Equivalent fractions, and adding fractions

Two names for the same amount

$\tfrac12$, $\tfrac24$ and $\tfrac36$ all cover the same part of a shape. Multiplying both top and bottom by the same number keeps the value: $\tfrac12=\tfrac{1\times3}{2\times3}=\tfrac36$. Changing only one of them changes the amount.

Simplifying

Going the other way, divide top and bottom by a common factor: $\tfrac{8}{12}=\tfrac{8\div4}{12\div4}=\tfrac23$. A fraction is in its simplest form when the only number dividing both is $1$.

Adding fractions

You may only add fractions with the same denominator, because the denominator names the size of the piece. $\tfrac15+\tfrac25=\tfrac35$: three fifths, not three tenths. To add $\tfrac12+\tfrac14$, first rename $\tfrac12$ as $\tfrac24$.