Q 1. Find the value of
36 ÷ 6 + 3
Ans. Given 36 ÷ 6 + 3
According to BODMAS rule we have to operate division first then we have to do addition
Therefore 36 ÷ 6 + 3 = 6 + 3 = 9
Q 2. Write five pair of integers (m, n) such that m ÷ n = – 3. One of such pair is (– 6, 2).
Ans.
(i) (–3, 1) = (–3) ÷ 1 = –3
(ii) (9, –3) = 9 ÷ (–3) = –3
(iii) (6, –2) = 6 ÷ (–2) = –3
(iv) (–24, 8) = (–24) ÷ 8 = –3
(v) (18, –6) = 18 ÷ (–6) = –3
Q 3. (−3) × (− 4) ÷ (−2) + (−1)
Ans. Given (–3) × (–4) ÷ (-2) + (–1)
According to BODMAS rule we have to perform division first followed by multiplication, addition and subtraction.
(–3) × (–4) ÷ (–2) + (–1) = –3 × 2 – 1
= – 6 – 1
= – 7
Q 4. If a = −35, b = 10 cm and c = −5, verify that:
a + (b + c) = (a + b) + c
Ans. Given that a = –35, b = 10, c = –5
LHS = a + (b + c) = (–35) + [10 + (–5)] = (–35) + 5 = –30
RHS = (a + b) + c = [(–35) + 10] + (–5) = (-25) + (–5) = –(25 + 5) = –30
LHS = RHS
Hence, verified
Q 5. (4) + (−15) ÷ (5 – 3)
Ans.
Given (-15) + 4 ÷ (5 – 3)
According to BODMAS rule we have to perform division first followed by addition and subtraction.
Therefore, (–15) + 4 ÷ (5 – 3) = (-15) + 4 ÷ 2
= – 15 + 2
= – 13
Q 6. Determine the integer whose product with (– 1) is
i) −26
ii) 26
iii) 0
Q 7. Fill in the blanks.
(i) 3 + ___= 0
(ii) – 2 + (– 7) = (– 7) +___
(iii) 8 + (– 8) = ____
(iv) − 51 + ___ = – 51
(v) 3 + [(– 7) + 8] = [3 + (____)] + 8
(vi) [3 + (– 8)] + _____ = 3 + [(– 8) + 7]
Ans.
(i) – 3
(ii) – 2
(iii) 0
(iv) 0
(iv) – 7
(v) 7
Q 8. Fill in the blanks using < or >.
(a) – 3 …… – 4
(b) 6 ……. – 20
(c) -8 …… – 2
(d) 5 …… – 7
Ans.
(a) –3 > – 4
(b) 6 > – 20
(c) – 8 < – 2
(d) 5 > – 7
Q 9. Solve the following:
(i) (− 8) × (− 5) + (− 6)
(ii) [(− 6) × (−3)] + (− 4)
(iii) (− 5) × [(− 6) + 5]
Ans.
(i) (– 8) × (– 5) + (– 6)
= (– 8) × (– 5) × [8 × 5] + (– 6)
= 40 – 6
= 34
(ii) [(–6) × (–3)] + (– 4)
= (– 6) × (– 3) × [6 × 3] + (– 4)
= 18 – 4
= 14
(iii) (– 5) × [(– 6) + 5]
= (– 5) × (– 1)
= (– 5) × (– 1) × 5 × 1
= 5
Q 10. Find the sum of:
(i) − 2035 and 297
(−2035) + 297 = −1738
(ii) 153 and – 302
153 + (−302) = −149
Q 11. Write a pair of integers whose difference gives:
(i) a negative integer
(ii) −9
(iii) a positive integer
(iv) 2
(v) 0
Ans. (i) 7 and 9
(ii) 7 and 16
(iii) 1 and – 2
(iv) 9 and 7
(v) 2 and 2
Q 12. Assertion: (−7) + (– 18) = – 25 is an integer is called closure property.
Reason: Two integers can be added in any order i.e. addition is commutative for integers.
(a) Both assertion and reason are correct and reason is the correct explanation for assertion.
(b) Both assertion and reason are correct but reason is not the correct explanation for assertion.
(c) Assertion is correct but the reason is incorrect.
(d) Both assertion and reason are incorrect.
Ans. (b) Both assertion and reason are correct but reason is not the correct explanation for assertion.
Q 13. The sum of two integers is 116. If one of them is −79, find the other integers.
Ans. Sum of two integers = 116
One integer = – 79
Other integer = Sum of integer – One of integer = 116 – (– 79) = 116 + 79 = 195
Q 14. On a number line, when we add a positive integer, we
(a) move to the right
(b) move to the left
(c) do not move at all
(d) none of these.
Ans. (a) move to the right
Q 15. Which of the following statements is wrong?
(а) When a positive integer and a negative integer are added, we always get a negative integer
(b) Additive inverse of 8 is (− 8)
(c) Additive inverse of (− 8) is 8
(d) For subtraction, we add the additive inverse of the integer that is being subtracted, to the other integer.
Ans. (а) When a positive integer and a negative integer are added, we always get a negative integer.
Q 16. On a number line, when we subtract a positive integer, we
(a) move to the right
(b) move to the left
(c) do not move at all
(d) none of these.
Ans. (b) move to the left
Q 17. When two negative integers are added, we get
(a) a positive integer
(b) a negative integer
(c) sometimes a positive integer, sometimes a negative integer
(d) none of these.
Ans. (b) a negative integer
Q 18. (– 1) × (– 1) × (– 1) × …….. 5 times is equal to
(a) 1
(b) −1
(c) 1 or −1
(d) none of these.
Ans. (b) – 1
Q 19. (– 10) × 0 × (– 15) is equal to
(a) 0
(b) 10
(c) 15
(d) 150
Ans. (a) 0
Q 20. (– 25) x [6 + 4] is not same as
(a) (−25) x 10
(b) (−25) x 6 + (–25) x 4
(c) −25 x 6 x 4
(d) – 250
Ans.
(c) (– 25) x [6 + 4] = (– 25) x 10
Also, (– 25) x [6 + 4] = – 25 x 6 + (– 25) x 4
[using distributive property, i.e. ax(b + c) = axb + axc] = -150 – 100 = – 250
Hence, (– 25) x (6 + 4) is not same as –25 x 6 x 4.