Integers Test

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Integers Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements is CORRECT?
Statement-$$1$$: When a positive integer and a negative integer are added, we always get a negative integer.
Statement-$$2$$: When two negative integers are added, we get a positive integer.

A
Only Statement-$$1$$

B
Only Statement-$$2$$

C
Both Statement-$$1$$ and Statement-$$2$$

D
Neither Statement-$$1$$ nor Statement-$$2$$

Solution

When a positive integer and a negative integer are added, we can get a positive or negative integer.
Therefore, statement $$1$$ is false.
Fro example: $$-4+3=-1$$ or $$4+(-3)=1$$
And when two negative integers are added, we get a negative integer.
$$\therefore$$ Statement $$2$$ is false.
For example: $$-3+(-4)=-7$$
Question 2
1 / -0

Which of the following options shows distributive property of multiplication over addition?

A
$$4+(5\times 8)=(4+5)\times (4+8)$$

B
$$4\times (5+8)=(4\times 5)+(4\times 8)$$

C
$$4\times (5\times 8)=(4\times 5)\times 8$$

D
$$(8+5)+4=8+(5+4)$$

Solution

Distributive Property of multiplication over addition is as follows:
$$a\times (b+c)=(a\times b)+(a\times c)$$
So, $$4\times (5+8)=(4\times 5)+(4\times 8)$$
Hence, Option B is correct.
Question 3
1 / -0

If $$a$$ and $$b$$ are integers and $$a\neq b$$, then which of the following is INCORRECT?

A
$$a+b=b+a$$

B
$$a-b=b-a$$

C
$$a+0=0+a=a$$

D
$$a-0=a\neq 0-a$$

Solution

Option $$B$$ is correct

Given, $$a$$ and $$b$$ are integers and $$a\neq b$$.

$$A)$$ $$a+b = b+a $$

$$\Rightarrow$$It is true because of the commutative property
$$\Rightarrow$$Ex: If $$a= 2, b=3$$ then $$ 2+3=3+2 = 5$$

$$B)a-b=b-a$$

$$\Rightarrow$$ $$a-b=b-a$$ is the incorrect statement in given options.
$$\Rightarrow$$ Because, we know value of $$a$$ and $$b$$ are not equal then $$a-b$$ and $$b-a$$ can not be equal.

$$C)a+0=0+a=a$$

$$\Rightarrow$$it is true beacuse of the identity property
$$\Rightarrow$$Ex: if $$a = 2$$ then $$2+0=0+2=2$$

$$D) a-0 = a≠0-a$$

$$\Rightarrow$$It is a false statement
$$\Rightarrow$$Ex: if $$a =2$$ then $$2-0=2$$ and $$0-2 = -2$$
$$\Rightarrow$$clearly $$2-0+2≠0-2$$
Question 4
1 / -0

Subtract $$-134$$ from $$-38$$

A
$$-96$$

B
$$96$$

C
$$-183$$

D
$$183$$

Solution

As per the question : $$-38-(-134)=-38+134=96$$
Question 5
1 / -0

For any two integers $$a$$ and $$b$$, which of the following suggests that the operation addition is commutative?

A
$$a \times b = b \times a$$

B
$$a + b = b + a$$

C
$$a - b = b - a$$

D
$$a + b > a$$

Solution

$$a+b=b+a$$ represents commutative property of integers under addition. Where, $$a$$ and $$b$$ are integers
Question 6
1 / -0

$$(- 35) + (-32)$$ is equal to

A
$$67$$

B
$$-67$$

C
$$-3$$

D
$$3$$

Solution

Now,
$$(-35)+(-32)$$
$$=-35-32$$
$$=-67$$.
Question 7
1 / -0

Which of the following statement is true?

A
$$- 7 > - 5 $$

B
$$- 7 < - 5 $$

C
$$(- 7) + (- 5) > 0 $$

D
$$(- 7)- (- 5) > 0$$

Solution

We know that,
$$7>5$$
then $$-7<-5$$.
Again,
$$(-7)+(-5)=-7-5=-12<0$$.
And, $$(-7)-(-5)$$
$$=-7+5=-2<0$$.
So option (B) is correct.
Question 8
1 / -0

Answer the following using number line.
$$6$$ more than $$- 7$$ is

A
$$1$$

B
$$-1$$

C
$$13$$

D
$$-13$$

Solution

$$-7+6=-1$$
Question 9
1 / -0

$$(-29)+5$$ is equal to

A
$$24$$

B
$$34$$

C
$$-34$$

D
$$-24$$

Solution

Let $$(-29)+5=x$$ we can see that $$29$$ has negative sign and $$5$$ has positive sign.
So $$+$$ and $$-$$ will be $$-$$
So $$-29+5=-24$$ because $$24$$ will have sign of $$29$$.

Option (D)
Question 10
1 / -0

What should be added to $$18 $$ to get $$- 34$$?

A
$$52$$

B
$$-52$$

C
$$-16$$

D
$$16$$

Solution

Let the number be $$x$$.
Then according to the problem we get,
$$x+18=-34$$
or $$x=-34-18$$
or $$x=-52$$.

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Re-Attempt Weekly Quiz Competition

Integers Test - 37

Result

Integers Test - 37

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Question 1

Only Statement-$$1$$

Only Statement-$$2$$

Both Statement-$$1$$ and Statement-$$2$$

Neither Statement-$$1$$ nor Statement-$$2$$

Solution

Question 2

$$4+(5\times 8)=(4+5)\times (4+8)$$

$$4\times (5+8)=(4\times 5)+(4\times 8)$$

$$4\times (5\times 8)=(4\times 5)\times 8$$

$$(8+5)+4=8+(5+4)$$

Solution

Question 3

$$a+b=b+a$$

$$a-b=b-a$$

$$a+0=0+a=a$$

$$a-0=a\neq 0-a$$

Solution

Question 4

$$-96$$

$$96$$

$$-183$$

$$183$$

Solution

Question 5

$$a \times b = b \times a$$

$$a + b = b + a$$

$$a - b = b - a$$

$$a + b > a$$

Solution

Question 6

$$67$$

$$-67$$

$$-3$$

$$3$$

Solution

Question 7

$$- 7 > - 5 $$

$$- 7 < - 5 $$

$$(- 7) + (- 5) > 0 $$

$$(- 7)- (- 5) > 0$$

Solution

Question 8

$$1$$

$$-1$$

$$13$$

$$-13$$

Solution

Question 9

$$24$$

$$34$$

$$-34$$

$$-24$$

Solution

Question 10

$$52$$

$$-52$$

$$-16$$

$$16$$

Solution

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