Rhythmic Dictation | The Tie
The tie is a curved line connecting the rhythmic values of two or more notes of equal pitch and letter name.
In other words, when two notes with the same vibrational frequency are joined together by a tie the rhythmic duration of each note is combined to form one longer duration.
A quarter note on any staff position sounds for one beat each.
If we place a tie between the quarter notes on beats three and four their rhythmic values are then combined to make the duration of the quarter note on beat three now worth two beats.
As you can see, a quarter note tied to another quarter results in a rhythmic duration which is essentially the same as a single half note.
When a tie is used to connect a half note to a quarter note the rhythmic duration of the half note extends from two beats to three beats.