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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 $185$.
Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

Find the value of A and B in the following sum:
$3 B$
$\underline {\times A}$
$\underline {2 5 2}$

  1. $B=6,A=7$
  2. $B=4,A=3$
  3. $B=3,A=4$
  4. $B=7,A=6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Now as $A \times B$ gives 2 in the product, the combinations could be

$2\times 1$ or $1 \times 2, 6 \times 2$ or $2\times 6, 3 \times 4$

or $4 \times 3, 6 \times 7$ or $7 \times 6$ or $8 \times 4$ or

$4\times 8, 9 \times 8$ or $8\times 9$. But to get 2 in hundred's

place and 5 in ten's place in the product, B has to be 6 and A has to be

7. Then $6\times 7=42$.
Write 2 and carry over 4. then $7\times 3= 21$ and add 4 to get 2 and 5 in the product.
The value of B is 6 and A is 7.

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

The least number which on division by 35 leaves a remainder 25 and on division by 45 leaves the remainder 35 and on division by 55 leaves the remainder of 45 is

  1. 2515

  2. 3455

  3. 2875

  4. 2785
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$35=5\times7$
$45=3\times3\times5$
$55=5\times11$
LCM of (35,45,55)=$3\times3\times5\times\times7\times11=3465$
Since difference between divisor and remainder is 10
Hence least number is $3465-10=3455$

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

If $\displaystyle a=(2^{-2}-2^{-3}),b=(2^{-3}-2^{-4})and: c=(2^{-4}-2^{-2})$ then find the value of 3 abc

  1. $\displaystyle \frac{-63}{1024}$
  2. $\displaystyle \frac{-63}{2048}$
  3. $\displaystyle \frac{-9}{2048}$
  4. $\displaystyle \frac{9}{1024}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$a=(2^{-2}-2^{-3}),b=(2^{-3}-2^{-4})and: c=(2^{-4}-2^{-2})$
So,  $3abc=3\times (2^{ -2 }-2^{ -3 })\times (2^{ -3 }-2^{ -4 })\times (2^{ -4 }-2^{ -2 })$
$3abc=3\times (1/4-1/8)\times (1/8-1/16)\times (1/16-1/4)$
$3abc=3\times (1/8)\times (1/16)\times (-3/16)$
$3abc=\frac { -9 }{ 2048 } $
Answer (C) $\displaystyle \frac{-9}{2048}$

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

Simplify : $\displaystyle\frac{9^{5/2}-3\times7^0-\begin{pmatrix}\displaystyle\frac{1}{81}\end{pmatrix}^{-\displaystyle\frac{1}{2}}}{(27)^{2/3}-\begin{pmatrix}\displaystyle\frac{8}{27}\end{pmatrix}^{2/3}}$

  1. $0$
  2. $16$
  3. $27$
  4. $77$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$
\frac { { 9 }^{ \frac { 5 }{ 2 }  }-{ 3\times 7 }^{ 0 }{ \quad -\frac { 1 }{ 81 }  }^{ -\frac { 1 }{ 2 }  } }{ { 27 }^{ \frac { 2 }{ 3 }  }-(\frac { 8 }{ 27 } )^{ \frac { 2 }{ 3 }  } } \quad \quad \ \ NR\quad =\quad { 3 }^{ 2\times \frac { 5 }{ 2 }  }-3-(\frac { 1 }{ 81 } )^{ -\frac { 1 }{ 2 }  }\quad =\quad { 3 }^{ 5 }-3-({ 3 }^{ -4\times \frac { -1 }{ 2 }  })\quad =243-3-9=\quad 231\quad \ Dr\quad =\quad { 3 }^{ 3\times \frac { 2 }{ 3 }  }-(\frac { 2 }{ 3 } )^{ 3\times \frac { 2 }{ 3 }  }\quad =\quad 9\quad -\quad \frac { 4 }{ 9 } \quad =\quad 77/9\ \frac { Dr }{ Nr } \quad =\quad \frac { 231 }{ 77/9 } \quad =\quad 3\times 9\quad =\quad 27
$