To most effectively add a positive and negative number, ignore the signs and pick the greater of the two numbers.

In this case the positive number has a higher value if we don’t pay attention to the signs. Due to this fact we know the answer will be positive.

We then subtract the smaller number value from the higher value which gives us

Then we add the sign of the greater value to arrive at our answer .

In order to solve this problem, we will use a number line. Numbers to the left of zero on the line are less than numbers to the right.

Therefore:

The sum of two negative numbers is always negative, hence, this is the right choice.

As for the other choices:

The product or quotient of two negative numbers is always positive.

A negative number taken to the power of a positive integer can be either negative or positive depending on whether the exponent is even or odd. , which is positive, and , which is negative.

The difference of negative numbers can be either negative, positive, or zero:

, but

When multiplying a negative number an odd number of times, the answer is negative. When multiplying a negative number an even number of times, the answer is positive. Order of operations also applies: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, from left to right. A mnemonic to remember the order of operations is “Please excuse my dear Aunt Sally.”

3(_–2)3 + (–_2)2

= 3(_–_8) + (4)

= _–_24 + 4

= _–_20

In order to solve this problem, we will use a number line. Numbers to the left of zero on the line are less than numbers to the right.

Therefore:

In order to solve this problem, we will use a number line. Numbers to the left of zero on the line are less than numbers to the right.

Therefore:

In order to solve this problem, we will use a number line. Numbers to the left of zero on the line are less than numbers to the right.

Therefore:

It is possible to rewrite the expression as:

Take the negative of the difference of 47 and 23.

The answer is .

The rule for multiplying integers with opposite signs is:
A negative times a positive is a negative.

By choosing a random negative number, for example: –4, we can input the number into each choice and see if we come out with another negative number. When we put –4 in for x, we would have –4 – (–(–4)) or –4 – 4, which is –8. Plugging in the other options gives a positive answer. You can try other negative numbers, if needed, to confirm this still works.