Tag: multiplication methods

Questions Related to multiplication methods

$21774\div 19\div 3$ is equal to 

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

  1. $1146$

  2. $7258$

  3. $3438$

  4. $382$

Show answer
Correct Option: D

What is the multiplicative inverse of $3-\sqrt8$ ?

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

  1. $\dfrac { 1 }{ 3+\sqrt { 8 } } $

  2. $3-\sqrt8$

  3. $8+\sqrt3$

  4. $3+\sqrt8$

Show answer
Correct Option: D
Explanation:

Let $x$ be the multiplicative inverse


$\Rightarrow 3-\sqrt { 8 } \times x=1$

$ \Rightarrow x=\dfrac { 1 }{ 3-\sqrt { 8 }  } $

Rationalising the number

$\Rightarrow x=\dfrac { 1 }{ 3-\sqrt { 8 }  } \times \dfrac { 3+\sqrt { 8 }  }{ 3+\sqrt { 8 }  } $

$ \Rightarrow x=\dfrac { 3+\sqrt { 8 }  }{ { (3 })^{ 2 }-{ ({ \sqrt { 8 }  })^{ 2 } } } =\dfrac { 3+\sqrt { 8 }  }{ 9-8 } =\dfrac { 3+\sqrt { 8 }  }{ 1 } $

$ \Rightarrow x=3+\sqrt { 8 } $

So option $D$ is correct.

If $4\times 5=1625$, $3\times 8=964$, $4\times 6=436$ then $1\times 9=?$

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

  1. $36$

  2. $150$

  3. $181$

  4. $218$

Show answer
Correct Option: C
Explanation:
If you see the given equation carefully then you may realize that $1625$ come because of $ { 4 }^{ 2 } $ and $ { 5 }^{ 2 } $
So by this logic we can write 
$ 1\times 9={ 1 }^{ 2 }{ 9 }^{ 2 }=181 $
So option $ C $ is correct.

The sum of all two digit numbers which when divided by $4$, yield unity as reminder is

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

  1. $1012$

  2. $1201$

  3. $1212$

  4. $1210$

Show answer
Correct Option: D
Explanation:

Sum of all $2$ digit number divided by $4$ yields unity as remainder

$=13+17+21+97$
Series is in $AP$ and total are
$=a+(n-1)d=97$
4413+(n-1)4=97$
$(n-1)4=84$
$n-1=21$
$n=22$ terms
Sum $=\cfrac{n}{2}(2a+(n-1)d)\=\cfrac{22}{2}(26+(21\times4)\=11(26+84)\=11(110)\=1210$
Answer $D$

The value of $\dfrac{(469 +174)^2 - (469-174)^2}{469 \times 174}$ is

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

  1. $2$

  2. $4$

  3. $689$

  4. $1023$

Show answer
Correct Option: B
Explanation:

$(a+b)^2-(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)=4ab$.


Using the above identity,

$\dfrac{(469+174)^2-(469-174)^2}{469\times{174}}=\dfrac{4\times{469}\times{174}}{469\times174}=4$.

$\therefore$  The answer is $4$.  $[B]$

The smallest number which must be added to $803642$ in order to obtain is multiple of $9$ is

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: D
Explanation:

803642 will be divided by 9, if 8+0+3+6+4+2 =23 is divided by 9.
$\Rightarrow$ needs 4 more for that.

Choose the correct answer from the alternatives given.
In a mixture of $35$ litres, the ratio of milk and water is $4: 1$. How many litres of water must be added to make the ratio $2 : 3$?

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

  1. $28$

  2. $40$

  3. $35$

  4. $70$

Show answer
Correct Option: C
Explanation:

Initial quantity of milk and water is Milk  $=\dfrac{4}{5} \times $ $35 = 28 $litres
Water $=\dfrac{1}{5} \times $ $35 =7 $litres.
Let $x$ liters of water is added, then, 
$\dfrac{28}{7 + x} = \dfrac{2}{3}$
$x = 35$
Hence , 35 liters of water is added.

What is the average of all numbers between $11$ and $80$ which are divisible by $6$?

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

  1. $46$

  2. $47$

  3. $44$

  4. $45$

Show answer
Correct Option: D
Explanation:

Required average $= \dfrac {12 + 18 + 24 + .... + 78}{12} = 45$.

What is the remainder when $6729$ is divided by $35$?

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

  1. $11$

  2. $7$

  3. $9$

  4. $13$

Show answer
Correct Option: C
Explanation:

$6729 = 6720 + 9 = 35\times 192 + 9$
Hence the remainder is $9$.

The estimated product of $15289$ and $587$ is

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

  1. $8000000$

  2. $8500000$

  3. $9000000$

  4. $9500000$

Show answer
Correct Option: C
Explanation:

$15289$ is estimated as $15300$ and $587$ is estimated as $600$.

So, the given product is estimated as $153000\times 600=918,0000$.
So the correct estimate is $900,0000$.