Tag: multiplication methods

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

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

  1. $\dfrac { 1 }{ 3+\sqrt { 8 } } $
  2. $3-\sqrt8$
  3. $8+\sqrt3$
  4. $3+\sqrt8$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. $36$
  2. $150$
  3. $181$
  4. $218$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

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

  1. $1012$
  2. $1201$
  3. $1212$
  4. $1210$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $D$

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

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

  1. $2$
  2. $4$
  3. $689$
  4. $1023$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $4$.  $[B]$

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

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 $2 : 3$?

  1. $28$
  2. $40$
  3. $35$
  4. $70$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.