Integer Worksheet

Introduction

• Integers are one of the most important concepts in mathematics, and most of them are relevant to this topic. You can practice this concept by practicing multiple integer worksheets.

• In mathematics, integers are characterized as numbers with a possible value of either positive, negative, or zero.

• These figures, however, cannot constitute a fraction.

• These numbers can be used to carry out a variety of mathematical operations, including addition, subtraction, multiplication, and division, according to the integer worksheet.

• According to the integer worksheet, examples of integers include 1, 2, 5, 8, -8, - 12, and 6. In this tutorial, we will discuss integers.

Integers

• The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.

• An integer, which can comprise both positive and negative numbers, including zero, is a number without a decimal or fractional portion.

• Integers include things like -5, 0, 1, 5, 8, 97, and 303.

• Z is the set of all integers that consists of the following −

Positive Numbers − If a number is greater than zero, it is considered positive

For example − 1, 2, 3, etc.

Negative numbers are those that are less than zero

For example − -1, -2, -3, etc

Note − Zero is described as being neither a positive nor a negative number

The Integer Rules

For integers, the following rules are specified −

• The sum of two integers will be an integer

• The product of two integers will be an integer

Algebra of Integers

Integers can be used in the following four fundamental arithmetic operations −

• Addition of Integers

• Subtraction of Integers

• Multiplication of Integers

• Division of Integers

Addition of Integers

Rules for Adding Integers −

The following guidelines are used when adding two integers −

When both integers have the same sign: add their absolute values and assign the result the same sign as the inputted integers.

When both integers have different signs: Determine the differences between the absolute value of the two numbers, and then add the sign of the greater of the two to the outcome.

For example, Simplify the following equation $\mathrm{1\:+\:9\:+\:11}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:Given\:equation\:is\:1\:+\:9\:+\:11}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:21}$

Subtraction of Integers

Rules for Subtracting with Integers −

To perform a subtraction of two integers, apply the following rules:

To perform a subtraction of two integers, apply the following rules −

Change the sign of the subtractor to turn the operation into an addition problem. Apply the same rules to add integers and solve the problem obtained in the steps above.

For example, Simplify the following equation $\mathrm{22\:-\:10\:-\:2}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:Given\:equation\:is\:22\:-\:10\:-\:2}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:22\:-\:12}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:10}$

Multiplication and Division of Integers

Rules for Multiplication or Division of Integers −

Multiply or Divide the Absolute value of the respective Integers and the sign of the result is determined by a simple rule − If both integers have the same sign then the result is positive, negative otherwise.

For example, Simplify the following equation $\mathrm{100\:\div\:(5\:\times\:4)}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:Given\:equation\:is\:100\:\div\:(5\:\times\:4)}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:100\:\div\:20}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:5}$

Integers on the number line

A straight line of numbers is shown visually as a number line. This line is used to compare integers that are spaced equally apart on an infinite line that extends horizontally on both sides.

On a number line, positive and negative integers can be represented visually. Representation of integers on a number line is useful for carrying out mathematical operations. The following are the fundamental considerations to bear in mind while arranging integers on a number line −

• Positive integers are positioned to the right of the number zero because they are bigger than 0

• Negative numbers are positioned to the left of zero because they are less than 0.

• Zero is typically positioned in the middle because it cannot be positive or negative.

Solved Examples

Example 1 − Simplify the following equations $\mathrm{2\:+\:8\:-\:(-5)}$

Solution − Given equation is $\mathrm{2\:+\:8\:-\:(-5)}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:10\:-\:(-5)}$.

