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CBSE Questions for Class 6 Maths Whole Numbers Quiz 2 - MCQExams.com
CBSE
Class 6 Maths
Whole Numbers
Quiz 2
Evaluate the following using number line:
$$5+8$$
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$$12$$
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$$13$$
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$$14$$
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$$15$$
Which is equal to (4 $$\times$$ 8) + (4 $$\times$$ 60) ?
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4 $$\times$$ (60 + 8)
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8 $$\times$$ (60 + 4)
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12 $$\times$$ (60 + 4)
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16 $$\times$$ (60 + 8)
Explanation
The distributive property of multiplication states that a number is multiplied by the sum of two numbers, when the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
So(4×8)+(4×60)=4×(8+60)
So, option A is the correct answer.
Which of the following satisfies commutative property?
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$$12+18=18+12$$
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$$12-18\neq 18-12$$
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$$5-6\neq 6-5$$
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None of the above
Explanation
Commutative property means : $$A + B = B + A$$
Since addition satisfies commutative property,
so option A is correct.
Which of the following represents whole numbers?
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$$2, 3, 4, 5, .....$$
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$$...., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ....$$
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$$1, 2, 3, 4, 5, .....$$
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$$0, 1, 2, 3, 4, 5, .....$$
Explanation
The number $$'0'$$ along with the natural numbers gives us the number set $$\{0, 1, 2, 3, 4, .....\}$$ which is known as set of whole numbers.
Hence, $$0,1,2,3,4....$$ are whole numbers.
Natural numbers are also known as ...........
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whole numbers
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counting numbers
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integers
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rational numbers
Explanation
$$1, 2, 3, 4, 5, .....$$ are called "natural numbers" and are also known as counting numbers.
If $$a, b$$ and $$c$$ are whole numbers, then $$a+(b+c)=(a+b)+c$$.
This property is called
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associative property
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commutative property
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distribution property
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none of the above
Explanation
$$a+(b+c)=(a+b)+c$$ is associative property of whole numbers.
Which of the following does not satisfy closure property for whole numbers?
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$$6\times 5=30$$
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$$4\times 4=16$$
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$$5-8=-3$$
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$$9+5=14$$
Explanation
$$5$$ and $$8$$ are whole numbers but $$-3$$ is not a whole number.
So, option C is correct.
Closure property is applicable to ........ operation of whole numbers.
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inverse
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division
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subtraction
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addition
Explanation
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 w
hole 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.
Which of the following numbers is not a natural number?
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$$3$$
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$$2$$
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$$1$$
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$$0$$
Explanation
The counting numbers $$1, 2, 3, 4, .....$$ are called natural numbers. The set of natural numbers does not include $$0$$.
Example of distributive property specific to whole numbers is
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$$-2 \times (1+10) = (-2 \times 1) + (-2 \times 10)$$
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$$(9+0) \times 5 = (9 \times 5) + (0 \times 5)$$
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$$12 \times (-2-8) = (12 \times -2) - (12 \times 8)$$
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none of these
Explanation
Apart from $$B,$$ the other options contain a negative sign.
Negative numbers do not belong to whole numbers.
Only
option $$B$$ is correct.
Commutative property is applicable to whole number in case of
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Addition
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Multiplication
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Division
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Subtraction
Explanation
For whole numbers,
Addition and multiplication are commutative.
i.e. operations on L.H.S and R.H.S give the same result.
irrespective of the sequence in which addition / multiplication is carried out.
For eg. $$6 + 7 = 7 + 6 = 13$$
and $$ 7 \times 6 = 6 \times 7 = 42$$
So, options $$A$$ and $$B$$ are correct.
Which of the following satisfies closure property for whole numbers?
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$$12+0=12$$
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$$13+0=13$$
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$$16+6=22$$
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All of the above
Explanation
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 .
For any two whole numbers, $$x$$ and $$y,\ x + y = ..........$$
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$$y + x$$
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$$y$$
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$$x$$
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Cannot be known
Explanation
Addition of whole numbers is commutative. So, for any two whole numbers, $$x$$ and $$y$$,
$$ x + y = y + x$$
Closure property is applicable to ......... operation of whole numbers.
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multiplication
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division
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subtraction
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none of these
Explanation
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.
Whole numbers are not closed under ......... operation.
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addition
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subtraction
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multiplication
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none of these
Explanation
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. $$2 - 5 = -3$$.
The sum of the smallest natural number and the smallest whole number is ............
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$$1$$
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$$0$$
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$$-1$$
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$$2$$
Explanation
The smallest natural number is $$1$$ and t
he smallest whole number is $$ 0.$$
$$\therefore 1 + 0 = 1$$
Commutative property for ........... operation holds true in case of whole numbers.
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Addition
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Subtraction
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Division
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None of these
Explanation
Commutative property for $$\underline{\text{addition}}$$ holds true in the case of whole numbers.
For example:
$$7+4=11$$
$$4+7=11$$
$$\Rightarrow 7+4=4+7$$
Which of the following statements is incorrect?
