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What are integers and why it is important?

There are many kinds of numbers that we come across in algebra. Some of these kinds of numbers are related to each other. Before we learn how these numbers are related to each other, we need to learn about them separately. In this article, you will learn about integers and their operations. Whenever you go to another country, you will have to exchange your

ǯǤǡbut the value of your

currency may also either increase or decrease in different countries. It is because each country has different values in relation to their currency. These positive and negative values are the building blocks of mathematics. On the number line they are represented as follows: - www.cuemath.com These numbers have many uses in real life as well as in math class. You will better understand with the following examples:

1. Money that we receive from somewhere as salary or gifts is added to

our account and the money that we give someone is subtracted from our account.

2. When you get your blood, pressure checked. It may come out to be high

or low. A value that is above normal pressure is called positive and a value that is below normal is called negative. www.cuemath.com

Definition of Integers

Integers are the natural numbers, the negatives of these numbers, or zero. An integer is a complete entity. Integers are the numbers that can be positive, negative, or zero, numbers with no fractional part (no decimals). The examples of integers are, 1, -2, 7, -8, 9, -12, etc. The collection of all integers is represented by a symbol DzZdz.

Some more examples:

If someone is overweight than normal, then it will be represented as positive and if someone is underweight than normal then it is represented as negative. www.cuemath.com Example: Which of the following options is not true with respect to a given number line? (a) B is greater than Ȃ10 (b) A is greater than 0 (c) A is greater than B (d) B is greater than 0 Answer: The first three options are correct, but B lies on the left side of 0, so it is not greater than 0. So clearly option (D) is not true. (d) B is greater than 0 www.cuemath.com Example: The six-day forecast for Antarctica lists the temperatures (in

Celsius) as Ȃ52°C, Ȃ53°C, Ȃ40°C, Ȃ58°C, Ȃ70°C, Ȃ79°C. Which choice

shows the temperatures in order from the lowest to the highest? (A) Ȃ79°C, Ȃ70°C, Ȃ52°C, Ȃ53°C, Ȃ40°C, Ȃ58°C (B) Ȃ52°C, Ȃ53°C, Ȃ58°C, Ȃ70°C, Ȃ79°C, Ȃ40°C (C) Ȃ79°C, Ȃ70°C, Ȃ58°C, Ȃ53°C, Ȃ52°C, Ȃ40°C (D) Ȃ40°C, Ȃ52°C, Ȃ53°C, Ȃ58°C, Ȃ70°C, Ȃ79°C Answer: On the number line, we see that the larger is the negative value the smaller is the number. Using this, we can say the option (C) is correct. (C) Ȃ79°C, Ȃ70°C, Ȃ58°C, Ȃ53°C, Ȃ52°C, Ȃ40°C

Operations on Integers

Integers are used to perform various arithmetic operations, like addition, subtraction, multiplication, and division. Let us understand them one by one.

Addition and Subtraction of Integers

www.cuemath.com Let us understand with movement on the number line. I am representing a positive movement with blue (right side) and negative movement with red (left side). Consider the following examples where we start from the first number. If a positive number is added, we move towards the right and if a negative number is added we move towards the left: Example: Which of the following number lines represents Ȃ1Ȃ4? Answer: From the above illustrations, option (A) is correct. Example: The difference between the sum of all the even numbers and the sum of all the odd numbers between 10 and 20 is ______. (A) Ȃ12 (B) Ȃ14 (C) Ȃ15 (D) Ȃ16 www.cuemath.com . (C) Ȃ15 Example: The distance above the ground is represented by positive integers and the distance below the ground by negative integers. An elevator begins to descend from 15 m above the ground at a rate of 5 m per minute. What will be its position after 45 minutes? (A) 210 m (B) Ȃ210 m (C) 215 m (D) Ȃ225 m (C) 215 m

Multiplication and Division of Integers

Integers follow the following rules for multiplication and division. www.cuemath.com Notice that the rule for the division of integers is the same for multiplying integers. Therefore, if you remember the rule for multiplying the integers, you already know it for the division of integers also. This can also be learned as the same signs will have a positive answer and opposite signs will have a negative answer. And for more than two numbers in multiplication or/and division, we can say if negative comes an odd number of times then the answer will be negative and if negative sign comes an even number of times then the answer is positive. www.cuemath.com

Properties of Integers

Summary

Integers are numbers that are positive, negative, and zero but not fractions/decimals. All mathematical operations can be applied to integers. Signs of the two numbers on which we apply any operation can affect the answer.

Integers in real life

Real-life integers are used to check accounts. If there are sufficient funds, it represents positive numbers. If money is overdrawn from the account, it represents negative numbers. If there is a profit, we have positive numbers. If there is a loss, we have negative numbers.