We know that the product of two negative signs gives a positive sign now apply this rule

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:10\:+\:5}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:15}$

Example 2 − Simplify the following equations $\mathrm{2\:\times\:(-3)\:+\:8\:(-5)}$

Solution − Given the equation is $\mathrm{2\:\times\:(-3)\:+\:8\:(-5)}$

We know that the product of positive and negative signs gives a negative sign now apply this rule

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:2\:\times\:(-3)\:+\:8\:(-5)}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:-6\:+\:8\:+\:-5}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:-3}$

Example 3 − Simplify the following equations $\mathrm{(2\:\times\:4\:+\:8)\:\div\:4}$

Solution − Given the equation is $\mathrm{(2\:\times\:4\:+\:8)\:\div\:4}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:(8\:+\:8)\:\div\:4}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:16\:\div\:4}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:4}$

Example 4 − Solve $\mathrm{5\:+\:9(2\:\times\:2)\:-\:4}$

Solution − Given equation is $\mathrm{5\:+\:9(2\:\times\:2)\:-\:4}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:5\:+\:9(4)\:-\:4}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:5\:+\:36\:-\:4}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:41\:-\:4}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:37}$

Example 5 − Solve $\mathrm{(12\:+\:14)\:\times\:16}$

Solution − Given equation is $\mathrm{(12\:+\:14)\:\times\:16}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:26\:\times\:16}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:416}$

Example 6 − Solve $\mathrm{(100\:\div\:20)\:+\:5}$

Solution $\mathrm{=\:(100\:\div\:20)\:+\:5}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:5\:+\:5}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:10}$

Example 7 − Simplify the following equation $\mathrm{900\:\div\:[(25\:\times\:4)\:-\:8\:-\:2]}$

Solution − Given equation is $\mathrm{900\:\div\:[(25\:\times\:4)\:-8\:-\:2]}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:900\:\div\:[(100)\:-\:8\:-\:2]}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:900\:\div\:[(100)\:-\:10]}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:900\:\div\:90}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:10}$

Example 8 − Simplify the following equation $\mathrm{(25\:\times\:4)\:-\:(20\:\times\:4)}$

Solution − Given equation is $\mathrm{(25\:\times\:4)\:-\:(20\:\times\:4)}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:100\:-\:8}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:20}$

Example 9 − If a unit test contains 100-question, 10 points are given for each correct response, and 4 points are subtracted for each incorrect response. If Vinod correctly answers 75 questions and he attempts all the question. What is Vinod’s overall score?

Solution − Total number of questions in unit test=100

Points given for each correct question=10

Points deducted for every wrong question=4

Total number question he attempts=100

Vinod’s overall score $\mathrm{=\:75\:\times\:10\:-\:(25\:\times\:4)}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:750\:-\:100}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:650}$

Example 10 − If a bus run at a speed of $\mathrm{10\:\frac{m}{s}}$ for 10min then find the total distance travelled by bus.

Solution $\mathrm{10\:\frac{m}{s}}$

$\mathrm{Total\:time\:=\:10\:min}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:10\:\times\:60\:=\:600\:s}$

$\mathrm{Distance\:travelled\:by\:bus\:=\:600\:\times\:10}$

$\mathrm{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:600\:m}$

Conclusion

The Integer Worksheet covers the addition and subtraction of integers, the addition and subtraction of multiple integers, and the multiplication and division of different integers. An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

FAQs

1. What do you mean by integers?

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion

2. Can negative integers be possible?

Yes, negative integers are possible. Negative integers, such as -1, -2,-3,-4, and so on, are the additive inverse of natural numbers.

3. How many types of integers are there in mathematics?

There are three types of integers: positive integers, zero, and negative integers

4. What do you mean by positive integers?

If a number is greater than zero, it is considered positive. For , 1, 2, 3, etc.

5. What do you mean by negative integers?

Negative numbers are those that are less than zero. For example − -1, -2, -3, etc

6. How to draw integers on number lines?

For drawing integers on number lines we have to follow the following steps.

• Positive integers are positioned to the right of the number zero because they are bigger than 0.

• Negative numbers are positioned to the left of zero because they are less than 0.

• Zero is typically positioned in the middle because it cannot be positive or negative.