Whole Numbers Test

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Whole Numbers Test - 18

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Question 1
1 / -0

Which of the three whole numbers that can be represented as triangles using dots are

A
$$2, 4, 6$$

B
$$3, 6, 7$$

C
$$4, 6, 9$$

D
$$3, 6, 10$$
Question 2
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Which of the following is correct representation of $$ 2 + 3 = 5$$ on number line?

A

B

C

D
None of these

Solution

As can be evident from the image going $$3$$ steps after $$2$$ yields $$5$$, which is similar in analogy to $$(2+3=5)$$
Question 3
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(38 + 83) + 38 = 38 + (83 + 38) is an example of ........... property.

A
Commutative

B
Associative

C
Closure

D
Distributive
Question 4
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If, A: Every whole number is a natural number
R : 0 is not a natural number.
Then which of the following statement is true?

A
A is false and R is the correct explanation of A.

B
A is true and R is the correct explanation of A.

C
A is true and R is false.

D
Both A and R are true.

Solution

The set of whole numbers is $${0,1,2,3,......}$$ where $$0$$ is the least whole number.

The set of natural numbers is $${1,2,3,......}$$.

From the above statements, we conclude that every natural number is a whole number but every whole number is not a natural number because $$0$$ is not a natural number.

Therefore, $$0$$ is not a natural number and this proves that every whole number is not a natural number.

Hence, the statement A is false and R is the correct explanation of A.
Question 5
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Closure property is satisfied in whole numbers w.r.t. to ......... and ......... .

A
addition and subtraction

B
addition and division

C
addition and multiplication

D
multiplication and division.

Solution

Closure property for addition :

If $$a$$ and $$b$$ are two whole numbers and their sum is $$c$$, i.e. $$a + b = c$$, then $$c$$ is will always a whole number.
For any two whole numbers $$a$$ and $$b$$, $$(a + b)$$ is also a whole number. For example:

$$3 + 4 = 7$$ which is also a whole number.

But $$3 - 4 = -1$$ which is not a whole number.

So, the property of closure for subtraction is not always true.

Closure property for multiplication :

If $$a$$ and $$b$$ are whole numbers then their multiplication is also a whole number.

For any two whole numbers $$a$$ and $$b$$, $$(a\times b)$$ is also a whole number.For example:

$$30\times 7 = 210$$ which is also a whole number.

But property of closure is not always true for division. For example:

$$45\div 0 =$$ not defined
As division with zero is not possible.

Hence, closure property is satisfied in whole numbers w.r.t. to addition and multiplication.
Question 6
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Which of the following satisfies closure property?

A
$$3+4=7$$

B
$$5+6=11$$

C
$$10+2=12$$

D
all of these

Solution

For any two whole numbers a and b, (a + b) is also a whole number. This is called the Closure-Property of Addition.

$$3$$ and $$4$$ are whole numbers
$$3+4=7$$
$$7$$ is also whole number.
Similarly, it is true for all whole numbers.
Thus the answer is all of these.
Question 7
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If $$a$$ & $$b$$ are two whole numbers then commutative law is applicable to subtraction if and only if

A
$$a = b$$

B
a $$\displaystyle \neq $$ b

C
$$a > b$$

D
$$a < b$$

Solution

If $$a = b$$ then $$a - b = 0$$ and $$b - a = 0$$
so $$a - b = b - a$$
Hence commutative law holds good
Question 8
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Simplify using distributive property:
$$(126\times 33) + (126\times 67)$$ is

A
$$1,260$$

B
$$12,600$$

C
$$1,26,000$$

D
$$1,000$$

Solution

The Distributive Property is easy to remember if you recall that "multiplication distributes over addition".

Formally, they write this property as $$"a(b + c) = ab + ac".$$

$$(126\times 33) + (126\times 67)$$
$$= 126 \times (33 + 67)$$ ($$\because$$ distributive property)
$$= 126\times 100$$
$$= 12,600$$
Question 9
1 / -0

Which of the following statements is correct?

A
Subtraction is commutative for integers.

B
Division is associative for rational numbers.

C
Multiplication is not associative for whole numbers.

D
Addition is closed for natural numbers.

Solution
Question 10
1 / -0

Simplify using distributive property:
$$24\times 3 + 7\times 24$$

A
$$240$$

B
$$72$$

C
$$24$$

D
$$108$$

Solution

The Distributive Property is easy to remember if you recall that "multiplication distributes over addition".
Formally, they write this property as $$"a(b + c) = ab + ac".$$

The word "associative" comes from "associate" or "group"; the Associative Property is the rule that refers to grouping.
For multiplication, the rule is $$"a(bc) = (ab)c"$$

$$24\times 3 + 7\times 24$$
$$= (24\times 3) + (24\times 7)$$ ($$\because$$ commutative property)
$$= 24\times (3 + 7)$$ ($$\because$$ distributive property)
$$= 24\times 10$$
$$= 240$$.