Integers Introduction: To score well in the exam, students must check out the Integers introduction and understand them thoroughly. The collection of negative numbers and whole numbers is known as an integer in mathematics. Integers, like whole numbers, do not contain the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. We can carry out all arithmetic operations on integers, including addition, subtraction, multiplication, and division. Integer examples include 1, 2, 5, 8, -9, -12, etc. “Z” stands for an integer.
Let’s now go over the definition of integers, their symbol, types, operations, laws, and properties, and how to display them on a number line with numerous worked-out examples.
Integers Introduction: What are Integers?
The word integer came from the Latin word “Integer.” It means intact or whole. Integers are a unique set of zero, negative, and positive numbers.
Negative Integers (Additive inverse of Natural Numbers)
Positive Integers (Natural numbers)
Zero is neither a negative nor a positive integer. Zero is a neutral number with no sign. Plus or Minus sign is not added with zero.
What are Positive Integers?
The positive integers are the natural numbers. The positive integers are also known as counting numbers. Z+ denotes these integers. On a number line, the positive integers can be found the right side of 0.
There are many practical uses for integers; they are more than just abstract numbers on a page. Positive and negative numbers have various effects in the real world. They typically represent two opposing circumstances.
For instance, positive numbers are used to represent temperatures above zero, whereas negative numbers are used to indicate temperatures below zero. They make it possible to compare and quantify two things, such as how big or little, how many or how few they are.
The ratings of movies or music, player scores in golf, football, and hockey competitions, the representation of credits and debits in banks, and other real-world scenarios all involve numbers.
Integers Introduction: Integers Examples
Check out some of the integer examples below.
Check out the 1st example.
Let us solve the following question.
5 + 3 = ?
5 + (-3) = ?
(-5) + (-3) = ?
(-5) x (-3) = ?
Here is the solution.
5 + 3 = 8
5 + (-3) = 5 – 3 = 2
(-5) + (-3) = -5 – 3 = -8
(-5) x (-3) = 15
Check out the 2nd example.
How to solve the following product of integers?
(+5) × (+10)
(12) × (5)
(- 5) × (7)
5 × (-4)
Check the solution below.
(+5) × (+10) = +50
(12) × (5) = 60
(- 5) × (7) = -35
5 × (-4) = -20
Check out the 3rd example.
How to solve the following division of integers?
(-9) ÷ (-3)
(-18) ÷ (3)
(4000) ÷ (- 100)
Check the solution below.
(-9) ÷ (-3) = 3
(-18) ÷ (3) = -6
(4000) ÷ (- 100) = -40
A Few Important Practice Questions on Integers Introduction
1. A positive integer is the sum of two positive integers. False or True?
2. What are the first five positive integers added together?
3. What is the first five positive odd-numbered integers’ product?
4. Draw a number line and plot the integers from -10 to +10.
Students who want to learn about the properties of integers and solve problems on this particular topic can download Embibe, the best learning App from Google Play Store. Many interactive videos are available there on this topic.
FAQs on Integers Introduction
Check out some of the frequently asked questions on integers.
Q1. What do integers mean?
A. The three elements that make up an integer are zero, the natural numbers, and their additive inverse. It can be shown on a number line but without the fractional portion, and Z stands for it.
Q2. Define an integer formula.
A. An integer is a collection of positive and negative numbers and zero, yet it lacks a mathematical formula.
Q3. Give us some integer examples.
A. Integers have instances like 3, 5, 0, 99, -45, etc.
Q4. Can Integers be negative?
A. Yes, negative integers are possible. Negative integers, such as -1,-2,-3,-4, and so on, are the additive inverse of natural numbers.
Q. Define the three categories of integers.
A. The three categories of integers are negative numbers, zero, and positive integers.
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