Integers Test

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Integers Test - 36

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Weekly Quiz Competition

Question 1
1 / -0

The set of odd integers is closed under

A
addition

B
subtraction

C
multiplication

D
division

E
none of these

Solution

In order to answer this question, take two odd numbers
Let the odd numbers be $$1$$ and $$3$$
$$1+3 = 4$$ (not odd)
$$3-1=2$$ (not odd)
$$1 \times 3 = 3$$ (odd)
$$ 1\div 3 = 1/3$$ (not an integer)
So, the odd integers are closed under multiplication.
Question 2
1 / -0

Obtain the following:
$$(+138) + (-234)$$

A
$$60$$

B
$$372$$

C
$$96$$

D
$$-96$$

Solution

Write given integers in addition expression and we get:

$$(+138) + (-234)$$

Subtract smaller integer $$138$$ from bigger integer $$234$$ as follows:

$$234-138=96$$

Since, the bigger integer $$234$$ is a negative integer, so the result should also be negative that is $$-96$$

Hence, $$138-234=-96$$.
Question 3
1 / -0

Find:
$$(+22) + (-16)$$

A
$$-6$$

B
$$6$$

C
$$5$$

D
$$-5$$

Solution

Write given integers in addition expression and we get:

$$(+22) + (-16)$$

Subtract smaller integer $$16$$ from bigger integer $$22$$ as follows:

$$22-16=6$$

Since, the bigger integer $$22$$ is a positive integer, so the result should also be positive that is $$+6$$ or $$6$$.

Hence, $$-16+22=6$$
Question 4
1 / -0

Evaluate:
$$(+5)+(-6)= ?$$

A
$$-1$$

B
$$1$$

C
$$2$$

D
$$-2$$

Solution

Write given integers in addition expression and we get:

$$(+5) + (-6)$$

Subtract smaller integer $$5$$ from bigger integer $$6$$ as follows:

$$6-5=1$$

Since, the bigger integer $$-6$$ is a negative integer, so the result should also be negative that is $$-1$$

Hence, $$+5-6=-1$$.
Question 5
1 / -0

Simplify using commutative and distributive property:
$$-4\times 3 - (-3) \times (-6) =$$ $$.....$$

A
$$-3$$

B
$$-30$$

C
$$30$$

D
$$10$$

Solution

$$-4\times 3 - (-3) \times (-6) = (-3) \times 4 - (-3)\times (-6)$$ ($$\because$$ commutative property)
$$= (-3) [4 - (-6)]$$ ($$\because$$ distributive property)
$$= (-3) \times 10$$
$$= -30$$
Question 6
1 / -0

Associative property is used between _______.

A
Two numbers

B
Three numbers

C
Four numbers

D
Ten numbers

Solution

Associative property rule say "If you are adding or multiplying it does not matter where you put the parenthesis". It used between three numbers.
So, option B is correct.
Question 7
1 / -0

Given $$-51\times x= 204$$ and $$-33\times y= -297$$, then find the value of $$-x\times y$$.

A
$$-36$$

B
$$33$$

C
$$36$$

D
$$-33$$

Solution

Given, $$-51\times x=204$$ and $$-33\times y=-297$$
Therefore, $$x=-\dfrac{204}{51}=-4$$
and $$ y=\dfrac{-297}{-33}=9$$
Thus $$-x\times y=-(-4)\times9=36$$
Question 8
1 / -0

The multiplicative identity for integers is

A
$$0$$

B
$$1$$

C
$$0.1$$

D
$$2$$

Solution

$${\textbf{Step-1: Identity of any integer a is a number.}}$$

$${\text{The multiplicative identity of any integer a is a number b which when multiplied }}$$
$$\text{with a, leaves it unchanged}$$
$${\text{ i.e. b is called as the multiplicative identity of any integer a if}}$$ $$a \times b = a.$$

$${\textbf{Step-2: When we multiply 1 with any integers.}}$$

$${\text{Now, when we multiply 1 with any of the integers a we get}}$$ $$a \times 1 = a = 1 \times a.$$
$${\text{So, 1 is the multiplicative identity for integers.}}$$

$${\textbf{Hence, The correct option is (C).The multiplicative identity for integers is 1.}}$$
Question 9
1 / -0

$$-42\times x= 336$$, $$-28\times y= -84$$
What is the value of $$x$$ and $$y$$ respectively?

A
$$8$$ and $$3$$

B
$$-8$$ and $$3$$

C
$$8$$ and $$-3$$

D
$$-8$$ and $$-3$$

Solution

Given, $$-42\times x=336$$ and $$-28\times y=-84$$

Thus $$x=\dfrac{336}{-42}=-8$$

and $$ y=\dfrac{-84}{-28}=3$$
Question 10
1 / -0

Simplify: $$\dfrac{(-33)\times(96)}{(11)\times(-24)}$$.

A
$$-14$$

B
$$12$$

C
$$10$$

D
$$-12$$

Solution

$$\dfrac{-33\times 96}{11\times -24}=(-3)\times (-4)=12$$

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Re-Attempt Weekly Quiz Competition

Integers Test - 36

Result

Integers Test - 36

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SHARING IS CARING

Question 1

addition

subtraction

multiplication

division

none of these

Solution

Question 2

$$60$$

$$372$$

$$96$$

$$-96$$

Solution

Question 3

$$-6$$

$$6$$

$$5$$

$$-5$$

Solution

Question 4

$$-1$$

$$1$$

$$2$$

$$-2$$

Solution

Question 5

$$-3$$

$$-30$$

$$30$$

$$10$$

Solution

Question 6

Two numbers

Three numbers

Four numbers

Ten numbers

Solution

Question 7

$$-36$$

$$33$$

$$36$$

$$-33$$

Solution

Question 8

$$0$$

$$1$$

$$0.1$$

$$2$$

Solution

Question 9

$$8$$ and $$3$$

$$-8$$ and $$3$$

$$8$$ and $$-3$$

$$-8$$ and $$-3$$

Solution

Question 10

$$-14$$

$$12$$

$$10$$

$$-12$$

Solution

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