Unit Test( Solutions): Integers | Mathematics (Maths) Class 7 (Old NCERT) PDF Download

Time: 1 hour
M.M.: 30

Attempt all questions.

Question numbers 1 to 5 carry 1 mark each.
Question numbers 6 to 8 carry 2 marks each.
Question numbers 9 to 11 carry 3 marks each.
Question numbers 12 & 13 carry 5 marks each.

Q1: Which of the following is a correct example of the commutative property of addition?(1 Mark)
(i) 5 + (-3) = (-3) + 5
(ii) 7 - 2 = 2 - 7
(iii) 8 × (-1) = (-1) × 8
(iv) 9 ÷ 3 = 3 ÷ 9
Ans: (i) 
The commutative property of addition means that changing the order of numbers does not change their sum. In option (i), $5+(-3)=(-3)+55\; +\; (-3)\; =\; (-3)\; +\; 5$, both expressions equal 2, demonstrating the commutative property.
Other options:
(ii) $7-2\ne 2-7$ (subtraction is not commutative),
(iii) shows multiplication's commutative property,
(iv) shows division, which is not commutative.

Q2: Which property states that the sum of two integers is always an integer?(1 Mark)
(i) Associative property
(ii) Distributive property
(iii) Closure property
(iv) Commutative property
Ans: (iii) 
The Closure Property for integers states that when you add, subtract, or multiply two integers, the result is always an integer. This property guarantees that performing these operations on integers will never result in a non-integer.

For example:

• $3+(-2)=13\; +\; (-2)\; =\; 1$(an integer),
• $5\times (-3)=-155\; \backslash times\; (-3)\; =\; -15$ (an integer).

Q3: Subtract (-3) from (-8). (1 Mark)
Ans: (-8) - (-3) = -8 + 3 = -5

Q4: Find the result of multiplying (-6) by (-4). (1 Mark)
Ans: (-6) × (-4) = 24

Q5: What is the additive identity for integers? (1 Mark)
Ans: The additive identity for integers is 0 because adding 0 to any integer does not change its value.

Q6: Find three integers whose sum gives 0. (2 Marks)
Ans: One possible combination is: 5, -3, and -2.
5 + (-3) + (-2) = 5 - 3 - 2 = 0.

Q7: Simplify: (-8) × (-7) + (-10) × (-2). (2 Marks)
Ans:
(-8) × (-7) = 56
(-10) × (-2) = 20
56 + 20 = 76

Q8: Subtract the integer -15 from 9 and check if subtraction is commutative for integers. (2 Marks)
Ans:
9 - (-15) = 9 + 15 = 24
-15 - 9 = -15 - 9 = -24
Since 9 - (-15) ≠ -15 - 9, subtraction is not commutative for integers.

Q9: Verify whether the following holds true for integers:  (3 Marks)
(-12) × (4 + 6) = (-12) × 4 + (-12) × 6.
Ans:
LHS = (-12) × (4 + 6) = (-12) × 10 = -120
RHS = (-12) × 4 + (-12) × 6 = -48 + (-72) = -120
Hence, LHS = RHS, the distributive property holds true.

Q10: In a quiz, team A scored (-50), 30, and (-20) in three successive rounds. Team B scored 20, (-40), and (-10) in three successive rounds.(3 Marks)
(i) Which team has a higher score?
(ii) What is the difference in their total scores?
Ans:
(i) Team A’s total score: (-50) + 30 + (-20) = -40
Team B’s total score: 20 + (-40) + (-10) = -30
Team B has a higher score.
(ii) The difference in their scores: |-40 - (-30)| = |(-40) - (-30)| = |-40 + 30| = |-10| = 10.

Q11: Starting from $(-2)\times 4(-2)\; \backslash times\; 4$, write a series of products showing a pattern that eventually leads to the result $(-2)\times (-1)=2(-2)\; \backslash times\; (-1)\; =\; 2$.(3 Marks)
Ans:

Let’s observe the following products:

1. $(-2)\times 4=-8(-2)\; \backslash times\; 4\; =\; -8$
2. $(-2)\times 3=-6(-2)\; \backslash times\; 3\; =\; -6$
3. $(-2)\times 2=-4$
4. $(-2)\times 1=-2$
5. $(-2)\times 0=0(-2)\; \backslash times\; 0\; =\; 0$
6. $(-2)\times (-1)=2$

The pattern shows that as the multiplier decreases, the product becomes less negative, and when multiplying by a negative number, the product becomes positive. Therefore, $(-2)\times (-1)=2$

Q12: A shopkeeper earns a profit of ₹2 by selling one notebook and incurs a loss of 50 paise per eraser while selling erasers from old stock. (5 Marks)

(i) In a particular month, the shopkeeper incurs a loss of ₹10. During this period, the shopkeeper sold 60 notebooks. How many erasers did the shopkeeper sell in this period?
(ii) In the next month, the shopkeeper neither makes a profit nor incurs a loss. If the shopkeeper sold 90 notebooks, how many erasers did the shopkeeper sell?

Ans:

(i) 

• Profit per notebook = ₹2
• Loss per eraser = ₹0.50

(i) Net loss ₹10; 60 notebooks sold
Let erasers sold = e.
Net profit = (profit from notebooks) − (loss from erasers)
⇒ 120 − 0.5e =−10
⇒ 0.5 e = 130
⇒ e = 260

 (ii) No profit, no loss; 90 notebooks sold

180 −0.5e = 0
⇒0.5e = 180
⇒e = 360

Q13: The temperature at 8 AM was 12°C above zero. If it decreases at the rate of 3°C per hour, at what time will the temperature be 9°C below zero? What will be the temperature at 6 PM? (5 Marks)

Ans:

$(-2)\; \backslash times\; (-1)\; =\; 2$