Here we will discuss the basics of integers. Integers are a bigger collection of numbers that include whole numbers, negative numbers, and zero. When we intend to do various operations with integers it is necessary that we make our concepts clear and learn the basics of integers. The chapter below shall help you understand the basics of integers in a better way.
Basics of Integers
Integer is a Latin word that means whole. An integer may comprise a set of whole numbers that include zero, positive number and negative number. Integers, however, do not include decimals, percents, and fractions. For understanding the basics of integers we need to represent it on a number line. The figure below shows numbers marked on a number line:
The numbers on the right side of zero (0) are positive numbers while those on the left side are negative numbers. When we arrange these numbers in ascending order, the negative numbers are the lowest while the positive numbers are the highest. So in the number line above, amongst the numbers-5, 1 and 2 the number -5 is the lowest whereas 2 is the highest.
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The numbers which have a plus (+) sign on them are called positive numbers. These numbers are present on the right of zero (0). Generally, a number without any sign is also considered a positive number. Every positive number is greater than its negative counterpart and zero. For example, 6 is greater than -6.
A negative number is a contradiction of a positive number. It is written with a -ve sign. Negative numbers are present on the left of a zero on a number line. Every negative number is less than its positive counterparts.
A number that neither a positive nor a negative is a zero. It occupies the center of the number line and is a neutral number.
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How do Operations work?
When we use a number line to do mathematical operations like addition and subtraction we follow the underwritten points:
- When we add a positive integer, on a number line we move to the right. For example, if we add 3 to-1 we move to the right on a number line.
- When we add a negative integer on a number line we move to the left. For example, if we add -4 to +3 then moving left we get the answer -1.
- When we subtract a positive integer, we move to the left on that line. For example, when we subtract +4 from +2 we get -2.
- When we subtract a negative integer, on a number line we move to the right. For example, if we subtract -3 from -2 we get +1.
- When we add one positive and one negative integer, then in such case we find the difference between the two integers. The sign, however, shall be the sign of the larger number. Her, we do not consider what the sign of larger number shall be for conducting the operation. This means that in any case, when there is a negative number, we have to subtract the lower from the higher.
- When we subtract two integers, we take them as the sum of one number with the additive inverse of that number. For example, if b has to be subtracted from a then we add the additive inverse of the integer b to get the answer. So when we subtract b from a, we write it as a + (-b) [-b is the additive inverse of b].
Now suppose if b itself is a negative integer then, a-(-b) = a+b. This means that when we subtract the negative integer from a positive integer, we ultimately end up adding the two integers. A minus sign, when combined with a minus sign, becomes a positive. Let’s take ‘a’ as a negative integer now.
When we take ‘a’ as a negative integer and b also as a negative integer then, -a-(-b) = -a+b= b-a. So when both the integers are negative, we find the difference between the two to get the answer. The sign, however, shall be of the higher integer.
For further understanding, the basics of Integers, another concept to understand is the additive inverse. An additive inverse. An additive inverse of an integer is the number with the contrasting sign. For +4 the additive inverse is -4. For -5 additive inverse shall be +5.
When we compare integers, we need to keep in mind the sign before the integer. A negative integer, no matter what the number is lower than any positive number. For example when we compare the integers -5 and 3, -5 is lower and 3 is higher. A negative sign makes the number lower.
Applications of Integers
Integers are generally used to signify two contradicting situations. These are not just any numbers, they are numbers with signs. Positive numbers and negative numbers can have varying applications. The most real application of integers is measuring the temperature.
The positive and negative aspects of a temperature let us know, compare and measure the change in temperature. Apart from measuring temperature integers are used in the credits and debits calculation by the banks. Integers help in quantifying things in a better way.
Sample Question For You
If a and b are two integers with values +5 and -7 respectively, then what shall be the sum and difference between the two:
a. 12, 2
Solution: b) Sum of a+b= +5 +(-7) =-2
a-b =+5-(-7) = +12