The expression p + q represents the number located |q| units from p in the positive or negative direction if q is positive or negative, respectively.

In this case, p = -5 and q = 7.
Since q is positive, -5 + 7 is 7 units from -5 in the positive direction.
This can be represented on a number line.

First, draw an arrow to represent -5.
Start at 0 and extend the arrow 5 units in the negative direction, which is to the left.

Next, draw an arrow to represent adding 7 to -5.
Start at -5 and extend the arrow 7 units in the positive direction, which is to the right.

The second arrow ends at 2. So, -5 + 7 = 2.

The expression p + q represents the number located |q| units from p in the positive or negative direction if q is positive or negative, respectively.

In this case, p = 1.75 and q = -2.5.
Since q is negative, 1.75 + (-2.5) is 2.5 units from 1.75 in the negative direction.
This can be represented on a number line.

The second arrow ends at -0.75. So, 1.75 + (-2.5) = -0.75.

First, draw an arrow to represent $1\frac{1}{2}$.
Start at 0 and extend the arrow $1\frac{1}{2}$ units in the positive direction, which is to the right.

Next, draw an arrow to represent subtracting $3\frac{1}{4}$ from $1\frac{1}{2}$.
Start at $1\frac{1}{2}$ and extend the arrow $3\frac{1}{4}$ units in the negative direction, which is to the left.

The second line ends at $-1\frac{3}{4}$. So, $1\frac{1}{2}-3\frac{1}{4}=-1\frac{3}{4}$.

A number and its opposite are additive inverses.
-8.4 is the opposite of 8.4, so -8.4 and 8.4 are additive inverses.

Additive inverses have a sum of 0, so the sum of 8.4 and -8.4 is 0.

Subtracting a rational number is the same as adding its additive inverse.

The additive inverse of $-\frac{1}{2}$ is $\frac{1}{2}$.
So, subtracting $-\frac{1}{2}$ is the same as adding $\frac{1}{2}$.

Multiply and divide from left to right.

-25 × 3 ÷ (-5)	=	-75 ÷ (-5)
	=	15