Free Practice Questions for Fraction in Maths

माना अभीष्ट भिन्न $x$ है।
प्रश्नानुसार,
$
\begin{aligned}
& & \frac{x}{6 / 7}-\frac{6}{7} x &=\frac{13}{70} \\
\Rightarrow & & \frac{7 x}{6}-\frac{6 x}{7} &=\frac{13}{70} \\
\Rightarrow & & \frac{49 x-36 x}{42} &=\frac{13}{70} \\
\Rightarrow & & \frac{13 x}{42} &=\frac{13}{70} \Rightarrow x=\frac{42}{70}=\frac{3}{5}
\end{aligned}
$

माना वह संख्या $=x$
प्रश्नानुसार,
$x \times \frac{3}{4}$ का $\frac{1}{2}=10$ का $2 \frac{1}{2}$
$\Rightarrow \quad x \times \frac{3}{4} \times \frac{1}{2}=10 \times \frac{5}{2}$
$\Rightarrow \quad x=\frac{10 \times 5 \times 4}{3}=\frac{200}{3}=66 \frac{2}{3}$

$\frac{1}{3+\frac{1}{2-\frac{1}{7 / 9}}}+\frac{17}{22}$
$=\frac{1}{3+\frac{1}{2-9 / 7}}+\frac{17}{22}=\frac{1}{3+\frac{1}{5 / 7}}+\frac{17}{22}$
$=\frac{1}{3+\frac{7}{5}}+\frac{17}{22}=\frac{5}{22}+\frac{17}{22}=\frac{5+17}{22}=\frac{22}{22}=1$

find difference of numerator and denominator of each fraction
$
\begin{gathered}
12-7=5 \\
16-11=5 \\
17-12=5 \\
18-13=5 \\
36-31=5
\end{gathered}
$

clearly here we can see difference of numerator and denominator are same. 

thus greatest numerator will be greatest fraction
$\therefore$ fraction $\frac{31}{36}$ greatest fraction

$ 3 \frac{2}{5}+1 \frac{3}{7}+ 1 \frac{6}{35} $

$=\frac{17}{5}+\frac{10}{7}+\frac{41}{35} $

$=\frac{119+50+41}{35}=\frac{210}{35}=6 $

$\begin{aligned} \frac{1}{1+\frac{1}{2+\frac{1}{3}}} &=\frac{1}{1+\frac{1}{7 / 3}} \\ &=\frac{1}{1+\frac{3}{7}}=\frac{1}{\frac{7+3}{7}}=\frac{7}{10} \end{aligned}$

$x+\frac{5}{6}+\frac{5}{7}+\frac{4}{9}=2 \frac{125}{126}$
$x=\frac{377}{126}-\frac{5}{6}-\frac{5}{7}-\frac{4}{9}$
$x=\frac{377-105-90-56}{126}=\frac{377-251}{126}=\frac{126}{126}=1$

Changing the given fractions in decimals we get,
$
\frac{7}{13}=.5384
$
$\frac{11}{13}=.84615$
$\frac{14}{33}=.4242$
$\frac{8}{15}=.5333$

Clearly, the smallest number is  $14 / 33$

Refraction is a bending of light (also occurs with sound, water and other waves) as it travels from one transparent surface to another.

• Our eyes, too, rely on this bending of light. Without refraction, we wouldn't be able to concentrate the light on our retina.
• For example, as light travels from air to water, it slows down, allowing it to begin to travel in a different angle or direction.
• The higher refractive index indicates that the light slows down and changes direction further when it reaches the material.

Additional Information-

• Scattering is a concept through which travelling particles or radiation, such as light or sound, is caused to deviate from a straight path by distributed non-uniformities in the medium through which they travel.
• Reflection is a transition in the path of the wavefront at the interface between two separate media such that the wavefront returns to the medium from which it originated.
• Diffusion is the net flow of something from a higher concentration to a lower concentration area.

• Optical instruments use refractive property of lens to form image.
• In case of lens image formation is based on the effect of refraction. 
• Periscope, kaleidoscope, binoculars, telescopes, microscopes are some examples of optical devices and instruments that are in common use.
• Our eye is of course, one of the most important optical device the nature has endowed us with.

Dispersion of light-

• The phenomenon of splitting of white light into its seven constituent colours when it passes through a glass prism is called dispersion of white light. 
• The various colours seen are Violet, Indigo, Blue, Green, Yellow, Orange and Red.

Scattering-

• Scattering is the splitting of light into different direction by the particles present in the path of light.
• Scattering of light causes many natural phenomenon like-
• Sun appears red due to scattering of light during sunrise and sunset
• Tyndall effect is observed due to scattering of light
• Sky appears blue during most part of the day
• Colour of ocean appears to be blue due to scattering

Reflection 

• Reflection of light is the phenomenon when light ray bounce back after striking on a shinny surface.

Laws of Reflection

• The angle of incidence is equal to the angle of reflection, and
• The incident ray, the normal to the mirror at the point of incidence and the reflected ray, all lie in the same plane.

$
\Rightarrow \frac{4+2 \sqrt{5}}{4-3 \sqrt{5}} \times \frac{4+3 \sqrt{5}}{4+3 \sqrt{5}}
$
Using identity:
$(a+b)(a-b)=a^{2}-b^{2}$
$\Rightarrow \frac{(4+2 \sqrt{5})(4+3 \sqrt{5})}{(4)^{2}-(3 \sqrt{5})^{2}}$
$\Rightarrow \frac{4(4+3 \sqrt{5})+2 \sqrt{5}(4+3 \sqrt{5})}{16-45}$
$\Rightarrow \frac{16+12 \sqrt{5}+8 \sqrt{5}+30}{-29}$
$\Rightarrow \frac{46+20 \sqrt{5}}{-29}$
$\Rightarrow \frac{-46}{29}+\frac{-20 \sqrt{5}}{29}=a+b \sqrt{5}$
On comparing, we get
$
\Rightarrow a=\frac{-46}{29}, b=\frac{-20}{29}
$