Tag: maths

Questions Related to maths

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

Show answer
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

Which natural number is nearest to $9217$, which is completely divisible by $88$ ?

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

  1. $9152$

  2. $9240$

  3. $9064$

  4. $9184$

Show answer
Correct Option: B
Explanation:

On dividing we get,
$\frac { 9217 }{ 88 } =104\frac { 65 }{ 88 } $

Therefore,

Required number 

$= 9217 + (88 - 65)$ ,Because (88 - 65) < 65.

$= 9217 + 23$

$= 9240$

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

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

  1. $B=6,A=7$

  2. $B=4,A=3$

  3. $B=3,A=4$

  4. $B=7,A=6$

Show answer
Correct Option: A
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.

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

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

  1. 2515

  2. 3455

  3. 2875

  4. 2785

Show answer
Correct Option: B
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 $3465-10=3455$

An integer is multiplied by 2 and the result is then multiplied by 5 The final result could be

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

  1. 64

  2. 32

  3. 12

  4. 30

Show answer
Correct Option: D
Explanation:

If a number is multiplied by 2 and 5 respectively. Then number should be divided by their L.C.M i.e  by 10.
Clearly, only number divisible by 10 is 30.
Hence, option D is correct.

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

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

  1. $\displaystyle \frac{-63}{1024}$

  2. $\displaystyle \frac{-63}{2048}$

  3. $\displaystyle \frac{-9}{2048}$

  4. $\displaystyle \frac{9}{1024}$

Show answer
Correct Option: C
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) $\displaystyle \frac{-9}{2048}$

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

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

  1. $0$

  2. $16$

  3. $27$

  4. $77$

Show answer
Correct Option: C
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
$

If $\div$ means $-$, $-$ means $\times$, $\times$ means $+$ and $+$ means $\div$, then
$20\times 60\div 40-20+10=$

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

  1. $40$

  2. $0$

  3. $80$

  4. $60$

Show answer
Correct Option: B
Explanation:

$20\times 60\div 40-20+10=$
After putting the true sign, we get
$20+ 60- 40\times20\div10=$
$20+60-80=$
$0=0$
Answer (B) 0