Download Free Worksheets & Tips for Excelling in Integers
The concept of integers questions is essential in mathematics and helps students practise operations like addition, subtraction, multiplication, and division of whole numbers, including negatives and zero. Being strong in integers questions benefits you in board exams and real-life scenarios.
Understanding Integers Questions
An integers question typically asks you to solve problems involving both positive and negative whole numbers. Integers include {..., -3, -2, -1, 0, 1, 2, 3, ...}, so they are different from natural numbers or whole numbers as negatives are included. Integers questions for class 6 and higher often test your skills in performing operations of integers, understanding ordering of integers, and applying them in word problems.
Key Rules and Properties of Integers
Here are some important rules you need when working on integers questions:
2. The sum of two negative integers is always negative.
3. The sum of a positive and a negative integer equals their difference. The sign will be of the greater absolute value.
4. Subtracting an integer is the same as adding its additive inverse.
5. Multiplying two integers with the same sign gives a positive result. With opposite signs, the result is negative.
6. Division follows the same sign rules as multiplication.
Table: Examples of Integer Operations
Here’s a helpful table to understand integers questions more clearly:
| Operation | Example | Result |
|---|---|---|
| Addition | -8 + 5 | -3 |
| Subtraction | 7 - (-4) | 11 |
| Multiplication | -2 × -3 | 6 |
| Division | -12 ÷ 3 | -4 |
This table shows how integers questions require understanding math operations with both positive and negative numbers.
Worked Example – Solving an Integers Question
Let’s solve an example from typical class 6–8 integers questions with all steps shown:
2. Step 1: Notice that subtracting a negative is the same as adding its positive.
3. Step 2: Calculate \( 22 - (-87) = 22 + 87 \)
4. Step 3: Add 22 and 87 to get 109.
Answer: \( 22 - (-87) = 109 \)
Practice Integers Questions
Try these practice integers questions for different classes:
2. Evaluate: \( -16 + 28 - (-32) \)
3. Out of 20 test questions, each correct answer scores 5 points, and each wrong answer deducts 2 points. If you got 15 answers correct, what’s your score?
4. If a room is cooled at 4⁰C per minute, starting from 45⁰C, what will be the temperature after 6 minutes?
5. True or False: The sum of two negative integers is always a positive integer.
Stepwise Solutions – Sample Answers
Let’s see stepwise solutions for two of the questions above:
- The additive inverse is the number which, when added to -39, results in zero.
- Additive inverse of -39 = -(-39) = 39.
Final Answer: 39
2. Evaluate \( -16 + 28 - (-32) \)
Step 1: \( -16 + 28 = 12 \)
Step 2: \( 12 - (-32) = 12 + 32 = 44 \)
Final Answer: 44
Common Mistakes to Avoid in Integers Questions
- Mixing up the subtraction sign and a negative integer (e.g., confusing -7 and “subtract 7”).
- Forgetting to change two negatives into a positive when subtracting (- minus - = +).
- Assuming the sum of two negatives gives a positive integer (it does not).
- Making sign errors in multiplication and division (like thinking - × - = - instead of +).
Real-World Applications of Integers
You use integers questions in daily life for situations like temperature changes above/below zero, profits and losses, elevator floors above/below ground, and banking credits or debits. Practising integers questions helps you develop strong number sense. At Vedantu, you can learn more about such examples and applications in maths.
Learn More – Related Topics
To master integers questions for class 6, class 7, class 8, or higher competitive exams, also review these helpful maths topics:
- What is an Integer?
- Integers
- Operations of Integers
- Ordering of Integers
- Addition and Subtraction of Integers
- Multiplication and Division of Integers
- Properties of Integers
- Integer Worksheet
- Number System
- Negative Numbers in Daily Life
We explored the idea of integers questions, how to solve them, and their importance in exams and life. Practise regularly with Vedantu to get better at these mathematical concepts and perform well in school assessments!
FAQs on Practice Top Integers Questions with Stepwise Solutions
1. What are integers?
Integers are the set of all whole numbers and their negatives, including zero. This means they include positive numbers (1, 2, 3, ...), negative numbers (–1, –2, –3, ...), and zero. Integers do not include fractions or decimals and form the foundation for many arithmetic operations and problem-solving scenarios in mathematics.
2. What is the best way to solve integer questions?
To solve integer questions effectively: (1) Identify the signs of the numbers involved; (2) Apply the correct integer operation rules for addition, subtraction, multiplication, or division; (3) Use a number line to visualize the problem if necessary; and (4) Verify each step carefully to avoid sign errors, especially with negatives and zero.
3. Can you give 10 integer examples?
Here are 10 examples of integers: –9, –5, –1, 0, 1, 4, 7, 12, –15, and 20. These include negative integers, zero, and positive integers, showing the entire range covered by the integer set.
4. What are the 4 types of integers?
The four types of integers commonly studied are: (1) Positive Integers (1, 2, 3,...), which are greater than zero; (2) Negative Integers (–1, –2, –3,...), which are less than zero; (3) Zero (0), which is neutral; and (4) Whole Numbers, which include zero and positive integers but no negatives. Understanding these types helps in solving various integer problems.
5. Where can I find integer questions with answers for class 6 and 7?
You can find integer questions with answers for class 6 and 7 on dedicated educational platforms like Vedantu. They offer practice worksheets, step-by-step solutions, and topic-wise questions aligned with CBSE and other syllabi, helping students prepare effectively for exams and homework.
6. Why do many students mix up negative integers with subtraction signs?
Many students confuse negative integers with the subtraction sign because both use the minus (–) symbol. The key difference is that the minus sign indicates an operation, while a negative integer is a number less than zero. To avoid confusion, always determine whether the minus represents an operation or a sign before proceeding.
7. What is the difference between zero and a positive integer in questions?
In integer questions, zero is the integer that represents 'no quantity' and is neither positive nor negative. In contrast, a positive integer is any integer greater than zero. This distinction is important for ordering numbers, operations, and properties linked to integers.
8. Why aren't fractions or decimals considered integers?
Integers only include whole numbers and their negatives without any fractional or decimal parts. Since fractions and decimals represent parts of a whole rather than whole units, they are classified differently under the number system—for example, as rational numbers—rather than integers.
9. Why does integer ordering sometimes confuse students in exams?
Students often struggle with integer ordering because comparing negative numbers is less intuitive than positives. Remember, on the number line, numbers increase from left to right, so a number farther to the left is smaller. For example, –10 is smaller than –7 because it is further left on the number line.
10. How do integer rules help in competitive exams like Olympiad/NTSE?
Mastering integer rules is essential for competitive exams such as Olympiad and NTSE because these exams test accuracy and speed in arithmetic operations involving positive and negative numbers. Understanding how to add, subtract, multiply, and divide integers quickly and correctly gives students an edge in problem-solving and ensures readiness for these challenges.
