How to Solve Integers Questions with Rules Properties and Examples
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
- 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 Integers Practice Questions and Solutions Guide
1. What are integers in maths?
Integers are whole numbers that include positive numbers, negative numbers, and zero, without any fractions or decimals.
- They include: ..., −3, −2, −1, 0, 1, 2, 3, ...
- Positive integers: 1, 2, 3, ...
- Negative integers: −1, −2, −3, ...
- Zero is neither positive nor negative.
2. What is the difference between integers and whole numbers?
The main difference is that integers include negative numbers, while whole numbers do not.
- Whole numbers: 0, 1, 2, 3, ...
- Integers: ..., −3, −2, −1, 0, 1, 2, 3, ...
3. How do you add integers with different signs?
To add integers with different signs, subtract their absolute values and keep the sign of the number with the larger absolute value.
- Step 1: Find the absolute values.
- Step 2: Subtract the smaller from the larger.
- Step 3: Keep the sign of the integer with the greater absolute value.
4. How do you subtract integers?
Subtracting integers means adding the opposite of the second number.
- Rule: a − b = a + (−b)
- Change the subtraction sign to addition.
- Change the sign of the second integer.
5. What are the rules for multiplying integers?
The rules for multiplying integers depend on their signs.
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
- Negative × Positive = Negative
6. What are the rules for dividing integers?
The rules for dividing integers are the same as multiplying integers with respect to signs.
- Same signs → Positive result
- Different signs → Negative result
7. What is the absolute value of an integer?
The absolute value of an integer is its distance from zero on the number line, always written as a non-negative number.
- Notation: |a|
- |5| = 5
- |−5| = 5
8. What are the properties of integers?
Integers follow important mathematical properties under addition and multiplication.
- Closure property: Sum or product of integers is an integer.
- Commutative property: a + b = b + a; a × b = b × a.
- Associative property: (a + b) + c = a + (b + c).
- Distributive property: a × (b + c) = ab + ac.
9. How do you represent integers on a number line?
Integers are represented on a number line with zero in the center, positive numbers to the right, and negative numbers to the left.
- Mark 0 at the center.
- Move right for positive integers (1, 2, 3...).
- Move left for negative integers (−1, −2, −3...).
10. What are some real-life examples of integers?
Integers are used in real life to represent quantities above and below a reference point.
- Temperature: −5°C and +10°C
- Bank balance: −₹500 (debt), +₹1000 (credit)
- Elevator floors: Basement (−1), Ground (0), 5th floor (+5)
