Question

$\frac{2}{10} = \frac{4}{a-3}$
Solve the proportion, then leave the fraction in a fraction as simplest form. Thanks! :)​

Answer 1

Answer:

$a= \frac{46}{2} \: or \: a = 23$

Step-by-step explanation:

$\frac{2}{10} = \frac{4}{a - 3} \\ multiply \: both \: sides \: by \: (a - 3) \\ = \frac{(a - 3) \times 2}{10} = \frac{(a - 3) \times 4}{a - 3} \\ = \frac{(a - 3 )\times 2}{10} = 4 \\ again \: multiply \: both \: side \: by \: 10 \\ = \frac{10(a - 3) \times 2}{10} = 4 \times 10 \\ =( a - 3) \times 2 = 40 \\ = 2a - 6 = 40 \\ = 2a = 40 + 6 \\ = 2a = 46 \\ = a = \frac{46}{2} \\ = a = 23$

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 :-

$Q) \: \sf \dfrac{2}{10} = \dfrac{4}{a - 3}$

By cross multiplication,

$\hookrightarrow\sf 2 \: (a - 3) = 4 \times 10$

Removing the brackets by multiplying 2 with a and 3,

$\hookrightarrow\sf 2a - 6 = 4 \times 10$

Multiplying 4 with 10,

$\hookrightarrow\sf 2a - 6 = 40$

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

$\hookrightarrow\sf 2a = 40 + 6$

Adding 6 to 40,

$\hookrightarrow\sf 2a = 46$

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

$\hookrightarrow\sf a = \dfrac{46}{2}$

Reducing the fraction to it's simplest form,

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

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

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

Now, solving the equation further,

$\hookrightarrow\sf a = \dfrac{23}{1}$

$\hookrightarrow\underline{\boxed{\sf a = 23}}$

• 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,

$\longmapsto\rm \dfrac{4}{23 - 3}$

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!

________________________________