Integers Test

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Integers Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

The greatest negative integer from the following given numbers is

A
$-1$

B
$-23$

C
$-10$

D
$-91$

Solution

-1 is greatest negative integer.
Question 2
1 / -0

$42(4+2)=(42 \times 4)+(42 \times 2)$ is an example of

A
closure property

B
commutative property

C
associative property

D
distributive property

Solution

$42(4+2)=(42 \times 4)+(42 \times 2)$ is an example of distributive property.

$a(b+c)=(a \times b)+(a \times c)$ is the basic form of distributive property.
Question 3
1 / -0

The result of the product of a positive integer with $-1$ will be

A
Positive

B
Negative

C
$0$

D
None

Solution

We can say that $-1$ is a negative integer and its product with any positive integer will be negative as well.

For example:-
$2\times (-1)=-2$
Question 4
1 / -0

Find the value of $(-144)\div(+16)$

A
$+9$

B
$+11$

C
$-9$

D
$-11$

Solution

$(-144)\div (+16)=\dfrac { -144 }{ 16 } \\ =-(\dfrac { 144 }{ 16 } )\\ =-(9)$
So correct answer will be option C
Question 5
1 / -0

Sign of the product of $231$ negative integers and $9$ positive integers is

A
negative

B
positive

C
$0$

D
none

Solution

Since $231$ is an odd number, the product of $231$ negative integers will be negative.
The product of all positive integers is a positive number. Hence, the product of $9$ positive integers will be a positive integer.
Therefore, the product of the two integers ( $231$ negative and $9$ positive) of unlike signs will be negative.
Question 6
1 / -0

Solve $(-28) + (-32) =$

A
$60$

B
$-60$

C
$0$

D
$30$

Solution

$(-28) + (-32)$
$(-28-32)$
$= -60$
Question 7
1 / -0

Multiplication is distributed over ____ and _____ in integer.

A
$-,\times$

B
$+,\times$

C
$+,-$

D
$\times,\div$
Question 8
1 / -0

Product of two integers with unlike signs is

A
Negative

B
0

C
Positive

D
None of these

Solution

Let us take two integers, one with positive sign and one with negative sign that is $+2$ and $-5$ then the product of these integers with different/unlike signs is:

$(+2)\times (-5)=-(2\times 5)=-10$ which is a negative integer.

Hence, product of two integers with unlike signs is always negative.
Question 9
1 / -0

Commutative property is satisfied in integers with respect to,

A
$-,\div$

B
$-,\times$

C
$+,-$

D
$+,\times$

Solution

Commutative property w.r.t addition of integers
When two integers are added, the result obtained is the same integer even if the sequence of addition changes.
Eg. $-1 + 5 = 4$ and $5+ (-1) = 4$
Hence, the commutative property is closed for addition with respect to integers.

Commutative property w.r.t subtraction of integers
When one integer is subtracted from the other, the result obtained is not the same integer, when the sequence of subtraction changes.
Eg. $-1 - 5 = -6$ but $5-(-1) = 5+1 = 6$
Hence, the commutative property is not closed for subtraction with respect to integers.

Commutative property w.r.t multiplication of integers
When two integers are multiplied, the result obtained is the same integer even if the sequence of multiplication changes.
Eg. $-1 \times 5 = -5$ and $5 \times (-1) = -5$
Hence, the commutative property is closed for multiplication with respect to integers.

Commutative property w.r.t division of integers
When one integer is divided by the other, the result obtained is not the same integer, when the sequence of division changes.
Eg. $-1 \div 5 = -\cfrac 15$ but $5 \div (-1) = -5$
Hence, the commutative property is not closed for division with respect to integers.

Therefore option D is correct.
Question 10
1 / -0

Product of two integers with like signs is

A
Negative

B
Positive

C
0

D
None of these

Solution

Let us take two integers with positive signs that is $+2$ and $+5$ then the product of these integers with same/like signs is:

$(+2)\times (+5)=2\times 5=10$ which is also a positive integer.

Now, let us take two integers with negative signs that is $-2$ and $-5$ then the product of these integers with same/like signs is:

$(-2)\times (-5)=2\times 5=10$ which is also a positive integer.

Hence, product of two integers with like signs is always positive.

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Re-Attempt Weekly Quiz Competition

Integers Test - 16

Result

Integers Test - 16

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Question 1

−1-1−1

−23-23−23

−10-10−10

−91-91−91

Solution

Question 2

closure property

commutative property

associative property

distributive property

Solution

Question 3

Positive

Negative

000

None

Solution

Question 4

+9+9+9

+11+11+11

−9-9−9

−11-11−11

Solution

Question 5

negative

positive

000

none

Solution

Question 6

606060

−60-60−60

000

303030

Solution

Question 7

−,×-,\times−,×

+,×+,\times+,×

+,−+,-+,−

×,÷\times,\div×,÷

Question 8

Negative

0

Positive

None of these

Solution

Question 9

−,÷-,\div−,÷

−,×-,\times−,×

+,−+,-+,−

+,×+,\times+,×

Solution

Question 10

Negative

Positive

0

None of these

Solution

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$-1$

$-23$

$-10$

$-91$

$0$

$+9$

$+11$

$-9$

$-11$

$0$

$60$

$-60$

$0$

$30$

$-,\times$

$+,\times$

$+,-$

$\times,\div$

$-,\div$

$-,\times$

$+,-$

$+,\times$