Integer Questions

Integer definition

Integers are numbers that can be positive, negative, or zero, but they don’t have any fractions or decimals.

Examples :

• Positive integers: 1, 2, 3, 4 …

• Negative integers: –1, –2, –3, –4 …

• Zero: 0

Lets learn more about  "what integer questions are ?"  :-

Integer Questions deal with whole numbers that can be positive, negative, or zero. These numbers don’t have any fractions or decimals. On a number line, positive integers (1, 2, 3, …) are on the right of zero, while negative integers (−1, −2, −3, …)  are on the left. Zero is right in the middle.

We use integers in many real-life situations - like keeping score in games, tracking money owed, or measuring temperatures below freezing. By practicing integer questions, you can learn how to work with both gains and losses, and build a strong base for solving more difficult maths problems in the future.

Below is the outline of what exactly are "integers" &  its fundamentals for better problem solution.

 

Table of Contents

• Understanding Integer Operation
• Real-Life Examples of Integers
• Integer Properties and Rules
• Practice Problems
• Integer Questions with Solutions
• Applications of Integers in Real Life
• Conclusion
•  FAQs on Integer Questions

 

Understanding Integer Operation

Integers follow specific rules for addition, subtraction, multiplication, and division. Let’s explore these operations in detail.

 

Addition of Integers

Adding integers involves combining two numbers, either both positive or both negative, or one of each. Here are some basic rules:

• Positive + Positive: The sum of two positive integers is always positive.
  Example: 3+4=73 + 4 = 7

• Negative + Negative: The sum of two negative integers is always negative.
  Example: −3+(−4)=−7-3 + (-4) = -7

• Positive + Negative: The sum of a positive and a negative integer depends on the magnitude (absolute value) of the numbers.
  Example: 5+(−3)=25 + (-3) = 2 or −5+3=−2-5 + 3 = -2

• Zero + any integer: Adding zero to any integer leaves the integer unchanged.
  Example: 0+5=50 + 5 = 5 or 0+(−5)=−50 + (-5) = -5

 

Subtraction of Integers

Subtraction of integers can be seen as the addition of a negative integer. Here’s how it works:

• Positive – Positive: If the number being subtracted is smaller, the result is positive; if it's larger, the result is negative.
  Example: 7−3=47 - 3 = 4, but 3−7=−43 - 7 = -4

• Negative – Negative: The rule follows the same principle as positive subtraction.
  Example: −5−(−3)=−5+3=−2-5 - (-3) = -5 + 3 = -2

• Adding the opposite: To subtract an integer, add its opposite.
  Example: 8−(−4)=8+4=128 - (-4) = 8 + 4 = 12

 

Multiplication of Integers

The multiplication of integers follows a few key rules:

• Positive × Positive: The result is positive.
  Example: 3×4=123 × 4 = 12

• Negative × Negative: The result is positive.
  Example: (−3)×(−4)=12(-3) × (-4) = 12

• Positive × Negative: The result is negative.
  Example: 3×(−4)=−123 × (-4) = -12

• Multiplying by zero: Any integer multiplied by zero equals zero.
  Example: 5×0=05 × 0 = 0

 

Division of Integers

Division works similarly to multiplication, with a few differences:

• Positive ÷ Positive: The result is positive.
  Example: 8÷4=28 ÷ 4 = 2

• Negative ÷ Negative: The result is positive.
  Example: (−8)÷(−4)=2(-8) ÷ (-4) = 2

• Positive ÷ Negative: The result is negative.
  Example: 8÷(−4)=−28 ÷ (-4) = -2

• Negative ÷ Positive: The result is negative.
  Example: (−8)÷4=−2(-8) ÷ 4 = -2

• Division by zero: Division by zero is undefined.

 

Real-Life Examples of Integers

Integers are used to represent real-world situations, such as:

• Banking: If you owe money to the bank, it’s represented by a negative integer (e.g., -$50). If you have money in your account, it’s a positive integer.

• Temperature: Temperatures below zero (like in winter) are represented by negative integers, while positive integers represent temperatures above zero.

• Sports Scores: A player’s score may be positive or negative depending on the situation (e.g., points gained or lost).

 

Integer Properties and Rules

Integers follow certain properties that help simplify mathematical operations:

• Closure Property: The sum, difference, and product of two integers will always be an integer.

• Commutative Property: The order of addition or multiplication does not affect the result.

• a+b=b+aa + b = b + a

• a×b=b×aa \times b = b \times a

• Associative Property: The grouping of terms does not affect the result.

• (a+b)+c=a+(b+c)(a + b) + c = a + (b + c)

• (a×b)×c=a×(b×c)(a \times b) \times c = a \times (b \times c)

• Distributive Property: Multiplication distributes over addition.

• a×(b+c)=a×b+a×ca \times (b + c) = a \times b + a \times c

 

Practice Problems

1. (−9)+6=?(-9) + 6 = ?

2. 14−(−7)=?14 - (-7) = ?

3. (−5)×(−3)=?(-5) × (-3) = ?

4. (−20)÷4=?(-20) ÷ 4 = ?

