Integers Test

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Integers Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following relations is correct?

A
(−39) ÷ (−3) = −42

B
(−21) ÷ (−7) = −3

C
(−6) ÷ (−2) = 8

D
(−15) ÷ (−5) = 3

Solution

We know that when two negative integers are divided, the quotient is always positive.

∴ (−15) ÷ (−5) = 3
Question 2
1 / -0

Which of the following expressions is equivalent to the expression (–41) × (–97)?

A
4100 + 123

B
4100 – 123

C
9700 – 810

D
9700 + 810

Solution

The given expression is (–41) × (–97).

(–41) × (–97)

= (–41) × [(–100) + 3]

= (–41) × (–100) + (–41) × 3 [Distributivity of multiplication over addition]

= 4100 + (–123)

= 4100 – 123

By using the properties of multiplication, the value of the given expression can be found in an easier way.

For instance, it was shown that

(–41) × (–97) = 4100 – 123

∴(–41) × (–97) = 3977
Question 3
1 / -0

If (−16) × 38 + 16 × 58 = (−16) × (38 − x), then what is the value of x?

A
58

B
32

C
−32

D
−58

Solution

The given expression is: (−16) × 38 + 16 × 58 = (−16) × (38 − x)

Consider L.H.S.

= −16 × 38 + 16 × 58

= (−16) × 38 + (−16) × (−58)

= (−16) × [38 + (−58)] [By Distributive law]

= −16 × (38 − 58)

Comparing it with R.H.S:

x = 58

Thus, the value of x is 58.
Question 4
1 / -0

What is the value of the expression 1533 ÷ [300 –{6 + 3 (21 + 4)}]?

A
7

B
8

C
14

D
16

Solution

The given expression can be simplified using BODMAS rule as follows:

1533 ÷ [300 – {6 + 3 (21 + 4)}]

= 1533 ÷ [300 – {6 + 3 × 25}]            (By solving simple bracket)

= 1533 ÷ [300 – {6 + 75}]                  (By performing multiplication in curly brackets)

= 1533 ÷ [300 – 81]                            (By performing addition in curly bracket)

= 1533 ÷ 219                                       (By performing subtraction in square bracket

= 7                                                       (By performing division)
Question 5
1 / -0

What is the value of the expression (100 – 27 × 2) ÷ {13 + (5 × 2)}?

A
0

B
2

C
3

D
4

Solution

The given expression can be simplified using BODMAS rule as follows:

(100 – 27 × 2) ÷ {13 + (5 × 2)}

= (100 – 54) ÷ {13 + 10}        (By performing multiplication in simple brackets)

= (46) ÷ {23}                          (By solving simple and curly brackets)

= 46 ÷ 23

= 2                                           (By performing division)
Question 6
1 / -0

What is the result obtained upon multiplying an integer with its additive identity?

A
Zero in all cases

B
The integer itself

C
The successor of the integer

D
The predecessor of the integer

Solution

Number 0 is said to be the additive identity of integers because the sum of 0 and any integer is the integer itself.

When 0 is multiplied with any integer, we always obtain 0 as the result.

Thus, we can say that upon multiplying an integer and its additive identity, we always get 0 as the result.
Question 7
1 / -0

Which of the following statements is correct?

A
The product of 4 negative integers and a positive integer is negative.

B
The product of 5 negative integers and 3 positive integers is positive.

C
The product of 2 negative integers and 3 positive integers is positive.

D
The product of 2 negative integers and 2 positive integers is negative.

Solution

The product of 2 negative integers is always positive. The product of any number of positive integers is always positive.

Thus, the product of 2 negative integers and 3 positive integers is always positive.

For example, (−1) × (−2) × (1) × (2) × (3) = 12.
Question 8
1 / -0

What is the sum of the integer −18 and the additive inverse of −23?

A
−41

B
−5

C
5

D
41

Solution

Additive inverse of −23 = −(−23) = 23

∴ Sum of −18 and 23 = −18 + 23 = 5

Thus, the the sum of the integer −18 and the additive inverse of −23 is 5.

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Re-Attempt Weekly Quiz Competition

Integers Test - 1

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Integers Test - 1

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SHARING IS CARING

Question 1

(−39) ÷ (−3) = −42

(−21) ÷ (−7) = −3

(−6) ÷ (−2) = 8

(−15) ÷ (−5) = 3

Solution

Question 2

4100 + 123

4100 – 123

9700 – 810

9700 + 810

Solution

Question 3

58

32

−32

−58

Solution

Question 4

7

8

14

16

Solution

Question 5

0

2

3

4

Solution

Question 6

Zero in all cases

The integer itself

The successor of the integer

The predecessor of the integer

Solution

Question 7

The product of 4 negative integers and a positive integer is negative.

The product of 5 negative integers and 3 positive integers is positive.

The product of 2 negative integers and 3 positive integers is positive.

The product of 2 negative integers and 2 positive integers is negative.

Solution

Question 8

−41

−5

5

41

Solution

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