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

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 $\frac{4}{10}$or $\frac{44}{10}.$

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

The $LCM$ of $8, 7, 6$ and $5$ is $840$, so we can convert each fraction into an equivalent fraction with denominator $840.$
$\frac{7}{8}=\frac{7}{8}\times\frac{105}{105}=\frac{735}{840}$
$\frac{6}{7}=\frac{6}{7}\times\frac{120}{120}=\frac{720}{840}$
$\frac{4}{5}=\frac{4}{5}\times\frac{168}{168}=\frac{672}{840}$
$\frac{5}{6}=\frac{5}{6}\times\frac{140}{140}=\frac{700}{840}$
When denominator is the same, the fraction with the largest numerator is the greatest.
Thus, $\frac{7}{8}$ is the greatest fraction among all.

Clearly from question denominator $= 3$ numerator $= 2$ Fraction = $\frac{2}{3}$

Converting the given decimals to like decimals, we have $15.80$ and $6.73.$
$\ \ 15.80\\ \underline{-\ 6.73\ \ }\\ \underline{\ \ \ \ \ 9.07\ \ }$
Note: Decimals having the same number of digits on the right of the decimal point are known as like decimals.

$36.2<\text{br}>\Rightarrow36+0.2=\frac{362}{10}=36\frac{2}{10}$

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

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

$0.004\frac{0.004}{1}$ Here, we have three numbers after decimal point.
So, we multiply by both numerator and denominator by $1000.$
$=\frac{0.004\times1000}{1\times1000}$
$=\frac{4}{1000}$
$\therefore $ Fraction for $0.0040.004$ is $\frac{4}{1000}$

To get the Equivalent fraction of $\dfrac {9}{11}$ we will multiply numerator and denominator by $26.$
$\dfrac{9}{11} \times \dfrac{26}{26} =\dfrac{234}{286}$

Here, whole part of numbers $0.27, 0.082$ and $0.103$ are same and is less than $1.5.$
Now, we will compare the tenths part of $0.27, 0.082$ and $0.103.$
Tenths part of $0.27 = \frac{2}{10}$
Tenths part of $0.082 = \frac{0}{10}$ and tenths part of $0.103 =\frac{1}{10}$
Clearly, tenths part of $0.082$ is smallest.
Hence, $0.082$ is the smallest decimal.

We have, $\frac{3}{5}$
$\therefore\frac{3}{5}=\frac{3}{5}\times\frac{2}{2}=\frac{6}{10}$

To get the Equivalent fraction of $\frac{9}{11}$ we will multiply numerator and denominator by $26.$
$\frac{9}{11}\times\frac{26}{26}=\frac{234}{286}$

$\begin{array}{c|c}2&4,6,12,3\\\hline2&2,3,6,3\ \ \\\hline3&1,3,3,3\ \ \\\hline&1,1,1,1\ \ \end{array}$
$​​L.C.M.$ of $4, 6, 12$ and $3 = (2 \times 2 \times 3) = 12$
Thus, we have:
$\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}$
$\frac{5}{6}=\frac{5\times2}{6\times2}=\frac{10}{12}$
$\frac{7}{12}=\frac{7\times1}{12\times1}=\frac{7}{12}$
$\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}$
Clearly, $\frac{7}{12}$ is the smallest fraction.

$?-\frac{8}{21}=\frac{8}{21}$
$?=\frac{8}{21}+\frac{8}{21}$
$?=\frac{16}{21}$

$\Big(\frac{45}{60}=\frac{\text{3}}{\text{x}}\Big)$
Now,
$3=\frac{45}{15}$
So, we have to multiply the denominator by $15$
Therefore, $\text{x}=\frac{60}{15}$
$\text{x}=4$

$0.000000375=375\times10^{-9}=3.75\times10^{-7}$ $=\frac{375}{100}\times10^{-7}=\frac{15}{4}\times10^{-7}=3\frac{3}{4}\times10^{-7}$

We hve, mixed fraction $=5\frac47$
Converting mixed fraction into improper fraction by using that formula, mixed fraction = Improper fraction
$=\Big(\frac{\text{Whole number}\times\text{Denominator}+\text{Numerator}}{\text{Denominator}}\Big)$
$=\frac{5\times7+4}{7}=\frac{39}{7}$

To round to the nearest tenth, write down the number with a decimal point, and find the tenths place directly to the right of the decimal.
Then, to the right of the tenths place, look at the number in the hundredths place.
In $6050.287$ the number in the hundredths is $2.$
So, $6050.287$ rounded to the nearest tenths will be $6050.3$

$\frac{\text{a}}{\text{b}}=4$
$\Rightarrow\text{a}=4\text{b}$
On putting the value of a in $\frac{\text{a}+\text{b}}{\text{a}-\text{b}},$ we get:
$\frac{\text{a}+\text{b}}{\text{a}-\text{b}}=\frac{4\text{b}+\text{b}}{4\text{b}-\text{b}}=\frac{5\text{b}}{3\text{b}}$
On dividing the numerator & denominator by b, we get $\frac{5}{3}.$

Proper fractionof $5\cfrac{4}{9}​= \cfrac{9 \times 5 + 4}{9}​= \cfrac{45 + 4}{9} = \cfrac{49}{9}$​

Since, fractions with same denominators can be added by simply adding the numerators and writing the common denominator as it is.
$\frac{4}{17}+\frac{15}{17}=\frac{4+15}{17}=\frac{19}{17}$

Largest mixed number using these digits will be $11\frac{9}{7}$
Smallest mixed number will be $7\frac{9}{11}$
Their sum $=11\frac{9}{7}+7\frac{9}{11}=\frac{86}{7}+\frac{86}{11}$
$=\frac{11\times86+7\times86}{77}$
$=\frac{1548}{77}$
$=20\frac{8}{77}$

$\frac{1}{3}+\frac{1}{2}+\frac{1}{\text{x}}=4$
$\Rightarrow\frac{1}{\text{x}}=4-\frac{1}{3}-\frac{1}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{4\times6}{1\times6}-\frac{1\times2}{3\times2}-\frac{1\times3}{2\times3}$
$\Rightarrow\frac{1}{\text{x}}=\frac{24}{6}-\frac{2}{6}-\frac{3}{6}$
$\Rightarrow\frac{1}{\text{x}}=\frac{24-2-3}{6}$
$\Rightarrow\frac{1}{\text{x}}=\frac{19}{6}$
$\text{x}=\frac{6}{19}$

Vulgar fraction is a fraction expressed by numerator and denominator, and not in form of decimal.
The given number is in decimal form: $0.23$ Here, the decimal point is before two digits.
So, in order to obtain vulgar fraction, we need to multiply both the numerator and denominator by $100.$
$\frac{0.23}{1}=\frac{0.23\times100}{1\times100}=\frac{23}{100}$

Fractions that are greater than $0$ 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
$\frac{2}{3}=.666<1$
$\frac{3}{4}=.75<1$
$\frac{5}{7}=71<1$
$\frac{6}{5}=1.2>1$
So $\frac{6}{5}$ is Not a Proper fraction.

$12\dfrac16=\dfrac {12\times6+1}{6}$
$=\dfrac {73}{6}$

Two sevenths $\frac{2}{7}$

Converting the given decimals to like decimals, we have $0.070$ and $0.008.$
$\ \ \ \ 0.070\\\underline{+\ 0.008\ \ }\\\underline{\ \ \ \ 0.078\ \ }$
Note: Decimals having the same number of digits on the right of the decimal point are known as like decimals.