Integer Worksheet

What is an Integer?

In mathematics, integers can be defined as numbers that can have a positive, negative, or zero value. However, these numbers cannot be a fraction. According to the integer worksheet, these numbers can be used to perform various arithmetic operations like subtraction, addition, division, and multiplication. The integer worksheet states that some examples of integers are 1, 2, 5, 8, -8, -12, and 6.

The symbol of ‘Z’ is also used to refer to integers in integers class 7 CBSE worksheet. Further, according to the terms of sets, the set of integers includes zero, a set of whole numbers, a set of natural numbers, which are also known as counting numbers, and the additive inverses of natural numbers like -1, -2, -3, and -4.

The integer class 7 CBSE worksheet also mentions that integers can be classified as a subset of real numbers. Some examples of integers include 100, -12, -2, 0, 2, 978, and 837. Also, as a set, these integers can be represented as:

Z = {.... -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, …}

According to the integers worksheet for class 6, there are different types of numbers in mathematics. Some of these different numbers are mentioned below.

• Natural numbers

• Real numbers

• Rational numbers

• Whole numbers

• Even numbers

• Odd numbers

• Irrational numbers

Integers fall under a similar classification system. It is also interesting to note that the word integer originated from the Latin word ‘integer.’ This world means whole. This is why the integers worksheet for class 6 classifies integers as a special set of whole numbers. This special set of numbers comprises zero, positive, and negative numbers. However, fractions, decimals, and percents are not a part of this basket.

Based on the integers worksheet for class 7, there are three types of integers. Those three types of integers are:

• Zero (0)

Zero is neither a positive nor a negative integer. This is a neutral number as zero has no sign.

• Positive Integers (Natural Numbers)

Positive integers are also known as natural numbers. These numbers are positive. These numbers are represented by a plus or positive (+) sign. These numbers lie on the right-hand side of the zero in the number line. This means that all positive integers are greater than zero in their value. For example, 1, 20, 4875, 2927, and 348.

• Negative Integers (Additive Inverse of Natural Numbers)

According to the integers worksheet for class 7, negative integers are also known as additive inverse of natural numbers. These numbers are represented by a minus or negative ( - ) sign. These numbers are also present at the left side of zero on a number line. For example, -1, -383, -828, and -84847.

Representing Integers on a Number Line

In integers worksheet grade 7 chapter, students also have to solve questions in which they have to plot integers on a number line. These questions are included in the CBSE class 7 maths integers worksheets with answers. This is why students need to learn how to solve these questions.

In this section, we are going to help students solve those types of integers worksheet grade 7 questions. It is recommended that students should look at the image of a number line that is mentioned below.

If a student has to solve number line integers questions for class 7, then he or she should begin by plotting a similar number line. Once the student has finished plotting the number line, then the next step is to simply circle or highlight the integer that one has to showcase.

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Rules of Integers

When it comes to solving integers questions for class 7, then there are some rules that students have to follow. We have created a list of those rules. And that list is mentioned below.

• The sum of any two positive integers is an integer

• Similarly, the sum of any two negative integers is an integer

• Product of two positive integers is an integer

• Product of any two negative integers is also an integer

• The sum of an integer and its inverse is equal to zero

• The product of an integer and its reciprocal value is equal to one

These are simple rules. However, these rules are not a lot of help for students when they are trying to solve CBSE class 7 maths integers worksheets with answers. This is why we have prepared a better explanation of these rules, along with examples. All of these important points are mentioned below.

Adding Signed Integer Numbers

If one has to solve questions of integers for class 6 pdf related to the addition of signed integer numbers, then one has to remember to add the numbers with the same sign. The absolute value should also be added, and the individual should write down the sum with the sign that is provided with the number.

For example, +4 + (+7) = + 11 and -6 + (-4) = -10

However, if one has to add two integers with different signs, then one needs to subtract the absolute value. After that, simply write down the difference with the sign of the number that has the largest absolute value.

For example, -4 + (+2) = -2 and +6 + (-4) = +2

Subtraction of Signed Integer Numbers

What should one a student do if he or she has to solve questions on integers for class 6 pdf that are related to subtraction of signed integer numbers? In that case, one should change the sign of the second number, which is being subtracted. Apart from that, the rules of addition should be followed.

For example, -7 - (+4) = -7 + (-4) = -11 and +8 - (+3) = (+8) + (-3) = +5

Multiplication and Division of Signed Integer Numbers

While solving integers questions for class 6, students must also come across questions related to multiplication and division of signed integer numbers. To solve those questions, students should check the sign of the integers. If both the numbers have the same sign, then the result will be positive, and if the integers have different signs, then the final result will be negative.

For example, +2 x +3 = +6, +3 x (-4) = -12, +6 / (+2) = +3, and (-16) / (+4) = -4

Students should strictly follow these rules to solve integer questions for class 6. These rules can also be very helpful in solving questions on integers for class 7 pdf.

The Properties of Integers

According to the integers worksheets with answers, there are some integral properties of integers. Students should be familiar with these properties if they want to solve questions on integers for class 7 pdf.

To help students, we have created a list of all those properties. And those properties are mentioned below.

• Closure property

• Associative property

• Commutative property

• Distributive property

• Additive inverse property

• Multiplicative inverse property

• Identity property

Students can learn more about these properties by referring to the integers worksheets with answers. These answers can be downloaded from Vedantu.

Fun Facts about Integers

Do you know that according to the integers worksheet grade 6, integers are not just numbers on a piece of paper, but they also have many real-life applications? In the real world, both positive and negative numbers are used to symbolize two contradicting situations.

For example, positive numbers can be used to highlight profit, while negative numbers can refer to loss. Also, different types of integers are also used to denote the current temperature. This means that the temperature of any location can be zero or a positive or negative number. These numbers also play an important role when it comes to keeping track of scores in various games like football, golf, and hockey.