### All HSPT Math Resources

## Example Questions

### Example Question #1 : Negative Numbers

Which of the following operations *always* gives a negative result?

**Possible Answers:**

A negative number taken to the power of a positive integer

A negative number multipled by a negative number

A negative number added to a negative number

A negative number divided by a negative number

A negative number subtracted from a negative number

**Correct answer:**

A negative number added to a negative number

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

### Example Question #1 : Negative Numbers

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

**Possible Answers:**

**Correct answer:**

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 #31 : Integers

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

**Possible Answers:**

x – x

x²

x – (–x)

x² – x

**Correct answer:**

x – (–x)

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 #1 : Negative Numbers

–7 – 7= x

–7 – (–7) = y

what are x and y, respectively

**Possible Answers:**

x = –14, y = 14

x = 0, y = 0

x = 14, y = –14

x = –14, y = 0

y = 0, x = 14

**Correct answer:**

x = –14, y = 0

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 #1 : How To Divide Negative Numbers

Solve for :

**Possible Answers:**

**Correct answer:**

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

or

### Example Question #1 : How To Divide Negative Numbers

Solve the following equation:

**Possible Answers:**

**Correct answer:**

The rule for dividing negative numbers is the same as for multiplying negative numbers.

If both numbers are negative, you will get a positive answer.

If either number is positive, and the other is negative, you will get a negative answer.

Therefore:

### Example Question #1 : Negative Numbers

Choose the answer which best solves the following equation:

**Possible Answers:**

**Correct answer:**

To solve, first put the equation in terms of :

First multiply the x to both sides.

Now divide by 12 to solve for x.

Here, because one of the numbers in the equation is positive, and the other is negative, the answer must be a negative number:

### Example Question #1 : Negative Numbers

Evaluate:

**Possible Answers:**

**Correct answer:**

To evaluate this, rewrite the expression with the correct signs.

Positive multiplied with a negative sign results in a negative, and a double negative results in a positive sign.

### Example Question #2 : Negative Numbers

Subtract:

**Possible Answers:**

**Correct answer:**

It is possible to rewrite the expression as:

Take the negative of the difference of 47 and 23.

The answer is .

### Example Question #1 : Negative Numbers

Solve:

**Possible Answers:**

**Correct answer:**

Evaluate the inner term inside the parenthesis first. The expression can then be simplifed to an integer.