I remember making a little thing about this about a year ago but I probably wouldn't be able to find it so I'll just recreate it again! (With examples)
Positive and Positive
I'm just assuming you already know how positives work :)
Adding:
1 + 2 = 3
Subtracting:
1 - 2 = -1
Multiplying:
1 x 2 = 2
Dividing:
1 ÷ 2 = 0.5
Postive and Negative (and vice versa)
Adding:
Whenever there is a negative during adding, if it is before the addition sign and there is a positive number after, just think of it as you have negative, but since you're adding a positive, it's taking away a negative. If there is a negative after the addition sign, the negative cancels out the positive and it turns into for example, 1 - 2 instead of 1 + (-2)
-2 + 1 = -1 or 1 + (-2) = -1
Subtracing:
Whenever there is a negative during subtracting, if it is before the subtraction sign and there is a positive number after, you simply subtract, so the negative number becomes bigger (technically smaller, but hopefully you get my drift). If there is a negative after the subtraction sign, the two negatives cancel out and turn into addition. (ex: 1 - (-2) = 1 + 2)
-2 - 1 = -3 or 1 - (-2) = 3
Multiplying:
Whenever there is a negative and a positive during multiplication, the negative always wins. The answer is always negative no matter whether the negative number is before or after the multiplication symbol.
-2 x 1 = -2 or 1 x -2 = -2
Dividing:
Whenever there is a negative and a posititive during division, it works the same as multiplication. The negative always wins.
-2 ÷ 1 = -2 or 1 ÷ -2 = -0.5
Negative and Negative
Adding:
Whenever there are two negatives during adding, the negative cancels out the addition sign and turns it into a subtraction sign
-1 + (-2) = -3 or -2 + (-1) = -3
Subtracting:
Whenever there are two negatives during subtracting, the negative and the subtraction sign cancel out and turn into addition.
-1 - (-2) = 1 or -2 - (-1) = -1
Multiplying:
Whenever there are two negatives during multiplication, the two negatives cancel out and the answer is always positive
-1 x -2 = 2 or -2 x -1 = 2
Division:
Whenever there are two negatives during division, they act the same as multiplication. The two negatives cancel out and the answer is always positive
-1 ÷ -2 = 0.5 or -2 ÷ -1 = 2
Hopefully this helps! :) Let me or anyone else know if you need more help or still don't understand