−3 3/4 ÷ 3 = ? this is quite easy, i forgot my calculator though, and i mostly rely on that.

-1 1/4

Step-by-step explanation:

Do it in pieces. Everything is divisible by 3, so you can do it in your head.

... (-3 3/4)/3 = (-3/3) -(3/4)*(1/3) . . . . . an integer part divisible by 3, and a fraction divisible by 3

... = -1 -(3*1)/(3*4) . . . . factors of 3 cancel

... = -1 -1/4

... = -1 1/4

Hopefully, it's no mystery that 3 quarters divided by 3 is 1 quarter, just as (3 whatever) divided by 3 is (1 whatever).

It really does help to play with blocks, Legos, chips, coins, rocks, or counters of any kind. Arrange them, deal them into piles, put them is rectangles or triangles (and be aware of how many you use). It also helps to cook from recipes that require use of fractional measures. The cups and spoons give you a sense of what size fractions are larger/smaller, and how they are related. Appropriate play with counting and arranging and measuring can help you develop your number sense, and help you learn to do problems like this in your head.