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

Numerator $<$ Denominator in all $4$ cases.

Since, fractions with same denominators can be subtracted by simply subtracting the numerators and writing the common denominator as it is.
$\frac{19}{9}-\frac59=\frac{19-5}9{}=\frac{14}{9}$

Factors of $24$ are $1, 2, 3, 4, 6, 8, 12, 24.$
Factors of $36$ are $1, 2, 3, 4, 6, 9, 12, 18, 36.$
Common factors of $24$ and $36$ are $1, 2, 3, 4, 6, 12.$
$H.C.F. = 12$
Dividing both the numerator and the denominator by $12:$
$\frac{24}{36}$
$=\frac{24\div12}{36\div12}$
$=\frac{2}{3}$

$\Rightarrow2\dfrac { 5 }{ 7 } \%$ of $280$
$=\dfrac { 19 }{ 7 }\% \%$ of $280$
$=\dfrac{19}{7}\times \dfrac{280}{100}$
$=19\times \dfrac{4}{10}$
$=\dfrac{76}{10}=7.6$
So $2\dfrac { 5 }{ 7 }$ of $280\ cm$ is $7.67.6\ cm$

This happens in only option $\text{B1}+\frac{1}{10}= \frac{11}{10}​= 11\times 1\times \frac { 1 }{ 10 }$

$\frac{\text{W N } \times \text{ D + N}}{\text{D}}$
$\dfrac {12\times 6+1}{6}$
$=\dfrac {72+1}{6}$
$=\dfrac {73}{6}$

$\frac{11}{7}=\frac{77}{\text{x}}$
On cross-multiplying, we get:
$11\times\text{x}=77\times4$
$\Rightarrow\text{x}=\frac{77\times4}{11}$
$\Rightarrow\text{x}=\frac{7\times11\times4}{11}$
$\text{x}=28$

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

$0.23=\frac{23}{100}$

$1008\times\frac{7}{8}-568\times\frac{3}{4}$
$=126\times7-142\times3$
$=882-426$
$=456$

A unit fraction is a rational number written as a fraction in which numerator is $11$ and denominator is a positive integer.
Example:
$\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{5}$ etc.

$\displaystyle 36.2 \Rightarrow 36 + 0.2\ = \frac {362}{10} = 36 \frac{2}{10}.$

Here, whole part of all numbers are same and tenths part of $0.0925$ and $0.038$ are same
i.e. $0$ and tenths part of $0.182 =\frac{1}{10}$
and tenths part of $0.29 =\frac{2}{10}$
Hence, $0.29$ is the greatest.

Here, numerator < denominator only in option $A.$

$\frac{232}{990}$ is equal to $0.234.$

$\displaystyle\frac{7}{11}$​ is not an improper fraction because the numerator is smaller than the denominator.
In Improper fraction, the Numerator is always larger than the denominator.

Let the blank part be $x$ Therefore,
$\frac{1}{7}+\frac{2}{7}+\frac{\text{x}}{7}=1\frac{3}{7}\Rightarrow\frac{3+\text{x}}{7}=\frac{10}{7}$
$\Rightarrow3+\text{x}=10$
$\Rightarrow\text{x}=10-3=7$

$\Box-\frac{5}{8}=\frac{1}{4}$
$\Rightarrow\Box=\frac{1}{4}+\frac{5}{8}$
$LCM$ of $4$ and $8$ is $8.$
$\Rightarrow\Box=\frac{1\times2}{4\times2}+\frac{5\times1}{8\times1}$
$\Rightarrow\Box=\frac{2}{8}+\frac{5}{8}$
$\Rightarrow\Box=\frac{2+5}{8}$
$\Box=\frac{7}{8}$

$\frac{1}{2\frac{1}{3}}+\frac{1}{1\frac{3}{4}}=\frac{1}{\frac{2\times3+1}{3}}+\frac{1}{\frac{1\times4+3}{4}}$
$=\frac{1}{\frac{7}{3}}+\frac{1}{\frac{7}{4}}$
$=\frac{3}{7}+\frac{4}{7}$
$=\frac{3+4}{7}$
$=\frac{7}{7}=1$

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 $100.$
$\displaystyle \frac{0.23}{1}\, =\, \frac{0.23 \times 100}{1 \times 100}\, =\, \frac{23}{100}$

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

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

We have, improper fraction $=\frac{11}7$
Now,

$\text { 7)11(1 }$
     $ \frac{7}{4}$

$\therefore\frac{11}{7}=1\frac47$
Note: In order ot express an improper fraction as a mixed fraction, we first devide the numerator by denominator and obtain the quotient and remainder and then we write the mixed fraction as, $\text{Quotient}\ \frac{\text{Remainder}}{\text{Denominator}}$

The first decimal digit from the decimal point is the tenth, the second decimal digit from the decimal point is the hundredth and the third decimal digit from the decimal point is the thousandths digit.
Read the whole set of three decimal digits as a number, and say, "tenths ", "hundredths" and “thousandths.” $0.012$ has $0$ tenths, $1$ hundredth, and $2$ thousandths. While $0.012$ is the sum of $\frac{0}{10}$, $\frac{1}{100}$, and $\frac{2}{1000}$, it is also $\frac{12}{1000}$.

$\begin{array}{c|c}2&5,3,6,10\\\hline5&5,3,3,5\ \\\hline3&1,3,3,1\ \\\hline&1,1,1,1\ \end{array}$
$L.C.M$. of $5, 3, 6$ and $10 = (2 \times 3 \times 5) = 30$
Thus, we have:
$\frac{3}{5}=\frac{3\times6}{5\times6}=\frac{18}{30}$
$\frac{2}{3}=\frac{2\times10}{3\times10}=\frac{20}{30}$
$\frac{5}{6}=\frac{5\times5}{6\times5}=\frac{25}{30}$
$\frac{7}{10}=\frac{7\times3}{10\times3}=\frac{21}{30}$
Therefore, The smallest fraction $=\frac{18}{30}=\frac{3}{5}$

Dividing $23$ by $100$ will give the answer $0.23$

Dividing $23$ by $100$ will give the answer $0.23$

To write it as a decimal we divide the numerator from the denominator.
$9/1000 = 0.009$
So, $0.009$ is the decimal representation for $9/1000.$

$\frac{45}{60}=\frac{3}{\text{x}}$
$\Rightarrow\frac{45\div15}{60\div15}=\frac{3}{\text{x}}$
$\Rightarrow\frac{3}{4}=\frac{3}{\text{x}}$
$\text{x}=4$

$0.23 = \displaystyle\frac{23}{100}$

In an improper fraction, the numerator is greater than the denominator.
Of the given fractions, $\frac{23}{22}$ has numerator greater than the denominator.
Hence, $\frac{23}{22}$ is an improper fraction

Given, $\frac{5}{8}=\frac{20}{\text{p}}$
We know that, if two fractions $\frac{\text{a}}{\text{b}}$ and $\frac{\text{c}}{\text{d}}$ are equvalent.
Then, $\text{a}\times\text{d}=\text{b}\times\text{c}$
$\Rightarrow5\times\text{p}=8\times20$
$\Rightarrow\text{p}=\frac{8\times20}{5}$
$\Rightarrow\text{p}=\frac{160}{5}=32$
Hence, the value of $p$ is $32.$

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

$1008\times \dfrac{7}{8}-568\times \dfrac{3}{4}$
$126 \times 7 - 142 \times 3$
$= 882 - 426$
$= 456$