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

We know that, if the numerator is less than the denominator, then the value of fraction is less than $1.$
Hence, the fraction $\frac57$ lies between $0$ and $1.$

$1\frac{3}{4}$ is a mixed fraction as:
$1+\frac{3}{4}=1\frac{3}{4}$

$\frac{15}{20}$ can be written in the simplest form $\frac{4}{3}.$
Now, look at the options, then option $D$ can also be written in the simplest form $\frac{4}{3}.$
That means option $D$ is equivalent to $\frac{15}{20}.$

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

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

Proper fraction of $6\cfrac{1}{5}​= \cfrac{5 \times 6 + 1}{5} ​= \cfrac{30 + 1}{5} ​= \cfrac{31}{5}$

$\Big(\frac{3}{4}=\frac{\text{x}}{20}\Big)$
We have,
$20 = 4 \times 5$
So, we have to multiply the numerator by $5.$
Therefore, $x = 3 \times 5 = 15$

A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number).
In given options $\frac{11}{23}$ is proper fraction.

Given, $\frac{20}{50}$ To obtain the lowest form of given fraction, divide it by $10.$
Then the lowest form of $\frac {20}{50}$ is $ \frac{2}{5}​$

Fractions can be compared by converting them into like fractions and then arranging them in ascending or descending order.
$\frac{3}{5}=\frac{3}{5}\times\frac{6}{6}=\frac{18}{30}$
$\frac{2}{3}=\frac{2}{3}\times\frac{10}{10}=\frac{20}{30}$
$\frac{5}{6}=\frac{5}{6}\times\frac{5}{5}=\frac{25}{30}$
$\frac{7}{10}=\frac{7}{10}\times\frac{3}{3}=\frac{21}{30}$
We know,
$18 < 20 < 21 < 25$
$\Rightarrow\frac{18}{30}<\frac{20}{30}<\frac{21}{30}<\frac{25}{30}$
$\Rightarrow\frac{3}{5}<\frac{2}{3}<\frac{7}{10}<\frac{5}{6}$
$\therefore$ the smallest fraction is $\frac{3}{5}.$
Hence, the correct option is $(b).$

For rounding off to tenths place, we look at the hundredths place.
Here, the digit at hundredths place is $7$ which is greater than $5.$
So, the digit at the tenths place $(5)$ will be increased by $1$ and digits at the hundredths and thousandths place will be written as equal to zero.
Hence, rounding off $13.572$ to nearest tenths, we get $13.6.$

Since, for comparing fractions with same denominators, fraction with smaller numerator is
$\therefore\frac38<\frac58<\frac78<\frac98$
Hence, $\frac38$ is the smallest fraction.

Let us check with all options:
$(A) 14$ tenths $4$ thousandths $=\frac{14}{10}+\frac{4}{1000}=1.4+0.004=1.404.$
$(B) 2$ tenths $13$ hundredths $=\frac{2}{10}+\frac{13}{10}=0.33.$
$(C) 4$ hundredths $2$ tenths $=\frac{4}{100}+\frac{2}{10}=0.24.$
$(D) 7$ tenths $17$ hundredths $=\frac{7}{10}+\frac{17}{100}=0.87.$ Hence, it is correct.

$\frac{5}{12}=\frac{\text{x}}{3}$
On cross-multiplying, we get:
$5\times3=\text{x}\times12$
$\Rightarrow\text{x}=\frac{5\times3}{12}$
$\Rightarrow\text{x}=\frac{15}{12}$
$\text{x}=\frac{5}{4}$

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 $\frac{2}{3}$ is $\frac{2\times5}{3\times5}.$
Hence, the correct option is $(c).$

$=\frac{5}{8}-\frac{1}{8}$
$=\frac{(5-1)}{8}$
$=\frac{4}{8}$
$=\frac{1}{2}$

Improper fraction of
$2\cfrac{3}{7}= \cfrac{7 \times 2 + 3}{7}​$
$= \cfrac{14 + 3}{7}​= \cfrac{17}{7}$

Proper fraction of
$6\frac{1}{5}=\frac{5\times6+1}{5}=\frac{30+1}{5}=\frac{31}{5}$

On dividing the numerator & denominator by $2$, we get $\frac{3}{5}.$

$L.C.M.$ of $3, 9, 2$ and $12 = ( 2 \times 2 \times 3 ​\times 3) = 36$
Now, we have:
$\frac{2}{3}=\frac{2\times12}{3\times12}=\frac{24}{36}$
$\frac{5}{9}=\frac{5\times4}{9\times4}=\frac{20}{36}$
$\frac{1}{2}=\frac{1\times18}{2\times18}=\frac{18}{36}$
$\frac{7}{12}=\frac{7\times3}{12\times3}=\frac{21}{36}$
Hence, $\frac{24}{36}=\frac{2}{3}$ is the largest fraction.

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

Improper fractions are the one who numerator is more than the denominator
In $ \frac{13}{2}​$ and $ \frac{7}{3}​, $ the numerator is greater than the denominator
So, they are not proper fractions Whereas in $\frac{2}{7}$​ and $\frac{7}{11},$ the numerator is less than the denominator
Thus, they are proper fractions.
Hence, $\frac{13}{2}​$ and $\frac{7}{3}​ $ are improper fractional numbers.

$1\frac{3}{4}$​ is a mixed fraction as:
$1\dfrac{3}{4}=1\dfrac{3}{4}$

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

Improper fractions are the one who numerator is more than the denominator
In $\displaystyle\frac{13}{2}$​ and $\dfrac{7}{3}$​, the numerator is greater than the denominator So, they are not proper fractions Whereas in $\dfrac{2}{7}$and $\dfrac{7}{11}$​, the numerator is less than the denominatorThus, they are proper fractions.Hence, $\dfrac{13}{2}$ and $\dfrac{7}{3}$ are improper fractional numbers.

Since, $0.023$ is greater than $0.02$ and less than $0.03.$
Therefore, $0.023$ lies between $0.02$ and $0.03.$
$0.02 < 0.023 < 0.03$

$\frac{3}{7}$ is a simple fraction because both numerator and denominator are integers.

$2 < 4 < 5 < 11$
$\Rightarrow\frac{2}{9}<\frac{4}{9}<\frac{5}{9}<\frac{11}{9}$
$\therefore$ the smallest fraction is $\frac{2}{9}.$
Hence, the correct option is $(d).$

This happens in only option
$\text{B}1+\frac{1}{10}=\frac{11}{10}=11\times1\times\frac{1}{10}$

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 $6050.3$

A proper or improper fraction which is completely divisible denotes the denominator is the divider and the numerator is the divident.
The quotient is the answer of that division. We see that option $D$ is the only option that shows this relationship through two different symbols.