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All questions of Integers for Grade 7 Exam

Which integer is greater than –5?
  • a)
    –7
  • b)
    –1
  • c)
    –9
  • d)
    –11
Correct answer is option 'B'. Can you explain this answer?

Hridoy Menon answered
An integer on the horizontal number line is greater than the number on its left and less than the number on its right. 
So -1 will be greater than -5.
So option B is the correct answer.  

−5 × (−6) = ?
  • a)
    5
  • b)
    -30
  • c)
    6
  • d)
    30
Correct answer is 'D'. Can you explain this answer?

Shalini Menon answered
-5 x -6 = 30  ( because - x - = + ) 
So option D is the correct answer. 

Can you explain the answer of this question below:

What is the absolute value of |340|?

  • A:

    1

  • B:

    -340

  • C:

    0

  • D:

    340

The answer is c.

**What is the absolute value of |340|?**

The absolute value of a number is its distance from zero on the number line. It tells us the magnitude or size of the number, irrespective of its sign. In this case, we are asked to find the absolute value of 340.

**Explanation:**

To find the absolute value of 340, we need to consider its distance from zero on the number line. Since 340 is a positive number, its absolute value will be the same as the number itself.

Here's a step-by-step breakdown of the solution:

1. Start by identifying the given number: 340.

2. Recall that the absolute value of a number is always non-negative.

3. Since 340 is a positive number, its absolute value will be the same as the number itself.

4. Therefore, the absolute value of 340 is 340.

**Conclusion:**

The absolute value of 340 is 340.

−5 × (−6) = ?
  • a)
    5
  • b)
    -30
  • c)
    6
  • d)
    30
Correct answer is option 'D'. Can you explain this answer?

Akshara Bajaj answered
-5 x -6 = 30  ( because - x - = + ) 
So option D is the correct answer. 

How many integers are there between –8 and 2 (excluding -8 and 2)?
  • a)
    7
  • b)
    4
  • c)
    0
  • d)
    9
Correct answer is option 'D'. Can you explain this answer?

Anuj Yadav answered
The integers between -8 & 2 are : -7 , -6 , -5 , -4 , -3 , -2 , -1 , 0 , 1 
So there are 9 integers between -8 & 2
So , option D is correct. 
 

−5 × (6) = ?
  • a)
    6
  • b)
    5
  • c)
    -30
  • d)
    30
Correct answer is option 'C'. Can you explain this answer?

Rishika Yadav answered
−5 × (6) = -30  (Negative sign is because
  - x + = - )
So option C is the correct answer. 

If a = 20, b = 40 and c = 80 then a x b + a x c must be equal to
  • a)
    2400
  • b)
    3200
  • c)
    1600
  • d)
    4000
Correct answer is option 'A'. Can you explain this answer?

Given values are :
a = 20
b = 40 and
c = 80
So a x b + a x c= 20 x 40 + 20 x 80 
= 800 + 1600
= 2400 
So optin A is correct answer. 

Which of the following order is used while evaluating an expression?
  • a)
    [],(),{}
  • b)
    {},(),[]
  • c)
    (),[],{}
  • d)
    (),{},[]
Correct answer is option 'D'. Can you explain this answer?

(),{},[] is the correct order of evaluation of brackets. The order of brackets used when evaluating an expression is [ { ( ) } ], which means that the innermost brackets (round brackets) are evaluated first, followed by the curly brackets, and finally the square brackets.

(−12 - 3) ÷ (− 6 + 3) = _________
  • a)
    5
  • b)
    3
  • c)
    -5
  • d)
    -3
Correct answer is option 'A'. Can you explain this answer?

(−12 - 3) = -15
(− 6 + 3) = -3
⇒ (−12 - 3) ÷ (− 6 + 3) = (-15) ÷ (-3) = 5

The value of [(-4) x (-9) x (-25)] ÷ [(-2) x (-3) x (-5)] is:
  • a)
    30
  • b)
    20
  • c)
    10
  • d)
    40
Correct answer is option 'A'. Can you explain this answer?

  • Firstly we will solve brackets according to BODMAS rule,
    (-4) x (-9) x (-25) = -900 (multiplication of odd number of negative integers gives a negative integer)
    (-2) x (-3) x (-5) = -30 (-900) / (-30) = 30 (division of even number of integers gives a positive integer)

If a x (b −c) is 8 for a = 2, b = 10 and c = 6 then a x b − a x c is equal to
  • a)
    (−8)
  • b)
    12
  • c)
    10
  • d)
    8
Correct answer is option 'D'. Can you explain this answer?

Using BODMAS
a x (b −c) = a x b - a x c
8 = 2 x 10 - 2 x 6
8 = 20 - 12 
8 = 8 
So option D is the correct answer. 

−4 × (−7) = ?
  • a)
    7
  • b)
    4
  • c)
    28
  • d)
    -28
Correct answer is option 'C'. Can you explain this answer?

Niharika Menon answered
−4 × (−7) =  -4 x -7   (By BODMAS rule)
                = 28          ( - x - = + )
So option C is correct answer.

(-20) × (-5) is equal to
  • a)
    100
  • b)
     20
  • c)
    – 100
  • d)
    5
Correct answer is option 'A'. Can you explain this answer?

Correct answer is D) 100.
we know 20×5=100 and -ve multiplied by a -ve gives a +ve value. So there is no -ve sign in 100.

−45 ÷ (−9) =?
  • a)
    -5
  • b)
    5
  • c)
    9
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Wahid Khan answered
−45 ÷ (−9) = -45 / -9 = 5 ( Because 9 x 5 = 45 )

So option B is the correct answer.

