Get the simplified Class 7 Maths Extra Questions and Class 7 Maths Part 2 Chapter 2 Operations with Integers Extra Questions and Answers with complete explanation.
Class 7 Operations with Integers Extra Questions
Operations with Integers Extra Questions Class 7
Operations with Integers Class 7 Very Short Question Answer
Question 1.
If 135 × 246 = 33210, without calculating, find the value of (-135) × (-246).
Solution :
Here, we have given that 135 × 246 = 33210.
Since we know that when both the multiplier and multiplicand are negative, the product is positive.
∴ (-135) ×(-246) = 33210
Question 2.
Replace the blank with an integer to make a true statement.
……… × (-9) = (-63)
Solution :
………… ×(-9) = (-63)
∴ (-63) ÷ 7 = -9 Thus, 7 ×(-9) = (-63)
Question 3.
Find the value of the following expression :
-4 ×(16 + (-5))
Solution :
-4 ×(16 + (-5)) = -4 ×(16-5)
= -4 × 11 = -44
Question 4.
Find the value of:
(12 ×(-16)) ÷(-32)
Solution :
(12 ×(-16)) ÷(-32) = \(\frac{12 \times(-16)}{-32}\)
= \(\frac{12}{2}\) = 6
Question 5.
Evaluate the following :
6 ×[8 + (-5)]
Solution :
6 ×[8 + (-5)] = 6 × 8 + 6 ×(-5)
= 48 – 30 = 18
Question 6.
In a quiz of 12 questions, students score +4 marks for each correct answer, -1 mark for each incorrect answer, and 0 marks for any question not attempted.
Ayan answers 7 questions correctly and 3 questions incorrectly, leaving the rest unattempted. What is his final score?
Solution :
Final score = (7 × 4) + 3 ×(-1) + 2 × 0
= 28-3 + 0 = 25 marks.
Operations with Integers Class 7 Short Question Answer
Question 1.
Find each of the following products :
(i) (-18) ×(-10) × 9
Solution :
(-18) × (-10) × 9
(-18) × (-10) = + 180
180 × 9 = 1620
(ii) (-20) ×(-2) ×(-5) × 7
Solution :
(-20) × (-2) × (-5) × 7
(-20) × (-2) = + 40
40 × (-5) = 200
-200 × 7 = -1400
(iii) (-1) × (-5) × (-4) × (-6)
Solution :
(-1) × (-5) × (-4) × (-6)
(-1) × (-5) = + 5
5 × (-4) = -20
-20 × (-6) = + 120
Question 2.
An elevator descends into a mine shaft at the rate of 6m/min. If the descent starts from 10 m above the ground level, how long will it take to reach – 350 m.
Solution :
Given :
Rate of descent = 6m/min (downward, so it is negative)
Starting position = + 10m (above ground level)
Final position = -350 m (below ground level)
Find the total distance travelled :
Total distance = (-350) – (+10) = -360 m
Using the formula :
Time = \(\frac{Distance}{Speed}\)
Time = \(\frac{-360}{-6}\) = 60 minutes
∴ The elevator will take 60 minutes to reach -350 m.
Question 3.
The product (-8) ×(-4) × (-5) × (-2) is positive whereas the product (-8) × (-4) × 5 × (-2) is negative. Why?
Solution :
Since, the product of integers is : Positive if the number of negative factors is even.
Negative if the number of negative factors is odd.
(-8) × (-4) × (-5) × (-2) = Positive
∵ Total = 4 negative numbers → an even number.
Therefore, the product is positive.
But (-8) × (-4) × 5 × (-2) = Negative
∵ Total = 3 negative numbers → an odd number.
Therefore, the product is negative.
Question 4.
What will be the sign of the product if we multiply together :
(a) 10 negative integers and 5 positive integers?
(b) 101 negative integers and 500 positive integers?
Solution :
We know that
Even number of negative integers → Product is positive
Odd number of negative integers → Product is negative
Positive integers do not change the sign.
(a) 10 negative integers and 5 positive integers Number of negative integers = 10 (which is even)
Hence, the product is positive.
(b) 101 negative integers and 500 positive integers
Number of negative integers = 101 (which is odd)
Hence, the product is negative.
Question 5.
Verify that p ÷ (q + r) ≠ (p ÷ q) + (p ÷ r) for each of the following values of p, q and r.
(a) p = -12, q = -4, r = 2
Solution :
p = -12, q = -4, r = 2
L.H.S. = p ÷ (q + r) = (-12) ÷ (-4 + 2)
= (-12) ÷(-2) = 6
R.H.S. = (p ÷ q) + (p ÷ r) = [(-12)] ÷ (-4) + [(-12)] ÷ 2
= 3 + (-6) = 3-6 = -3
Hence, L.H.S. ≠ R.H.S.
(b) p = -30, q = 3, r = 2
Solution :
p = -30, q = 3, r = 2
L.H.S. = p ÷(q + r) = (-30) ÷(3 + 2)
= (-30) ÷ 5 = -6
R.H.S. = (p ÷ q) + (p ÷ r) = (-30) ÷ 3 + (-30) ÷ 2
= (-10) + (-15)
= -10 – 15 = -25
Hence, L.H.S. ≠ R.H.S.
Question 6.
State the property.
(a) a ×(b + c) = a × b + a × c
Solution :
Distributive property of multiplication over addition
(b) a × b = b × a
Solution :
Commutative property of multiplication
(c) a + b = b + a
Solution :
Commutative property of addition
(d) a + (-a) = 0
Solution :
Additive inverse property
(e) a × 1 / a = 1
Solution :
Multiplicative inverse property
Question 7.
The mountain is at the height of 8850 m. Its base is at an elevation of 5400 m. The temperature here drops at the rate of 1 degree per 100 meters. If the temperature at the base of -5°C, what is the temperature at the top?
Solution :
Given :
Height of the mountain top = 8850 m
Height of the base = 5400 m
Temperature drop = 1°C per 100 m
Temperature at the base = -5°C
Step 1: Find the difference in height
8850-5400 = 3450 m
Step 2: Find the total temperature drop
\(\frac{3450}{100}\) = 34.5°C
So, the temperature drops by 34.5°C
Step 3: Find the temperature at the top.
5-34.5 = -39.5°C
The temperature at the top of the mountain is -39.5°C.