# SAT Math : Negative Numbers

## Example Questions

### Example Question #1 : Negative Numbers

If x is a negative integer, what else must be a negative integer?

x² – x

x – (–x)

x – x

x – (–x)

Explanation:

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.

### Example Question #2 : Negative Numbers

–7 – 7= x

–7 – (–7) = y

what are x and y, respectively

x = –14, y = 0

x = –14, y = 14

x = 14, y = –14

y = 0, x = 14

x = 0, y = 0

x = –14, y = 0

Explanation:

x: –7 – 7= –7 + –7 = –14

y: –7 – (–7) = –7 + 7 = 0

when subtracting a negative number, turn it into an addition problem

### Example Question #3 : Negative Numbers

Evaluate:

Explanation:

Reconvert  into single signs.  Remember that double negatives will turn into a positive.

### Example Question #34 : Integers

Subtract:

Explanation:

Subtracting a negative number moves the number farther left of the zero digit on the number line.

### Example Question #3 : Negative Numbers

Subtract:

Explanation:

Simplify the expression by eliminating the double negative signs.  Two negatives multiplied by one another will result in a positive number.

Convert the signs.

Add the right side of the equation.

### Example Question #35 : Integers

Simplify the following expression:

Explanation:

Simplify the following expression:

To subtract negative numbers, we must recall that subtracting negative numbers is the same as adding a positive. The two negatives cancel each other out to become positive.

So our answer is negative 220

### Example Question #4 : Negative Numbers

If  is a positive number, and  is also a positive number, what is a possible value for ?

Explanation:

Because is positive,  must be negative since the product of two negative numbers is positive.

Because  is also positive, must also be negative in order to produce a prositive product.

To check you answer, you can try plugging in any negative number for .

### Example Question #5 : Negative Numbers

Multiply the following negative numbers: .

Explanation:

When two negative numbers are multiplied by each other, the result is a positive number.

When a negative and a nonnegative number are multiplied with each other, the result is a negative number.

Therefore, since  and  are negative numbers, the product must be positive.

Therefore, the answer is positive .

### Example Question #5 : Negative Numbers

Multiply:

Explanation:

Simplify the expression term by term.

A negative number multiplied by a negative number gives a positive number.

A negative number multiplied by a positive number gives a negative number.

Multiply: