I'm currently learning theory for grade 3, but i hit sort of a roadblock. In the image, the question asks to "Add time signatures to these bars". Now, I do know that let's say 3/4 and 6/8 differ in that one's in simple time and means 3 crotchet per bar and the other is in compound time an means 2 dotted crotchet beats per bar. However, I still don't understand why, say for the second exercise, I still don't understand why the time couldn't be something like 6/8 (that is if 3/4 is even correct to begin with) because aren't there still 6 quaver beats in that bar? 
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5 Answers
Yes, both 6/8 and 3/4 'add up' to six quavers or three crotchets.
The difference is in how they are grouped. The second example is clearly grouped as three groups of two quavers - three crotchet beats. The triplet makes this abundantly clear - attempting to notate the bar as two groups of three quavers each would require re-writing the triplet in a very ungainly way!
The basic point is that although 2+2+2 and 3+3 both add up to six, it MATTERS whether they're grouped as 2+2+2 or 3+3. The former is 3/4, the latter 6/8.
If you put a 6/8 meter on this...
...you must do something to deal with the tuplets.
In 6/8 the beat is equal to 3 eighth notes (quavers.) So the triplet figure becomes redundant in 6/8. The two beats here are the same in time values...
Back to the example, the 3 quavers are one beat with or without the triplet marking. That leaves six semiquavers and one quaver for the other beat, and that is one quaver too many. Two beats worth of notes in yellow boxes, the extra note in red...
One way to put this measure into 6/8 and keep the same number of note heads is this...
...use a tuplet to put the 4 eighths (quavers) into one beat.
Of course the workbook question did not ask you to change the written notes, but I just wanted to walk through the implications of changing the meter as you asked.
EDIT
I tried to keep the tuplet on a full beat. But to do it like @LarsPetersShultz said - with no changes to the note values - the tuplet is only fit a partial beat. Then the beaming changes to this...
...notice how in the original the first note of the triplet coincides with the start of the beat, but in the 6/8 form the beats are metrically re-positioned - visually represented through the beaming - and the first note of the triplet is off the beat.
answered Oct 29, 2019 at 13:07
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If you want to write the bar as 6/8 you should keep the exact same note values 100%. The only difference is that you divide the bar in two parts in 6/8 while with 3/4 the bar is divided in 3 parts. So with 6/8: First part: 6 sixteenth notes, second part: 1 eight note followed by the 3 triplet eight notes. Commented Oct 29, 2019 at 13:44
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@LarsPetersShultz, I see what you mean and made an edit. Commented Oct 29, 2019 at 14:10
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ahh mate this is so helpful. appreciate the time you spent to edit the images so you could make me understand :)– LeoCommented Oct 30, 2019 at 5:51
It’s do to with how the quavers are grouped. In 6/8 the quavers are grouped in 3s (dotted crotchet beats) and in 3/4 they are in pairs (crotchet beats).
The grouping of the notes suggests a division of three quarter notes, thus 3/4. Remember, 6/8 is a compound binary time, meaning it is divided into two dotted quarter notes. Also, the triplet eighth notes are different from regular eighth notes, as they’re equivalent to two regular eighth notes, i.e a quarter note, so even a different grouping of the notes wouldn’t make 6/8 possible.
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A different grouping of notes would make 6/8 possible, it's just very ugly (as Michael Curtis' answer demonstrates) Commented Nov 5, 2019 at 17:14
3/4 time is split differently from 6/8. 3/4 is a bar of basically three crotchets, which is how that bar is organised. 1st beat = 4 semis, 2nd beat = 2 semis and 1 quaver, 3rd beat is 3 triplet quavers.
If the bar was 6/8, it would be written out so it could be split equally into two halves. Were that the case, there would be emphasis on the single quaver, which in 3/4 is quite unaccented.
