Explanation:
you really need to understand this. you need that "feeling" about negative and positive numbers and how they represent a virtual line.
that understanding is essential for further topics.
7.C.
-2 + (-7) = -2 - 7 = -9
and that is 7 numbers to the left (getting smaller or lower) of -2.
8.
well, what is the difference between 3 and 9 that are indicated in the graph ? their value difference is 6 (9 - 3 = 6). but their graphical distance is 2 units.
that means that 2 graphical units represent 6 value units. our simplified : 1 graphical unit represents 3 value units.
I, now we go 2 graphical units to the left of 3 to the blue dot. that means 6 value units to the left. and again, to the left means smaller or lower.
so, 3 - 6 = -3
that blue dot represents -3.
9.
1 + (-2/3) - (-m) for m = 9/2
that only means we have to put 9/2 everywhere where we find "m" in the expression.
that is the only purpose of variables : a placeholder for real values.
1 + (-2/3) - (-9/2) = 1 - 2/3 + 9/2
to add fractions with different denominators we need to bring them to the same, common denominator.
that is the LCM (the lowest common multiple) of the denominators.
in case of 2 and 3 that is 6.
so, we need to bring everything to .../6.
remember, whatever we do (multiplication or division) for the transformation, we need to do it to the numerator and the denominator equally to maintain the original value of the fraction.
1 = 6/6
2/3 = 2/2 × 2/3 = 4/6
9/2 = 3/3 × 9/2 = 27/6
and so, our result is
6/6 - 4/6 + 27/6 = 29/6 = 4 5/6 = 4.833333333...