Q1
1 Mark
What is the sum of -7 and 3?
A-4
B-10
C10
D-3
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Correct answer: Option 1 — -4
Chapter 7 · Class 7 Mathematics
Integers — Important Questions
SUMMARY: The chapter on Integers in Class 7 Mathematics introduces students to the concept of integers, their properties, and operations involving them.
KEY TOPICS: Introduction to integers, representation on number line, addition of integers, subtraction of integers, properties of addition and subtraction of integers, multiplication of integers, division of integers, properties of multiplication and division of integers, word problems involving integers.
Multiple Choice Questions (MCQs)
5 questions
Q2
1 Mark
Which of the following is equal to -12 + 5?
A-7
B-17
C-8
D7
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Correct answer: Option 1 — -7
Q3
1 Mark
If a temperature drops from -5°C to -12°C, what is the change in temperature?
A-7°C
B7°C
C-17°C
D17°C
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Correct answer: Option 1 — -7°C
Q4
1 Mark
What is the product of -6 and -4?
A24
B-24
C10
D-10
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Correct answer: Option 1 — 24
Q5
1 Mark
Evaluate: -3 × (4 - 7) + 5
A6
B9
C2
D-2
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Correct answer: Option 1 — 6
Short Answer Questions
5 questions
Q6
3 Marks
What is the sum of -7 and 5?
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The sum of -7 and 5 is -2. This is because when you add a positive integer to a negative integer, you subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value.
Q7
3 Marks
Calculate the product of -3 and 4.
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The product of -3 and 4 is -12. When multiplying a negative integer by a positive integer, the result is always negative.
Q8
3 Marks
If you have -10 and you add 15, what is the result?
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The result of adding -10 and 15 is 5. This is because you subtract 10 from 15, which gives you 5.
Q9
3 Marks
What is the result of -8 - (-3)?
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The result of -8 - (-3) is -5. Subtracting a negative number is the same as adding its positive counterpart, so this simplifies to -8 + 3, which equals -5.
Q10
3 Marks
Explain why the product of two negative integers is positive, using an example.
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The product of two negative integers is positive because of the rules of multiplication. For example, -2 multiplied by -3 equals 6. This can be understood as reversing the direction of the number line twice, resulting in a positive value.
Long Answer Questions
5 questions
Q11
6 Marks
Explain the concept of integers and provide examples of positive and negative integers. How do integers differ from natural numbers and whole numbers? Discuss their significance in real-life situations.
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Integers are a set of numbers that include all positive whole numbers, negative whole numbers, and zero. For example, -3, -2, -1, 0, 1, 2, and 3 are all integers. Unlike natural numbers, which only include positive numbers starting from 1, and whole numbers, which include all natural numbers plus zero, integers encompass both negative and positive values. Integers are significant in real life as they can represent temperatures below and above zero, financial debts and credits, and various other situations where quantities can be both positive and negative.
Q12
6 Marks
Demonstrate how to perform addition and subtraction of integers with examples. What rules do we follow when adding or subtracting integers with different signs?
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To perform addition and subtraction of integers, we follow specific rules based on their signs. For example, when adding two integers with the same sign, we add their absolute values and keep the common sign. For instance, (-4) + (-3) = -(4 + 3) = -7. When adding integers with different signs, we subtract the smaller absolute value from the larger absolute value and take the sign of the integer with the larger absolute value. For example, (-5) + 3 = -(5 - 3) = -2. Subtraction can be converted to addition by changing the sign of the integer being subtracted. For example, 5 - (-3) becomes 5 + 3 = 8.
Q13
6 Marks
Solve the following integer problems: a) -7 + 5 - 3 + 2 b) 6 - (-4) + (-2). Show your calculations step by step and explain each step.
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To solve a) -7 + 5 - 3 + 2, we first add -7 and 5, which gives us -2. Next, we subtract 3 from -2, resulting in -5. Finally, we add 2 to -5, leading to -3. Therefore, the answer is -3. For b) 6 - (-4) + (-2), we first convert the subtraction of a negative to addition: 6 + 4 = 10. Then we add -2 to 10, which results in 8. Thus, the final answer is 8. Each step involves applying the rules of integer addition and subtraction carefully to arrive at the correct results.
Q14
6 Marks
Discuss the multiplication of integers, including the rules for multiplying integers with the same and different signs. Provide examples to illustrate your explanation.
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The multiplication of integers follows specific rules based on their signs. When multiplying two integers with the same sign, the result is always positive. For example, (-3) × (-4) = 12 and (5) × (2) = 10. Conversely, when multiplying integers with different signs, the result is negative. For instance, (-3) × (4) = -12 and (3) × (-4) = -12. Understanding these rules is crucial for solving problems involving integers, as they help in determining the sign of the product based on the signs of the factors involved.
Q15
6 Marks
Explain the concept of absolute value in integers. How does it apply to both positive and negative integers? Provide examples and discuss its importance in mathematical operations.
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The absolute value of an integer is defined as its distance from zero on the number line, regardless of direction. It is always a non-negative value. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5, denoted as |5| = 5 and |-5| = 5. Absolute value is important in mathematical operations as it allows us to compare magnitudes without considering their signs. This concept is particularly useful in solving equations and inequalities involving integers, as it helps in simplifying expressions and understanding the relationships between different integer values.
Assertion–Reason Questions
5 questions
Q16
1 Mark
Assertion (A): The sum of two negative integers is always negative.
Reason (R): Adding two negative numbers results in a larger negative number.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q17
1 Mark
Assertion (A): The product of two integers is always positive.
Reason (R): The product of two negative integers is negative.
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Correct answer: Option 3 —
A is true, but R is false.
Q18
1 Mark
Assertion (A): Zero is an integer.
Reason (R): Zero is neither positive nor negative.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q19
1 Mark
Assertion (A): The difference between two integers can be negative.
Reason (R): Subtracting a larger integer from a smaller integer results in a positive number.
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Correct answer: Option 3 —
A is true, but R is false.
Q20
1 Mark
Assertion (A): The absolute value of an integer is always positive.
Reason (R): Absolute value measures the distance from zero.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Statement-Based Questions
5 questions
Q21
1 Mark
Statement 1: -5 is greater than -10.
Statement 2: -3 is less than -1.
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Correct answer: Option 1 —
Both statements are true.
Q22
1 Mark
Statement 1: The sum of -7 and 4 is -3.
Statement 2: The product of -2 and 5 is -10.
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Correct answer: Option 2 —
Only Statement 1 is true.
Q23
1 Mark
Statement 1: -12 + 8 = -4.
Statement 2: -6 + 6 = 0.
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Correct answer: Option 3 —
Only Statement 2 is true.
Q24
1 Mark
Statement 1: -9 is less than -8.
Statement 2: -15 is greater than -20.
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Correct answer: Option 4 —
Both statements are false.
Q25
1 Mark
Statement 1: The absolute value of -4 is 4.
Statement 2: The absolute value of -7 is -7.
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Correct answer: Option 1 —
Both statements are true.
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