Tag: maths

Questions Related to maths

Each piece of cardboard is $0.3\ cm$ thick. If Marie stacks $8$ pieces of cardboard on top of one another, how thick will the stack be?

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. $2.4\ cm$

  2. $24\ cm$

  3. $2.1\ cm$

  4. $21\ cm$

Show answer
Correct Option: A
Explanation:

It is given that each piece of cardboard is $0.3$ cm thick which means that one piece is $0.3$ cm thick.


If Marie stacks $8$ pieces of cardboard, then the thickness of $8$ pieces of cardboard will be:

$0.3\times 8=2.4$ cm

Hence, the stack will be $2.4$ cm thick.

If $100\times \text{ ? }=352$. Then, find the missing number.

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. $0.352$

  2. $352$

  3. $35.2$

  4. $3.52$

Show answer
Correct Option: D
Explanation:

Let $x$ be the missing number.


$100\times x=352\ \Rightarrow 100x=352\ \Rightarrow x=\dfrac { 352 }{ 100 } \ \Rightarrow x=352\times 0.01\quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ 10 } =0.1,\dfrac { 1 }{ 100 } =0.01,.... \right} \ \Rightarrow x=3.52$

Hence, the missing number is $3.52$.

Calculate $456.78\times 8$.

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. $36542.4$

  2. $365.424$

  3. $3,654.24$

  4. $36.5424$

Show answer
Correct Option: C
Explanation:
Let us first multiply the two given numbers $456.78$ and $8$ without decimal point:

$45678\times 8=365424$

Since, $456.78$ has two decimal places, therefore the answer $365424$ should also have two decimal places that is $3654.24$.

Hence, $456.78\times 8=3,654.24$.

$45.678\times \text{ ? }=1187.628$. Find $?$.

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. $26$

  2. $27$

  3. $28$

  4. $29$

Show answer
Correct Option: A
Explanation:

Let $x$ be the missing number.


$45.678\times x=1187.628\ \Rightarrow 45.678x=1187.628\ \Rightarrow \dfrac { 45678x }{ 1000 } =\dfrac { 1187628 }{ 1000 } \quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ 10 } =0.1,\dfrac { 1 }{ 100 } =0.01,.... \right} \ \Rightarrow x=\dfrac { 1187628 }{ 1000 } \times \dfrac { 1000 }{ 45678 } \ \Rightarrow x=26$

Hence, the missing number is $26$.

Multiply $43.09$ with $23$.

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. $99.107$

  2. $991.07$

  3. $9910.7$

  4. $9.9107$

Show answer
Correct Option: B
Explanation:
Let us first multiply the two given numbers $43.09$ and $23$ without decimal point:
$4309\times 23=99107$
Since, $43.09$ has two decimal places, therefore the answer $99107$ should also have two decimal places that is $991.07$.
Hence, $43.09\times 23=991.07$.

(Three rupees $5$ paise) $\times$ (five rupees $40$ paise) is equal to

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. $Rs. 18.90$

  2. $Rs. 16.47$

  3. $Rs. 17.64$

  4. $RS. 15.37$

Show answer
Correct Option: B
Explanation:

We know that 100 paise is nothing but 1 Rupee.

So $5Paise =  0.05 Rupees$
Also $40 Paise = 0.4 Rupees$
Now Three Rupees $5 Paise = 3 Rupees + 0.05 Rupees$
                                               $=3.05 Rupees$
Also Five Rupees $40 Paise= 5 Rupees + 0.40 Rupees$
                                              $= 5.40 Rupees$
Now to find $(Three\quad rupees\quad 5paise)×(fiverupees\quad 40paise)$
$3.05\times 5.40 = 16.47$

Solve the following:
$210.01\times 5$ = $1050.05$

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Step 1 : $21001 x 5 = 105005$

Step 2 : Total number after decimal $= 2$
So, $210.01 \times  5 = 1050.05$

Solve the following:
$1.5\times 0.3$


Ans : $0.45$

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. True

  2. False

Show answer
Correct Option: A

Using  identity the value obtained from the product $25.4 \times 24.6$ is

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. $624.84$

  2. $642.84$

  3. $264.84$

  4. $62.84$

Show answer
Correct Option: A
Explanation:


Given

$25.4\times24.6$

we can re-wright them as

$(25+0.4)\times (25-0.4)$

$\because \ we \ have \ an\ identity \ (a+b) (a-b)=a^2-b^2$

$a=25,\ b=0.4$


$= (25)^2-(0.4)^2$

$= 625- 0.16$

$=624.84$

$\therefore option\ A\ is\ correct.$


Without actual multiplication, the value $79.01 \times 79.01 + 2 \times 79.01 \times 20.99 + 20.99 \times 20.99$

maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

  1. $10,009$

  2. $1000.06$

  3. $10,000$

  4. $1007$

Show answer
Correct Option: C
Explanation:
$79.01\times 79.01+2\times 79.01\times 20.99+20.99\times 20.99....(1)$
$\dfrac {7901}{100}\times \dfrac {7901}{100}+2\times \dfrac {7901}{100}\times  \dfrac {2099}{100}+\dfrac {2099}{100}\times \dfrac {2099}{100}....(2)$

$7901\times 7901=(7901)^2 =(7900 +1)^2$    $\quad [\because \ 79^2=(80-1)^2\\ =80^2+1-2.80\\ =6400+1-160\\ =6241]$
$=(7900)^2 +1^2+2(7900)(1)$
$=62410000+1+15800$
$=62425801$ 

$2099\times 2099 =(2099)^2=(2100-1)^2$ $\quad [\because \ 21^2=(20+1)^2\\ =20^2+1+2.20\\ =400+40+1\\ =441]$
$=(2100)^2+1^2-2(2100)(1)$
$=4410000+1-4200$
$=4405801$

$7901\times 2099=(7900+1) (2100-1)$
$=(7900)(2100)-7900+2100-1$
$=16590000-7900+2100-1$
$=16584299\ =16584199$
from $(2)$
$\dfrac {62425801}{10000}+\dfrac {2\times 16584199}{10000}+\dfrac {4405801}{10000}$
$6242.5801+\dfrac {33168398}{10000}+440.5801$
$6242.5801+3316.8398+440.5801$
$=10,000$