Free Practice Questions for Fraction in Maths

Let $x$ be the number.

According to question,
$
\begin{aligned}
&\Rightarrow\frac{3 x}{5}=54 \\
&\Rightarrow x=\frac{54 \times 5}{3}=90
\end{aligned}
$
Required number $=90 \times \frac{2}{9}=20$

Concept used:
Terminating decimals are those numbers that come to an end after few repetitions from the decimal point.
Non-terminating decimals are those numbers that keep on continuing from the decimal point.
Calculation:
$
\begin{aligned}
&3 / 7=0.428 \ldots \ldots \\
&7/4=1.75 \\
&1 / 2=0.5 \\
&3/2=1.5
\end{aligned}
$
$\therefore$ The non-terminating decimal is $3 / 7$.

ATQ,
$\frac{2}{3}, \frac{4}{6}, \frac{6}{9}$
$\frac{2}{3}=\frac{2}{3}=\frac{2}{3}$ is a equivalent fraction

Let the number is $4$ and when it was multiplied by $x$ it increases by $75\%$

New number $=\frac{175}{100}\times4 = 7$

According to question - 

$4\times x = 7$

$x = \frac{7}{4}$

$
\begin{array}{ll}
\frac{7}{8}=0.875 & \frac{3}{11}=0.2727 \\
\frac{1}{3}=0.33333 & \frac{17}{24}=0.7083 \\
\frac{9}{10}=0.9 & \frac{26}{29}=0.8965
\end{array}
$
Hence proof correct ans is (c), $\frac{17}{24}$

GIVEN:

Aditi get $=2 / 7$ th of total toffees
Amol get $=1 / 6$ th of total toffees
Farhan get $=2 / 5$ th total toffees
Jery get $=1 / 7$ th of total toffees
Merlin get $=2$ toffees
$\Rightarrow$ Let, total toffees $=x$
According to the question,
$
\begin{aligned}
&(2 / 7) x+(1 / 6) x+(2 / 5) x+(1 / 7) x+(2)=x \\
\Rightarrow & x(2 / 7+1 / 6+2 / 5+1 / 7)=x-2 \\
\Rightarrow &(209 / 210) x=x-2 \\
\Rightarrow & x-(209 / 210) x=2 \\
\Rightarrow &(1 / 210) x=2 \\
\Rightarrow & x=2 \times 210=420
\end{aligned}
$
$\therefore$ Total 420 toffees were there in the packets.

$\frac{0.325 \times 0.325+0.175 \times 0.175+25 \times 0.00455}{5 \times 0.0065 \times 3.25-7 \times 0.175 \times 0.025}-\frac{0.5}{1.5}$
$=\frac{(0.325)^2+(0.175)^2+2 \times 0.325 \times 0.175}{0.325 \times 0.325-0.175 \times 0.175}-\frac{0.5}{1.5}$
$=\frac{(0.325+0.175)^2}{(0.325)^2-(0.175)^2}-\frac{0.5}{1.5}$
$=\frac{(0.325+0.175)^2}{(0.325+0.175)(0.325-0.175)}-\frac{0.5}{1.5}$
$=\frac{0.5}{0.15}-\frac{0.5}{1.5}=\frac{1}{0.3}-\frac{1}{3}$
$=3$

Applying BODMAS rule, we have,

$\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}-\left(5 \div 2\right.$ of $\left.\frac{1}{2}\right)$
$=\left(\frac{21}{4} \div \frac{3}{14}\right) \div\left(\frac{46}{9}-\frac{63}{8} \div \frac{189}{20}\right) \times \frac{11}{21}-(5 \div 1)$
$=\left(\frac{49}{2}\right) \div\left(\frac{46}{9}-\frac{5}{6}\right) \times \frac{11}{21}-5$
$=\frac{49}{2} \times \frac{18}{77} \times \frac{11}{21}-5$
$=3-5=-2$

$3 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}+\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)$
$=\frac{10}{3} \div \frac{5}{2}$ of $\frac{8}{5}+\left(\frac{3}{8}+\frac{1}{7} \times \frac{7}{4}\right)$
$=\frac{10}{3} \div 4+\left(\frac{3}{8}+\frac{1}{4}\right)$
$=\frac{5}{6}+\frac{5}{8}$
$=\frac{20+15}{24}=\frac{35}{24}$

A ray of light travels from water to glass, It bends towards the normal and slows down.

Important Points:

• When a ray of light enters from one transparent medium to another transparent medium, it bends from its direction. This bending of the light path is called refraction of light.
• Refraction of light takes place only through transparent materials like glass, air and water etc.
• When a ray of light enters from a rarer medium to a denser medium, it bends towards the normal.
• When a ray of light enters from a denser medium to a rarer medium, it bends away from the normal.

$\frac{x^{-1}-1}{x-1}=\frac{\frac{1}{x}-1}{x-1}=\frac{1-x}{x(x-1)}=\frac{x-1}{x(x-1)}=\frac{1}{x}$