Whole Numbers Test

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Whole Numbers Test - 13

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Question 1
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Natural numbers are also known as ...........

A
whole numbers

B
counting numbers

C
integers

D
rational numbers

Solution

$$1, 2, 3, 4, 5, .....$$ are called "natural numbers" and are also known as counting numbers.
Question 2
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If $$a, b$$ and $$c$$ are whole numbers, then $$a+(b+c)=(a+b)+c$$. This property is called

A
associative property

B
commutative property

C
distribution property

D
none of the above

Solution

$$a+(b+c)=(a+b)+c$$ is associative property of whole numbers.
Question 3
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Which of the following does not satisfy closure property for whole numbers?

A
$$6\times 5=30$$

B
$$4\times 4=16$$

C
$$5-8=-3$$

D
$$9+5=14$$

Solution

$$5$$ and $$8$$ are whole numbers but $$-3$$ is not a whole number.
So, option C is correct.
Question 4
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Closure property is applicable to ........ operation of whole numbers.

A
inverse

B
division

C
subtraction

D
addition

Solution

A) The closure property of the inverse tells that the result of the inverse of the whole number is not always a whole number. Whole numbers are not closed under inverse i.e., the inverse of a = 1 ÷ a is not always a whole number. From the property, we have, 1 ÷ 2 = 0.5 (not a whole number)

B) The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division i.e., a ÷ b is not always a whole number. From the property, we have, 14 ÷ 7 = 2 (whole number) but 7 ÷ 14 = ½ (not a whole number).

C) When one whole number is subtracted from another, the difference is not always a whole number. This means that the whole numbers are not closed under subtraction. If a and b are two whole numbers and a − b = c, then c is not always a whole number. Take a = 7 and b = 5, a − b = 7 − 5 = 2 and b − a = 5 − 7 = −2 (not a whole number).

D) Two whole numbers add up to give another whole number. This is the closure property of the whole numbers. It means that the whole numbers are closed under addition. If a and b are two whole numbers and a + b = c, then c is also a whole number. 3 + 4 = 7 (whole number).

Hence option $$D$$ is correct.
Question 5
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Which of the following numbers is not a natural number?

A
$$3$$

B
$$2$$

C
$$1$$

D
$$0$$

Solution

The counting numbers $$1, 2, 3, 4, .....$$ are called natural numbers. The set of natural numbers does not include $$0$$.
Question 6
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Example of distributive property specific to whole numbers is

A
$$-2 \times (1+10) = (-2 \times 1) + (-2 \times 10)$$

B
$$(9+0) \times 5 = (9 \times 5) + (0 \times 5)$$

C
$$12 \times (-2-8) = (12 \times -2) - (12 \times 8)$$

D
none of these

Solution

Apart from $$B,$$ the other options contain a negative sign.
Negative numbers do not belong to whole numbers.
Only option $$B$$ is correct.
Question 7
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Which of the following satisfies closure property for whole numbers?

A
$$12+0=12$$

B
$$13+0=13$$

C
$$16+6=22$$

D
All of the above

Solution

All numbers are whole numbers.
For closure property,
whole number $$+$$ whole number $$=$$ whole number.
In all the cases, the above property is satisfied.
So, option $$D$$ is correct .
Question 8
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For any two whole numbers, $$x$$ and $$y,\ x + y = ..........$$

A
$$y + x$$

B
$$y$$

C
$$x$$

D
Cannot be known

Solution

Addition of whole numbers is commutative. So, for any two whole numbers, $$x$$ and $$y$$,
$$ x + y = y + x$$
Question 9
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Closure property is applicable to ......... operation of whole numbers.

A
multiplication

B
division

C
subtraction

D
none of these

Solution

A) Multiplication of two whole numbers will result in a whole number.
Suppose, a and b are the two whole numbers and a × b = c, then c is also a whole number.
Let a = 10, b = 5, 10 × 5 = 50 (whole number). The whole number is closed under multiplication.

B) The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division i.e., a ÷ b is not always a whole number. From the property, we have, 14 ÷ 7 = 2 (whole number) but 7 ÷ 14 = ½ (not a whole number).

C) When one whole number is subtracted from another, the difference is not always a whole number. This means that the whole numbers are not closed under subtraction. If a and b are two whole numbers and a − b = c, then c is not always a whole number. Take a = 7 and b = 5, a − b = 7 − 5 = 2 and b − a = 5 − 7 = −2 (not a whole number).

Option A is correct.
Question 10
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Whole numbers are not closed under ......... operation.

A
addition

B
subtraction

C
multiplication

D
none of these

Solution

Whole numbers are not closed under subtraction operation because when any two whole numbers are considered and from them one is subtracted from the other, the difference so obtained is not necessarily a whole number. Eg. $$2 - 5 = -3$$.

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Whole Numbers Test - 13

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Whole Numbers Test - 13

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Question 1

whole numbers

counting numbers

integers

rational numbers

Solution

Question 2

associative property

commutative property

distribution property

none of the above

Solution

Question 3

$$6\times 5=30$$

$$4\times 4=16$$

$$5-8=-3$$

$$9+5=14$$

Solution

Question 4

inverse

division

subtraction

addition

Solution

Question 5

$$3$$

$$2$$

$$1$$

$$0$$

Solution

Question 6

$$-2 \times (1+10) = (-2 \times 1) + (-2 \times 10)$$

$$(9+0) \times 5 = (9 \times 5) + (0 \times 5)$$

$$12 \times (-2-8) = (12 \times -2) - (12 \times 8)$$

none of these

Solution

Question 7

$$12+0=12$$

$$13+0=13$$

$$16+6=22$$

All of the above

Solution

Question 8

$$y + x$$

$$y$$

$$x$$

Cannot be known

Solution

Question 9

multiplication

division

subtraction

none of these

Solution

Question 10

addition

subtraction

multiplication

none of these

Solution

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