Tag: ways to multiply and divide

Quizzes (8) Questions (122)

Questions Related to ways to multiply and divide

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.