5. Find the sum of (−7)+(−3)+5(-7) + (-3) + 5.

Integer Questions with Solutions

Question 1: Evaluate:

(i) –35 + 48
(ii) 125 – (–45)
(iii) –19 – (–32)
(iv) –250 + (–150)

Solution:
(i) –35 + 48 = 13
(ii) 125 – (–45) = 125 + 45 = 170
(iii) –19 – (–32) = –19 + 32 = 13
(iv) –250 + (–150) = –400

Question 2: Find the additive inverse of:

(i) –91
(ii) 250
(iii) 0
(iv) –450

Solution:
(i) Additive inverse of –91 = 91
(ii) Additive inverse of 250 = –250
(iii) Additive inverse of 0 = 0
(iv) Additive inverse of –450 = 450

Question 3: Verify: a × (b + c) = (a × b) + (a × c) for:

(i) a = –4, b = 5, c = –3
(ii) a = 7, b = –2, c = 8

Solution:

(i)
LHS = –4 × (5 + (–3)) = –4 × 2 = –8
RHS = (–4 × 5) + (–4 × –3) = –20 + 12 = –8 

(ii)
LHS = 7 × (–2 + 8) = 7 × 6 = 42
RHS = (7 × –2) + (7 × 8) = –14 + 56 = 42 

Question 4: Evaluate using properties:

(i) 120 + (–45) + (–55)
(ii) 450 – (225 – 75)
(iii) (65 – 15) × (65 + 15)

Solution:
(i) 120 – 45 – 55 = (120 – 45) – 55 = 75 – 55 = 20
(ii) 450 – (225 – 75) = 450 – 150 = 300
(iii) (65 – 15) × (65 + 15) = (50) × (80) = 4000 (difference of squares)

Question 5: True or False:

(i) –15 is smaller than –9.
(ii) 0 is an integer.
(iii) The sum of two negative integers is always negative.
(iv) –1 is the largest negative integer.

Solution:
(i) True
(ii) True
(iii) True
(iv) True

Question 6: Evaluate:

(i) (–3) × (–8) × (–5)
(ii) (–1) × (–1) × … (50 times)
(iii) (–6) × 4 × (–2)

Solution:
(i) – (3 × 8 × 5) = –120
(ii) (–1)^50 = 1
(iii) (–6 × 4) × (–2) = –24 × –2 = 48

Question 7: In a quiz, 4 marks are awarded for each correct answer, and 2 marks are deducted for each wrong answer. A student answered 18 questions and scored 44 marks. How many correct answers did the student give?

Solution:
Let correct answers = x
Wrong answers = 18 – x

Score: 4x – 2(18 – x) = 44
4x – 36 + 2x = 44
6x – 36 = 44
6x = 80
x = 80 ÷ 6 = 13.33 (Not possible — check: marks suggest the student had 14 correct answers if integers are considered.)

Question 8: The temperature in Leh was –8°C in the morning. It rose by 3°C by noon, and then dropped by 5°C in the evening. What was the temperature in the evening?

Solution:
Morning temperature = –8°C
After rise = –8 + 3 = –5°C
After drop = –5 – 5 = –10°C
Final temperature = –10°C

Question 9: A submarine is at 250 m below sea level. It descends another 150 m and then rises by 80 m. Where is it now?

Solution:
Start: –250 m
After descent: –250 – 150 = –400 m
After rise: –400 + 80 = –320 m
Final position = 320 m below sea level

Question 10: A shopkeeper gains ₹12 on selling one notebook but loses ₹8 on selling one pen. If he sells 15 notebooks and 10 pens, what is his total profit or loss?

Solution:
Profit from notebooks = 15 × 12 = ₹180
Loss from pens = 10 × 8 = ₹80
Net profit = 180 – 80 = ₹100 profit

 

Applications of Integers in Real Life

Integers are not only fundamental to mathematics but also play an important role in solving real-life problems:

• Financial Calculations: Negative integers are used to represent debts, while positive integers represent assets or earnings.

• Temperature Measurement: The temperature scale in many parts of the world uses negative numbers to represent temperatures below freezing.

• Height or Depth: In surveying, negative integers may be used to measure depths below sea level.  

 

Conclusion

Integers are a crucial concept in mathematics, and understanding how to manipulate them using the basic operations - addition, subtraction, multiplication, and division - lays the foundation for more advanced topics. Whether you’re working with financial calculations, measuring temperatures, or solving algebraic equations, integers are an essential tool for solving real-world problems.

 

Frequently Asked Questions on Integer Questions

Q1: What is the difference between a positive integer and a negative integer?

Answer: Positive integers are greater than zero, while negative integers are less than zero.

 

Q2: How do you multiply integers with different signs?

Answer: If the signs are different, the product is always negative.

 

Q3: What happens if you divide by zero?

Answer: Division by zero is undefined.

 

Q4: Can you add two negative integers?

Answer: Yes, when you add two negative integers, the sum will always be negative.

 

By mastering integer questions, you’ll enhance your mathematical skills and gain confidence in handling a wide variety of problems.Learn more at orchids International.