What is the absolute value of |-2677|?
  • a)
    2677
  • b)
    -2677
  • c)
    0
  • d)
    1
Correct answer is option 'A'. Can you explain this answer?

Shilpa Das answered
Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative.

So, absolute value of |-2677| = 2677.

Manish deposits Rs 2000 in his bank account and withdraws Rs 1000 from it, the next day. Find the balance in Manish’s account after the withdrawal.
  • a)
    Rs 2000
  • b)
    Rs 3000
  • c)
    Rs 1000
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Manish deposits amount = 2000
Manish withdraws amount = -1000 [ writing -ve as  it is withdrawl ]
Balance of Manish's account = 2000 + (-1000) = Rs 1000
Thus option C is correct.

(-1) × (-1) × (-1) × ......... (2m + 1) times, where m is a natural number, is equal to:
  • a)
    -1
  • b)
    1
  • c)
    1 or -1
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Write down the given expression
The given expression is
( - 1) × ( - 1) × ( - 1) × ____ 2m times where m is a natural number,

Since m is a natural number
So 2m is even
Thus we get
( - 1) × ( - 1) × ( - 1) × ____ 2m times

With respect to which of the following operations is closure property satisfied by the set of integers?
  • a)
    +,×                    
  • b)
    +,÷,×
  • c)
    +,×,−                   
  • d)
    +,−,÷
Correct answer is option 'C'. Can you explain this answer?

Lavanya Menon answered
The closure property states that when you perform an operation on any two numbers in a set, the result of the computation is another number in the same set .Since division can result in changing an integer in decimals. So its closed in addition, subtraction and multplication.

6 × (−15 + 10) = ______
  • a)
    30
  • b)
    -21
  • c)
    -30
  • d)
    21
Correct answer is option 'C'. Can you explain this answer?

Ananya Das answered
According to BODMAS,
6 × (−15 + 10) = 6 × (-5) = -30
[∵ -15 + 10 = -5]

What will be the additive inverse of 7?
  • a)
    -6
  • b)
    -7
  • c)
    -5
  • d)
    -4
Correct answer is option 'B'. Can you explain this answer?

  • The additive inverse of a number a is the number that, when added to a, gives zero. This number is also known as the opposite number.
  • So, when -7 is added to 7 it gives 0. 
    -7 + 7 = 0 
  • Thus, -7 is the additive inverse of 7.

The multiplicative identity for integers is:
  • a)
    1
  • b)
    -1
  • c)
    0
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Gaurav Menon answered
**Multiplicative Identity for Integers**

The multiplicative identity for integers is the number which, when multiplied by any integer, results in the original integer. In other words, it is the number that leaves any integer unchanged when multiplied by it.

The multiplicative identity for integers can be represented by the number 1.

**Explanation:**

When we multiply any integer by 1, the result is always the original integer. For example,

- 7 x 1 = 7
- (-5) x 1 = -5
- 0 x 1 = 0

No matter what integer we choose, multiplying it by 1 will always give us the same integer.

**Properties of Multiplicative Identity:**

The multiplicative identity has some important properties:

1. **Identity Property**: The multiplicative identity is often referred to as the identity element because it preserves the identity of other numbers when they are multiplied.

2. **Unique Property**: The multiplicative identity is unique, meaning there is only one number that can act as the multiplicative identity for all integers. In the case of integers, this number is 1.

3. **Closure Property**: The closure property of multiplication states that when two integers are multiplied, the result is always an integer. The multiplicative identity, being an integer, also follows this property.

**Conclusion:**

In conclusion, the multiplicative identity for integers is 1. When any integer is multiplied by 1, the result is always the original integer. This property is known as the identity property of multiplication, and the number 1 is the unique number that satisfies this property for all integers.

What is the absolute value of |-45|?
  • a)
    -45
  • b)
    1
  • c)
    45
  • d)
    0
Correct answer is 'C'. Can you explain this answer?

The absolute value of a number is how far away the number is from zero. The absolute value is ALWAYS positive. So, absolute value of |-45| is 45.

What is the opposite of earning Rs. 100?
  • a)
    + Rs. 100     
  • b)
    Profit of Rs. 100
  • c)
    Gain of Rs. 100
  • d)
    Spending Rs. 100  
Correct answer is option 'D'. Can you explain this answer?

Opposite of earning Rs. 100 is spending Rs. 100.

Explanation:
Earning Rs. 100 means acquiring or receiving Rs. 100 as income or profit. On the other hand, spending Rs. 100 involves utilizing or giving away Rs. 100 to purchase goods or services. Let's break down the concept further:

Earning Rs. 100:
- When you earn Rs. 100, it implies that you have gained Rs. 100 as a result of your work, investment, or any other source of income.
- Earning money typically involves receiving payment for goods sold, services rendered, or work performed.

Spending Rs. 100:
- Conversely, spending Rs. 100 means you are using Rs. 100 to purchase something.
- Spending money is a common activity where individuals exchange their currency for goods, services, or experiences.

Opposite Relationship:
- Earning and spending are opposing actions when it comes to money management.
- When you earn money, you accumulate wealth or increase your financial resources.
- Conversely, spending money reduces your financial resources as you exchange it for goods and services.

Options Analysis:
a) Rs. 100: This option represents the same amount of money, so it cannot be the opposite of earning Rs. 100.
b) Profit of Rs. 100: Profit refers to the positive difference between revenue and expenses. It is not the opposite of earning Rs. 100.
c) Gain of Rs. 100: Gain is similar to earning and does not represent the opposite action.
d) Spending Rs. 100: This option aligns with the opposite relationship as explained above. When you spend money, you are utilizing it rather than earning it.

Therefore, the correct answer is option 'D' - Spending Rs. 100.

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