Question

$\ \textless \ br /\ \textgreater \ \frac{2}{10} = \frac{4}{a-3} \ \textless \ br /\ \textgreater \ \ \textless \ br /\ \textgreater \ ​ \ \textless \ br /\ \textgreater \ \ \textless \ br /\ \textgreater$


Solve the proportion, then leave the fraction in a fraction as simplest form. Thanks! :)​​

Answer 1

Explanation:

come in Jaipur only rajput allowed rnn-aers-vrz

Answer 2

Answer :-

• The fraction in it's simplest form is 23/1.

• The value of a is 23.

What to do?

• Solve the equation, and leave the fraction in it's simplest form.

Step-by-step explanation :-

$q)\: \sf \dfrac{2}{10} \: = \dfrac{4}{a - 3} \: \: q)102 = a -34$

By cross multiplication,

$\hookrightarrow \sf2 \: (a - 3) = 4 \times 10↪2(a - 3) = 4 \times10$

Removing the brackets by multiplying 2 with a and 3,

$↪ \sf \: 2a - 6 = 4 \times 10$

Multiplying 4 with 10,

$↪ \sf 2a - 6 = 40$

Transposing 6 from LHS to RHS, changing it's sign,

$↪ \sf 2a = 40 + 6$

Adding 6 to 40,

$↪ \sf2a = 46$

Transposing 2 from LHS to RHS, changing it's sign,

$↪ \sf a = \dfrac{46}{2}$

Reducing the fraction to it's simplest form,

$↪ \underline{ \boxed{ \sf \: a = \dfrac{23}{1}}}$

Hence, the fraction in it's simplest form is 23/1.

--------------------------------------

Now, solving the equation further,

$↪ \underline{ \boxed{ \sf \: a = 23}}$

The value of a is 23.

________________________________

V E R I F I C A T I O N :

To check our answer, let's put 23 in the place of a and see whether LHS = RHS.

LHS

$\longmapsto \rm \dfrac{2}{10}$

Reducing the fraction to it's simplest form,

$\longmapsto \rm \dfrac{1}{5}$

RHS

$\longmapsto \rm \dfrac{4}{a - 3}$

Substituting the value of a,

$\longmapsto \rm \dfrac{4}{20}$

Subtracting 3 from 23,

$\longmapsto \rm \dfrac{4}{20}$

Reducing the fraction to it's simplest form,

$\longmapsto \rm \dfrac{1}{5}$

Since LHS = RHS,

Hence verified!

________________________________