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Whole numbers are closed under addition
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Whole numbers are closed under multiplication
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Whole numbers are closed under subraction
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Whole numbers are not closed under subtraction
Explanation
The difference of two whole numbers is not necessarily a whole number. The statement whole numbers are closed under subtraction is an incorrect statement.
Whole numbers are commutative under which of the following operations?
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addition and multiplication
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addition and subtraction
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multiplication and division
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division and subtraction
Explanation
Whole numbers are commutative under addition and multiplication.
For example
Take two whole numbers $$2$$ and $$5.$$
Addition $$=2+5=7$$ also $$5+2=7$$, You can add whole nos. in any order which gives same results.
Subtraction $$2-5=-3$$ also $$5-2=3$$
Multiplication$$=2\times 5=10$$ also $$5\times 2=10$$ You can multiply whole nos. in any order which gives same results.
Division$$=2\div 5=0.4$$ also $$5\div2=2.5 $$
Whole numbers are commutative under addition and multiplication.
For any two whole numbers $$a$$ and $$b$$ which of the following statements is incorrect?
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$$a + b = b + a$$
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$$a\times b = b\times a$$
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$$a + b = a\times b$$
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$$b + a = a + b$$
Explanation
The sum of any two whole numbers and the product of the same are not necessarily equal.
Eg. $$2 + 2 = 4 = 2 \times 2$$, but $$3 + 3 = 6$$ and $$3\times 3 = 9$$ which are not equal.
Rest all options depicts commutative property which whole numbers satisfy.
For any two whole numbers $$p$$ and $$q, p\times q = .........$$
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$$p$$
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$$q$$
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$$q\times p$$
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None of these
Explanation
The value of the product does not change when the order of multiplication gets changed. This is the commutative property of multiplication.
Let the two whole numbers be p and q, then $$p × q = q × p ⇒ 4 × 9 = 36 = 9 × 4$$.
Whole numbers are commutative under multiplication.
Whole numbers are not closed under __________ operation.
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addition
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multiplication
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division
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none of these
Explanation
When any whole number is divided by another whole number, the result is not always a whole number. Eg. $$2\div 3 = \dfrac {2}{3} = 0.666$$. Thus, whole numbers are not closed under division operation.
.......... is associative for whole numbers.
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Addition
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Subtraction
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Division
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None of these
Which of the following depicts associative property under addition?
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$$a + b = b + a$$
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$$a + 0 = 0 + a$$
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$$a + (b + c) = (a + b) + c$$
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$$a + (b + c) = a + (b + c)$$
Explanation
Associative property for addition states that for any three numbers, it does not matter which two are added first and then their sum is added to the third integer the final result will be same
$$\therefore a + (b + c) = (a + b) + c$$
Find the unknown space: $$....... + 142 = ...... +73$$
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$$73, 142$$
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$$142, 73$$
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$$142, 142$$
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$$73, 73$$
Explanation
Whole numbers are commutative under addition. i.e. $$a + b = b + a$$.
$$\therefore 73 + 142 = 142 + 73$$.
$$\therefore$$ The missing numbers are $$73, 142$$.
Find the unknown value: $$11 + ... = 13 + 11$$
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$$13$$
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$$11$$
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$$3$$
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$$24$$
Explanation
Whole numbers are commutative under addition. i.e. $$a + b = b + a$$. Therefore, $$11 + 13 = 13 + 11$$.
Find the missing values: $$14\times (.......\times ......) = (14\times 2)\times 10$$
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$$2, 10$$
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$$14, 2$$
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$$2, 5$$
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$$10, 14$$
Explanation
Multiplication is associative for whole numbers. i.e. $$a\times (b\times c) = (a\times b)\times c$$
$$\therefore 14\times (2\times 10) = (14\times 2)\times 10$$
$$\therefore$$ The missing terms are $$2, 10$$.
Find the missing term: $$24\times (6\times 5) = (24\times 6) \times ......$$
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$$24$$
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$$6$$
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$$5$$
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$$1$$
Explanation
Multiplication is associative for whole numbers. i.e. $$a\times (b\times c) = (a\times b)\times c$$
$$\therefore 24\times (6\times 5) = (24\times 6)\times 5$$.
Find the missing value: $$(3 + 14) + 9 = 3 + (14 + .....)$$
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$$3$$
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$$9$$
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$$14$$
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$$1$$
Explanation
Addition is associative for whole numbers.
$$i.e. (a + b) + c = a + (b + c)$$
$$\therefore (3 + 14) + 9 = 3 + (14 + 9)$$
Which of the following depicts associative law for multiplication?
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$$a + b = b + a$$
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$$a \times b = b\times a$$
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$$a + (b + c) = (a + b) + c$$
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$$(a\times b) \times c = a\times (b\times c)$$
Explanation
Associative property for multiplication states that the product of any three or more numbers remains the same irrespective of the order in which the multiplication is carried out.
$$\therefore (a\times b)\times c = a\times (b\times c)$$.
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