Addition of Integers: Formula, Rules, Examples | Turito
Adding Integers: Definition and Examples
An integer is a number written without fractions. For example, 3, 71, 902, -66, -877 - these are all integers. The simplest way to define an integer is to consist of an absolute value and a positive or negative sign.
The digit Zero (0) is neither a positive nor a negative integer. Positive natural numbers are called positive integers (1, 2, 3, etc.) and additive reciprocals are called negative integers (-1, -2, -3, etc.). This is very easy to see by adding an integer.
Arithmetic main features:
Arithmetic is one of the most basic and fundamental parts of mathematics. Basic knowledge also allows you to understand various applications and studies such as algebra, trigonometry, measurement, geometry and other related topics. The foundations of arithmetic are the driving force behind all other aspects of mathematics.
Some common basic problem statements about integers are how to add and subtract integers and how to add integers of the same sign. These, along with several other functions, form the basis of mathematics
The basic operations of arithmetic operations are:
Addition(Sum; `+`)
Subtraction (difference; `-`)
Multiplication (product; `x`)
Division (÷)
How to add integers is explained in detail in this article. In the meantime, let's take a quick look at the other three features.
Subtraction
The arithmetic operation of subtraction shows the difference between two numbers. The symbol "-" represents it. Subtraction is primarily used to find out what is left when things are removed. That is, one number is subtracted from another.
For example, I had 10 apples. Two apples are taken from me. Now we have (10-2) = 8 apples.
Multiplication
Repeated addition is called multiplication. The symbol "x" represents it. Multiplication as an arithmetic operation is useful for finding sums when a number is repeated several times. Example: 3 times 4 is 12. Mathematically, we can write 3 × 4 = 12. Multiplicand and multiplier are terms used in the multiplication process. Product is the term we use for the result of multiplying a multiplicand by a multiplier.
Example: I ate 2 apples every day for 3 consecutive days. So there were 2 x 3 = 6 apples.
Division
Dividing something into equal parts or groups is called division. One of the four basic arithmetic operations that produce an evenly distributed fair result. The inverse of multiplication is division. The symbol "÷ represents that".
Example: For me, Andrew and Michael split his 12 mangoes evenly between us. So there were 12 ÷ 3 = 4 mangoes each.
How to add an integer
Addition is one of four basic operations: arithmetic, subtraction, multiplication, and division. In general, adding two positive integers yields a positive integer. Adding two negative integers yields a negative integer. Adding a negative integer and a positive integer yields the integer containing the greater value between the two negative numbers. You can read more about how to add integers here. Append represents a value added to an existing value. For example, if I had 3 of his pens and 4 more were added to this list, the addition would result in a total of 7 pens. Addition is affected by both irrational and rational numbers. Therefore addition applies to both real and complex numbers.
In summary, how do you add like and opposite integers?
Adding two positive integers always results in a positive integer.
Adding two negative integers always results in a negative integer.
When adding a positive integer to another negative integer, the larger of the two integers determines the sign.
Basic example:
14+15=29
7 + 5 = 12
(-3)+3 = 0 [Addition of two equal inverse integers always results in zero]
(-50)+4 = (-46)
10 + (-1) = 9
(-20) + (-10) = (-30)
Properties of Integer Addition and MultiplicationClosure property : x + y is an integerAssociative property : x + (y + z) = (x + y) + zCommutative property : x + y = y + xExistence of identity element: x + 0 = xExistence of inverse: x + (−x) = 0Distributive law: x × (y + z) = (x × y) + (c × z)Closure propertyThe sum of two integers is results into an integer. If a and b are two integers, their sum is also an integer.Examples: 5 + 6 = 11 ; -5 + 8 = 3.Commutative lawThe commutative law of addition states that the order of terms does not affect the result. Also, changing the conditions does not affect totals or products.Examples: 2 + 4 = 4 + 2 ; -6 + 8 = 8 + (-6)Associative propertyThe associative property of addition states that it makes no difference how the numbers are grouped. the result is the same. Anyway, the answer is the same.Example: 2 + (3 + (-4)) = 1 = (2 + (−4)) + 3Distributive PropertyThe distributive law describes how mathematical operations within one parenthesis should be distributed among other parentheses. It is either the law of distributive addition or the law of distributive subtraction. In this case, the integer is added or subtracted first, then multiplied or divided by each number in brackets, and then added or subtracted. Example: −5 (3 + 2) = −25 = (−5 × 2) + (−5 × 3)How to add an Integers using the number lineThe following principles apply to adding integers on the number line.• To add positive numbers, move the cursor to the right (or positive side) of the number line.• Adding negative integers is done by moving them to the left (or negative) side of the number line. • Each specified integer is a starting point for movement on the number line.Examples and step-by-step guides can be found here:The first step is to choose a scale for the number line. For example, whether a number is expressed as a multiple of 1, 5, 10, or 50 depends on the integer specified. For example, if you need to add 10 and 20, you can use a number line with a scale of 10.If you need to add -4 and 9, you can take the number scale starting at 1.The next step is to find any integer on the number line. A larger absolute value is desirable. For example, if you need to add 3 and 22, first find 22 and then jump right twice is better than first finding 3 and then jumping right twenty two. The final step is to jump left or right and add a second integer to the number from the previous step. This depends on the number whether it is positive or negative.Practical implementation of integer addition and subtractionI had 10 cookies. I borrowed 5 from my father. How many cookies do I currently have?A: The answer is 10 + 5 = 15 (real example of how to add like-signed integers)The temperature in the room is 20 degrees Celsius. My mother asked me to go up three times. What will be the final temperature of the room when it rises?A: 20 + 3 = 23.Mike got -3 points in the pre-final quiz competition. He scored 10 more points to qualify for the final. What was his total score?A: Add integers. -3 + 10 = 7 (integer addition and subtraction example)