Maths M.C.Q. [1 Marks Each]

$\begin{array}{c|c}3&3,6,9\\\hline2&1,2,3\\\hline3&1,1,3\\\hline&1,1,1\end{array}$
$\frac{5}{6}+\frac{2}{3}-\frac{4}{9}$
$​​L.C.M.$ of $3, 6$ and $9 = (2 \times 3 \times 3) = 18$
$=\frac{(15+12-8)}{18}$
$\Big(\frac{18}{6}=3,3\times5=15\Big)$
$\Big(\frac{18}{3}=6,6\times2=12\Big)$
and $\Big(\frac{18}{9}=2,2\times4=8\Big)$
$=\frac{(27-8)}{18}$
$=\frac{19}{18}$
$=1\frac{1}{18}$

$9275$ Meters in km, as decimal fraction$=\frac{9275}{1000} \ \text{KM} =9.275 \ \text{KM}$

In $\dfrac{6}{5}$​, the numerator $6$ is greater than the denominator $5.$
Therefore, $\dfrac{6}{5}$ is not a proper fraction.

A fraction whose numerator is less than the denominator is called a proper fraction.
Here, $\frac{3}{5}$ is a proper fraction.
Hence, the correct option is $(a).$

since it is a mixed fraction.. it can be written as $\frac{9}{4}..$. then the reciprocal of $\frac{9}{4}$ is $\frac{4}{9}..$

Since, $0.7499$ is greater than $0.749$ and less than $0.75$. Therefore, $0.7499$ lies between $0.749$ and $0.75.$
$0.749 < 0.7499 < 0.75$

$\frac{26}{4}+\frac{14}{3}$
$=\frac{78+56}{12}=\frac{134}{12}=11\frac{2}{12}=11\frac{1}{6}$

Fractions that are greater than $00$ but less than $1$ are called proper fractions.
In proper fractions, the numerator is less than the denominator.
When a fraction has a numerator that is greater than or equal to the denominator, then the fraction is an improper fraction.
An improper fraction is always $1$ or greater than $1.$
Now looking at options
$\cfrac {2}{3} = .666 < 1$
$\cfrac {3}{4} = .75 < 1$
$\cfrac {5}{7} = .71 < 1$
$\cfrac {6}{5}= 1.2 < 1$
So $\cfrac {6}{5}$ is Not a Proper fraction.

The first decimal digit from the decimal point is the tenth.
$4.4$ has $4$ on the ones, after decimal point on the tenths is $4$ tenths.
$4.4$ is the sum of $4$ and$\displaystyle{\frac{4}{10}}$ or $\displaystyle{\frac{4}{10}}$.
So option $B$ is the correct answer.

Given, $3\frac{1}{2}\text{m}$ of cloth cost $Rs. 168.$
Then $4\frac{1}{3}\text{m}$ of cloth cost Rs. $\frac{168\times\frac{13}{3}}{\frac{7}{2}}=208.$

Since, numerator > denominator, $\frac{5}{4}$ is not a proper fraction.

Since, numerator > denominator, $\frac {5}{4}$ is not a proper fraction.

In an improper fraction, the numerator is greater than the denominator.
Of the given fractions, $\frac{15}{14}$ has numerator greater than the denominator.
Hence, $\frac{15}{14}$​ is a proper fraction.

The smallest possible decimal fraction upto three decimal places $=\dfrac{1}{1000}=.001$

Improper fraction of
$2\cfrac{1}{2}​= \cfrac{2 \times 2 + 1}{2}$
$= \cfrac{4 + 1}{2}$
$=\cfrac{5}{2}$

Number of dresses she had to stiches $= 35$
Number of dresses she has finished $= 21$
$\therefore$ Fraction of dresses she has finished = $\dfrac{21}{35} =\dfrac{3}{5}$

$\frac{1.5}{0.2 \ + \text{ x} } = 5$
cross multiplying$\Rightarrow 5 \times (0.2 + x) = 1.5$
$\Rightarrow 5 \times 0.2 + 5x = 1.5$
$\Rightarrow 1 \times 5x = 1.5$
$\Rightarrow 5x = 1.5 - 1 = 0.5$
$\Rightarrow 5x = 0.5$
$\Rightarrow x = 0.1$

Proper fractions are the one whose numerator is less than the denominator
In $\dfrac{3}{2}$ and $ \dfrac{8}{3},$ the numerator is greater than the denominatorSo, they are not proper fractionsWhereas in $\dfrac{2}{5}$​ and $\dfrac{1}{7}$ the numerator is less than the denominatorThus, they are proper fractions.Hence, $\dfrac{2}{5}$ and $\dfrac{1}{7}$are proper fractional numbers.

