is An Integer?

“A number with no fractional or decimal part is known as the integer.”

Basically, integers include all the numbers that may be positive or negative. Also, you can perform addition, subtraction, multiplication, and division on these numerals. And if it comes to speed up the process, this best consecutive integers calculator is the best way to do this.

Examples:

The numbers 2, -4, 6, 33333, 9378 etc are integers.

Number Line:

number line
A number line is said to be the graphical representation of the integers. Whether you are going to perform integers subtraction or adding positive and negative numbers, you must first try to understand the number line scenario. Also, our best integer calculator also follows the ame theory to perform mathematical analysis on these numbers.

Positive Numbers on Number Line:

All the numbers on the right side slide of the zero (also an integer) are considered as positive numbers. In other words, we can also assume that the numbers on the right of zero are continuously increasing in a definite manner.

Negative Numbers on Number Line:

If you take a look at the left of the integer zero, all numbers with negative signs are said to be negative. In mathematics, these negative numbers are considered the mirror images of the positive numbers.

Adding and Subtracting Integers:

This negative and positive calculator takes into consideration the addition and subtraction of either only positive numbers, only negative numbers, or even both. Let’s move forward towards various basic rules defined:

Addition Rules:

There lies two categories that are as below:

Same sign:

If you have two positive numbers, then simply add them and put a positive sign with the resultant number

(+a) + (+b) = (a + b)

Adding negative numbers goes by the rule as defined below:

(-a) + (-b) = – (a + b)

Different Sign:

Adding integers with opposite signs considers the rule as follows:

(-a) + (+b) = (a – b)

You can also commence this free adding integers calculator to depict the addition of integers in a fragment of seconds.

Subtraction Rules:

The rules for subtracting integers are the same as defined for the addition. The only change is the change of the sign, which is minus instead of addition here. But we will also try to remember integer rules subtraction here.

Same sign:

Keep subtracting two positive integers as you add them but consider the negative sign among them:

(+a) – (+b) = (a – b)

If both the numbers are negative, then focus on the generic expression below:

(-a) – (-b) = -(a – b)

Different Signs:

Two numbers with opposite signs are supposed to be subtracted by following the rule as below:

(-a) + (+b) = (a – b)

Multiplying and Dividing Integers:

In practice, the multiplication and subtraction of the integers is quite the same process. The only variation exists here is the sign that depends on the sign of divisor or dividend in case of multiplying and dividing them, respectively.

Integer Multiplication Rules:

Pay heed to the following multiplication rules used to find the product of two integers:

Same Signs:

If both the numbers are positive or negative, then they are multiplied by subjecting to the expressions:

(+a) * (+b) = (a * b)

(-a) * (-b) = + (a * b)

Different Signs:

Get two integers multiplied with one another in case both of them are having opposite signs by considering the key points as mentioned below:

(+a) * (-b) = – (a * b)

Integer Division Rules:

Keep in mind the rules set for dividing integers with either same or different signs:

Same Signs:

(+a) / (+b) = (a / b)

(-a) / (-b) = + (a / b)

Different Signs:

When two integers are divided having the different signs, then the sign with the bigger integer is supposed to be put with the final answer.

(+a) / (-b) = (a / b)                         If sign with bigger number is positive

(+a) / (-b) = – (a / b)                      If sign with bigger number is negative

All of these rules are the pivot theme on which this free integer calculator works.

Integer Exponent Rules:

In case when there are positive exponents involved, the final generated number will be equal to the actual number multiplied times the power mentioned.

a^b = a*a*a*…                 where this multiplication repetition depends on the value of b.

In case when the exponents become negative, the final result is computed by inverting it:

a^-b = 1/a*a*a*…           where this multiplication repetition depends on the value of b.

Integer Roots Calculation:

As every operation has its opposite one, root is considered as the opposite image of exponents. Moreover, you can also find the radical with the help of our radical calculator. But what you need to keep in mind is that you can not figure out the radicals of negative integers.

$$ \sqrt[a]{b} $$ where b must need to be positive for sure

Integer Logarithms Calculations:

So we are here interested in figuring out the log of integers. One of the conveniences here is that the log of negative integers does not exist. So, you can only take the log of positive numbers. Moreover, we have also designed another log calculator for this purpose that provides you with the detailed computations of the logarithms.

How To Perform Operations On Integers?

Let us resolve a couple of examples to understand the theory better! Stay with us!

Example # 01:
How to subtract negative numbers given below:

-7 and -9

Solution:

Subtracting negative numbers given:
(-a) – (-b)

= (-7) – (-9)

= -7+9

= +2                         Since the sign with the bigger integer is positive

You can also verify the results by subjecting to a free subtracting integers calculator.

Example # 02:

How to add negative numbers that are as follows:

-4 and -7

Solution:

(-a) + (-b)
= (-4) + (-7)
= -4-7
= -11                           Since the sign with a larger integer is negative.

Here the free adding negative numbers calculator also goes for generating the same results but in seconds.

How Integer Calculator Works?

This free calculator integers performs various arithmetic operations on the integers and generates accurate outputs in a couple of seconds. What about having a look at its operation? Let’s move forward!

Input:

  • From the first drop-down list, select the type of operation you want to perform on numbers
  • After that, write the asked numbers in their designated fields
  • At the end, tap the calculate button

Output:

The free positive and negative calculator performs the following operations on the integers:

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Root
  • Exponent
  • Logarithm

Here you can also perform more advanced mathematical operations on numbers with the help of our math calculator.

FAQ’s:

Which is the largest integer?

The number 2,147,483,647 is the one which is supposed to be the greatest integer number.

Do numbers end?

No, not at all! If you think that you have written the greatest number, just go for adding 1 to it. You will get a bigger number. This is why numbers can never be considered as an end.

What number is the smallest integer considered?

The smallest integer in mathematics is 0 that could also be checked by using this free integer calculator.

Which is the largest negative integer?

-1 is the biggest negative integer as after this, we get zero and then positive integers. If you do not get it, scroll up and read the number line sectio again.

How do you compare integers?

  • Whenever comparing integers, the one with more numbers is considered the bigger among the two.
  • Now if we have two integers with the same number of digits, then start from most left and move towards the right, comparing numbers. When you get two different numbers, stop there and look for the bigger one or smaller one.
  • Whenever there are more complex integers to be compared, the free integer calculator is the best way to compare them.

What are neutral numbers?

Zero is a number that lies in the middle of the number line. It is neither positive nor negative. This is why this integer is considered as the neutral number.

What is the difference between absolute value and integer?

For instance, let us be clear that absolute numbers can never be negative. While on the other hand, the integers can also be negative rather than the positive numbers.

Conclusion:

Many real-world applications are concerned with the addition and subtraction of integers. They allow us to make variations in calculations for achieving far better results. This is why our best integer calculator with negative sign and positive is widely used by professionals and scholars to get maximum accuracy in their basic maths calculations.

References:

From the source of Wikipedia: Integer, Algebraic properties, Order-theoretic properties, Cardinality

From the source of Khan Academy: Ordering negative numbers, Adding numbers with different signs, Adding & subtracting negative numbers

From the source of Lumen Learning:  Real Numbers, Classify a Real Number, Irrational Numbers, Sets of Numbers as Subsets