Tag: ways to multiply and divide

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Questions Related to ways to multiply and divide

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

The number of positive n in the range $12\le n\le 40$ such that the product (n -1) (n -2).... 3.2.1 is not divisible by n is :

  1. 5

  2. 7

  3. 13

  4. 14
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The product (n-1)! is divisible by n if n is composite and n > 4 (Wilson's Theorem related logic). For n in [12, 40], (n-1)! is not divisible by n only if n is prime. The primes between 12 and 40 are 13, 17, 19, 23, 29, 31, 37. There are 7 such numbers.

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

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

  1. An even number

  2. An odd number
  3. Divisible by $4$
  4. Divisible by $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. $2$
  2. $4$
  3. $6$
  4. $8$
Reveal answer Fill a bubble to check yourself
A,B Correct answer
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 $4,2$.

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

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

  1. Closure property

  2. Commutative property

  3. Associative property

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. 195

  2. 185

  3. 175

  4. 193
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $185$.