$0.000000375=375\times { 10 }^{ -9 }=3.75\times { 10 }^{ -7 }$
$=\cfrac { 375 }{ 100 } \times { 10 }^{ -7 }$
$=\cfrac { 15 }{ 4 } \times { 10 }^{ -7 }=3\cfrac { 3 }{ 4 } \times 10^7.$

Fraction equivalent to a given fraction can be obtained by multiplying or dividing its numerator and denominator by a non-zero number.
Therefore, the fraction equivalent to $\frac{30}{45}$ is $\frac{30\div15}{45\div15}=\frac{2}{3}.$
Hence, the correct option is $(c).$

If the numerator is less than the denominator then the fraction is called as proper fraction.
Hence,$\frac{7}{8}$ is a proper fraction.

$\text{Addition of like fractions} =\frac{\text{Sum of the numerators}}{\text{ Common denominator}}$
$=\frac{5}{8}+\frac{1}{8}$
$=\frac{(5+1)}{8}$
$=\frac{6}{8}$
$=\frac{3}{4}$

A fraction whose numerator is less than the denominator is called a proper fraction, otherwise it is called an improper fraction.
Here, $\frac{34}{13}$ is an example of an improper fraction.
Hence, the correct option is $(b).$

$\Rightarrow2\frac{5}{7}\text{%} $ of $280$
$=\frac{19}{7}\text{%}$ of $280$
$=\frac{19}{7}\times\frac{280}{100}$
$=19\times\frac{4}{10}$
$\frac{76}{10}=7.6$
So $2\frac{5}{7}\text{%}$ of $280\text{cm}$ is $7.6\text{cm}.$

Here, Numerator > denominator only in option $A.$

Given, $\frac{11}{12}\times\frac{16}{4}\times\frac{9}{16}=\frac{11}{12}\times4\times\frac{9}{16}$
$\rightarrow\frac{11}{3}\times\frac{9}{16}$
$\rightarrow11\times\frac{3}{16}=\frac{33}{16}=2\frac{1} {16}$

In a proper fraction, the numerator is smaller than the denominator. Of the given fractions, $\displaystyle \frac{5}{7}$ has numerator smaller than the denominator.
Hence, $\displaystyle \frac{5}{7}$​ is a proper fraction.

Let us compare $3\frac{1}{3}$ and $\frac{33}{10}$
or $\frac{10}{3}$ and $\frac{33}{10}$
$10 \times 10 = 100$ and $3 ​\times 33 = 99$
Clearly,$ 100 > 99$
Therefore, $\frac{10}{3}<\frac{33}{10}$
or $3\frac{1}{3}<\frac{33}{10}$

Games won $= 6$
Total Games $= 6 + 4 = 10$
$\therefore$ required fraction $\frac{6}{10}$

According to number system , every fraction in $\frac{p}{q} $ form can be converted into decimal number. and vice versa.

In an improper fraction, the numerator is always greater than the denominator.
Eg $ \displaystyle \frac{9}{5}​,\displaystyle \frac{5}{3}.$

$\frac{7}{3},$ because in an improper fraction, the numerator is more than the denominator.

$0.231=\dfrac{0.231}{1}$​Multiplying numerator and denominator by $100.\dfrac{231}{1000}$​ Hence.

Converting fraction to decimal = $\frac{3}{10} = 0.3$

A Mixed Fraction is a whole number and a proper fraction combined.
Divide the numerator by the denominator.
Write down the whole number answerThen write down any remainder above the denominator.
$\dfrac{39}{12}=\dfrac{36}{12}+\dfrac{3}{12}$
$=3+\dfrac{3}{12}=3\dfrac{3}{12}$

$\frac{-1}{2}=-0.5$