Solve the proportion, then leave the fraction in a fraction as simples

1.	Solve the proportion, then leave the fraction in a fraction as simplest form. Thanks! :)
Answer» 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! ________________________________