Answer:
1. Answer: (a) move to the right
Explanation: When we add positive integers, we move to the right on the number line. For example, to add +2 and +4 we move 4 steps to the right of +2. Thus, +2 +4 = +6.
2. Answer: (b) move to the left
Explanation: Add a negative integer, we move to the left. subtract a positive integer, we move to the left. Subtracting a negative integer, we move to the right.
3. Answer: (a) move to the right
Explanation: Add a positive integer, we move to the right. add a negative integer, we move to the left. subtract a positive integer, we move to the left. Subtracting a negative integer, we move to the right.
4. Answer: (d) Both p and q are false
Explanation: When we add a positive integer and negative integer then it is not necessary that the result would be a negative integer. It can be a positive integer also. For eg- (+8)+(−6)=2. Hence the p statement is false. When we add two negative integers, we will always get a negative integer. For eg- (−7)+(−9)=−16. Hence q statement is also false.
5. Answer: (b) (- 8) + (- 4) < (- 8) – (- 4)
Explanation: (-8) + (-4) = -12
(-8) – (-4) = -4
Hence (- 8) + (- 4) < (- 8) – (- 4)
6. Answer: (b) 50 and 30
Explanation:Let the two numbers be x and y.
It is given that three times one number is equal to five times the other that is:
3x=5y
3x−5y=0..........(1)
Also, the sum of the numbers is 80 that is:
x+y=80..........(2).
Multiply the equation 2 by 3:
3x+3y=240..........(3)
Now subtract equation 1 from equation 3 to eliminate x, because the coefficients of x are the same. So, we get
(3x−3x)+(3y+5y)=240−0
i.e. 8y=240
i.e. y=30
Substituting this value of y in (1), we get
3x−150=0
i.e. 3x=150
i.e. x=50
Hence, the two numbers are 50 and 30.
7. Answer: (b) 16
Explanation: Given, 40% of [100−20% of 300]
\(=\frac{40}{100}\times[100-\frac{20}{100}\times300]\)
\(=\frac{40}{100}[100-60]\)
= 16.
8. Answer: (b) 1
Explanation:((2)0+(3)0+(5)0)0
= (1 +1 +1)0
= 30
= 1
9. Answer: (а) 0
Explanation: (−10)×0×(−15)
0 multiplied with anything gives 0.
Hence (−10)×0×(−15)=0
10. Answer: (b) 1
Explanation:−1
=−1×1.
11. Answer: (d) 5
Explanation:x/5 =1
Multiply both sides by 5 we get
\(\frac{x}{5}\times5=1\times5\)
x=5
∴x=5
12. Answer: (c) 0
Explanation: An identity element that in a given mathematical system leaves unchanged any element to which it is added. We know that any number added to 0 is still the same number and hence the system doesn’t change for any integer we will have a+0=a=0+a ⟹0 is an additive identity. Thus, the additive identity for integers is 0.
13. Answer: (a) 1
Explanation: The multiplicative identity of any integer a is a number b which when multiplied with a, leaves it unchanged, i.e. b is called as the multiplicative identity of any integer a if a× b = a. Now, when we multiply 1 with any of the integers we get a × 1 = a = 1 × a.So, 1 is the multiplicative identity for integers.
14. Answer: (c) Distributive property
Explanation: Distributive property says that multiplication and division can be distributed over parenthesis. a x (b+c) = a x b + a x c
15. Answer: (c) Rs 1000
Explanation: 2000 – 1000
= Rs 1000
16. Answer: (a) – 32
Explanation: The product of 2 numbers of opposite signs is negative.
17. Answer: (c) -10
Explanation: If a is an integer then (- a) is its additive inverse.
18. Answer: (b) (a + b) + c
Explanation: addition of an integer is associative.
19. Answer: (a) -10
Explanation: Division of 2 numbers of opposite signs is negative.
20. Answer: (b) 0
Explanation: Zero divided by any non-zero integer, the result is zero.
21. Answer: (d) – 4
Explanation: The predecessor of an integer is just before it on the number line.
22. Answer: (d) 12
Explanation: The successor of an integer is right to it on a number line.
23. Answer: (c) 5 is greater than 3
Explanation: Greater number is on the right of smaller on a number line.
24. Answer: (b) –
Explanation: The product of 3 negative integers is a negative integer.
25. Answer: (b) <
Explanation:because (-9) + (-4) = -13
= and (-9) – (-4) = (-9) + 4
= -5 – 13 < – 5
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