Test paper 1
Page-15Question 1:
The sum of two integers is −12. If one of them is 43, find the other.
Answer 1:
Let the other integer be a. Then, we have:
a + (−12) = 43
⇒ a = 43 − (−12) = 55
Hence, the other integer is 55.
Question 2:
The difference of an integer p and −8 is 3. Find the value of p.
Answer 2:
Given:
p − (−8)= 3
⇒ p = 3 + (−8)
⇒ p = −5
Hence, the value of p is −5.
Question 3:
Add the product of (−16) and (−9) to the quotient if (−132) by 6.
Answer 3:
Product of (−16) and (−9) = = 144
Now, gives the quotient −22.
∴ 144 + (−22) = 122
Question 4:
By what number should (−240) be divided to obtain 16?
Answer 4:
Suppose that a divides −240 to obtain 16. Then, we have:
(−240) a = 16
⇒ a = (−240) 16 = −15
Hence, −15 should divide −240 to obtain 16.
Question 5:
What should be divided by (−7) to obtain 12?
Answer 5:
Let a be divided by (−7) to obtain 12. Then, we have:
⇒ a =
Hence, should be divided by −7 to obtain 12.
Question 6:
Evaluate:
(i) (−6) × (−15) × (−5)
(ii) (−8) × (−5) × 9
(iii) 9 × (−12) × 10
(iv) (−75) × 8
(v) (−5) × (−5) × (−5) ...... taken 5 times
(vi) (−1) × (−1) × (−1) ×...... taken 25 times
Answer 6:
(i) −450
(ii) 360
(iii) −1080
(iv) −600
(v)
(vi)
Question 7:
Evaluate
(i) (−16) × 12 + (−16) × 8
(ii) 25 × (−33) + 25 × (−17)
(iii) (−19) × (−25) + (−19) × (−15)
(iv) (−47) × 68 − (−47) × 38
(v) (−105) ÷ 21
(vi) (−168) ÷ (−14)
(vii) 0 ÷ (−34)
(viii) 37 ÷ 0
Answer 7:
(i) (−16) × 12 + (−16) × 8
= (−16) × (12 + 8) [Associative property]
= (−16) × 20
= −320
(ii) 25 × (−33) + 25 × (−17)
= 25 × ((−33) + (−17)) [Associative property]
= 25 × (−50) = −1250
(iii) (−19) × (−25) + (−19) × (−15)
= (−19) × ((−25) + (−15)) [Associative property]
= (−19) × (−40) = 760
(iv) (−47) × 68 − (−47) × 38
= (−47) × (68 − 38) [Associative property]
= (−47) × 30 = −1410
(v) (−105) ÷ 21 = −5
(vi) 12
(vii) 0 (zero). Dividing 0 by any integer gives 0.
(vii) Not defined. Dividing any integer by zero is not defined.
Question 8:
Mark (✓) against the correct answer
The sum of two integers is −6. If one of them is 2, then the other is
(a) −4
(b) 4
(c) 8
(d) −8
Answer 8:
(d) −8
Let the other integer be a. Then, we have:
2 + a = −6
⇒ a = −6 − 2 = −8
∴ The other integer is −8.
Question 9:
Mark (✓) against the correct answer
What must be subtracted from −7 to obtain −15?
(a) −8
(b) 8
(c) −22
(d) 22
Answer 9:
(b) 8
Suppose that a is subtracted from −7. Then, we have:
−7 − a = −15
a = −7 + 15 = 8
∴ 8 must be subtracted from −7 to obtain −15.
Question 10:
Mark (✓) against the correct answer
(?) ÷ (−18) = −6
(a) −108
(b) 108
(c) 3
(d) none of these
Answer 10:
(b)108
(108) ÷ (−18) = −6
Question 11:
Mark (✓) against the correct answer
(−37) × (−7) + (−37) × (−3) = ?
(a) 370
(b) −370
(c) 148
(d) −148
Answer 11:
(a) 370
We have:
(−37) × (−7) + (−37) × (−3)
= (−37) × {(−7) + (−3)} [Associative property]
= (−37) × (−10)
= 370
Question 12:
Mark (✓) against the correct answer
(−25) × 8 + (−25) × 2 = ?
(a) 250
(b) 150
(c) −250
(d) −150
Answer 12:
(c) −250
(−25) × 8 + (−25) × 2
= (−25) × (8 + 2) [Associative property]
= −250
Question 13:
Mark (✓) against the correct answer
(−9) − (−6) = ?
(a) −15
(b) −3
(c) 3
(d) 15
Answer 13:
(b) −3
(−9) − (−6)
= (−9) + 6
= −3
Question 14:
Mark (✓) against the correct answer
How much less than −2 is −8?
(a) 6
(b) −6
(c) 10
(d) −10
Answer 14:
(b) −6
−8 − (−6) = 2
Hence, −8 is −6 less than −2.
Question 15:
Fill in the blanks.
(i) (−35) × ... = 35
(ii) (−53) × (...) = −53
(iii) (−14) × (...) = (−16) × (−14)
(iv) (−21) × (...) = 0
(v) (−119) ÷ 17 = (...)
(vi) (−247) ÷ (...) = 13
(vii) (...) ÷ 31 = 0
(viii) (...) ÷ (−19) = −8
Answer 15:
(i) −1
(ii) 1
(iii) (−16) [Commutative property]
(iv) 0 [Property of zero]
(v) −7
(vi) −19
(vii) 0
(viii) 152
Question 16:
Write 'T' for true and 'F' for false for each of the following:
(i) 0 ÷ (−16) = 0
(ii) (−8) ÷ 0 = 0
(iii) (−1) ÷ (−1) = −1
(iv) (−36) ÷ (−1) = 36
(v) (−52) ÷ 13 = −4
(vi) 68 ÷ (−17) = 4
Answer 16:
(i) True (T).
(ii) False (F). Dividing any integer by zero is not defined.
(iii) False (F). (−1) ÷ (−1) = 1
(iv) True (T).
(v) True (T).
(vi) False (T). 68 ÷ (−17) = −4
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