Tag: mental multiplication

Questions Related to mental multiplication

The value of $4 \times 378 \times 25$ is 

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 37800

  2. 3780

  3. 9450

  4. 30078

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Correct Option: A
Explanation:

$4 \times 378 \times 25$


$=378 \times 4 \times 25$


$=378 \times 100$

$=37800$

The value of $47 \times 99$ is:

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 4635

  2. 4653

  3. 4563

  4. 6453

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Correct Option: B
Explanation:

Now,

$47\times 99$
$=47\times (100-1)$
$=4700-47$
$=4653$

Mark the correct alternative of the following.
The product of a whole number(other than zero) and its successor is?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. An even number

  2. An odd number

  3. Divisible by $4$

  4. Divisible by $3$

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Correct Option: A
Explanation:

Consider whole number is $a$


Case-I

$a$ is odd
So $a=2n+1$
Successor $a\neq 1$
                  $=2n+1+1$
                  $=2n+2$
product $=(2n+1)(2n+2)$ 
              $=2(2n+1)(n+1)$
              $=2r\rightarrow Even$

Case - II
$a$ is even
So $a=2n$
Successor $=2n+1$
Product $=2n(2n+1)$
              $=2r\rightarrow\,even$

So, The product of a whole number(other than zero) and its successor is an even number.

Mark the correct alternative of the following.
The product of the predecessor and successor of an odd natural number is always divisible by?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $2$

  2. $4$

  3. $6$

  4. $8$

Show answer
Correct Option: A,B
Explanation:

odd Natural Number

$2n+1$

Predecessor $=2n+1-1$
                      $=2n$

Successor     $=2n+1+1$
                      $=2n+2$


Product $=2n.(2n+2)$
              $=2n.2(n+1)$
              $=4.n(n+1)$
             $=4r$
                   $\downarrow$
          divisible by $4,2$

The product of the predecessor and successor of an odd natural number is always divisible by $4,2$.

6(7 x 3) = (6 x 7) x 3 is an example of

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. Associative property

  2. Closure property

  3. Commutative property

  4. Distributive property

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Correct Option: A
Explanation:

a(b x c ) = (a x b) x c is an example of associative property.

(98 + 14) x 0 is ________

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 112

  2. 1

  3. 0

  4. 0 + 98 + 14

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Correct Option: C
Explanation:

We know that for any number $n$ multiplied by $0$ is always $0$ that is $n\times 0=0$.


Now, let us consider the given expression $(98+14)\times 0$ and solve as follows:

$(98+14)\times 0=112\times 0=0$

Hence, $(98+14)\times 0=0$

What number should replaced M in This multiplication problem ? 

 3 M 4
$\displaystyle \frac{4}{\underline {1\, 2\, 1\, 6}}$

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 0

  2. 5

  3. 7

  4. 8

Show answer
Correct Option: A
Explanation:

$0$ should be replaced M because
$304\times 4 = 1216$

Which of the following property is not applicable to addition of whole numbers?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. Closure property

  2. Commutative property

  3. Associative property

  4. None of these

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Correct Option: D
Explanation:

Let us have a look at the properties of whole numbers under addition:


(i) Closure property : When we add or multiply any two whole numbers we get a whole number. For example:

$9 + 8 = 17$ which is also a whole number.

Therefore, whole numbers are closed under addition.

(ii) Commutative property : You can add whole numbers in any order. This property is known as commutative property for addition. For example:

$5 + 11 = 11 + 5=16$ 

Therefore, whole numbers are commutative under addition.

(iii) Associative of addition : This means that in an addition expression; even if we make different groups with same given whole numbers, then also the sum in all the groups always remains the same. This property is also known as Associative property of Addition of Whole Numbers. For example:

Group 1 $= (5 + 6) + 7=11+7=18$  

Group 2 $= 5 + (6 + 7)=5+13=18$ 
 
As, in both the groups the sum is same that is $18$.
 
Therefore, whole numbers are associative under addition.

Hence, none of the property is not applicable to addition of whole numbers.

On dividing 55,390 by 299 the remainder is 75. The quotient is

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 195

  2. 185

  3. 175

  4. 193

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Correct Option: B
Explanation:
It is given that the dividend is $55390$, divisor is $299$ and the remainder is $75$.

Let the quotient be $x$.

We know that 

Dividend = Divisor × quotient + remainder

Therefore, by substituting the values, we have,

$55390=299\times x+75$
 $\Rightarrow 55390=299x+75$

$\Rightarrow 299x=55390-75$

$\Rightarrow 299x=55315$

$\Rightarrow x=\dfrac { 55315 }{ 299 }$

$\Rightarrow x=185$

Hence, the quotient is $185$.

72 $\times $ b = 4572a then the value of a + b is (where a is a single digit whole number and b is a natural number)

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 635

  2. 471

  3. 640

  4. None of these

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Correct Option: A