Negative numbers - HSPT Math

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.

x: –7 – 7= –7 + –7 = –14

y: –7 – (–7) = –7 + 7 = 0

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

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 .

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

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

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:

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:

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.

In order to combine like terms correctly, it is necessary to simplify every term and eliminate the parentheses. Double negatives equal a positive sign.

Combine like terms. The answer is:

A difference is the result of a subtraction. The time difference between the two cities will be the result of subtracting the numbers along the top of the map for their respective time zones, and taking the absolute value of the difference. The numbers for Paris and Dallas, respectively, are 1 and , so the difference in hours between their times is .

The time difference between Winnipeg and the Azores is the result of subtracting the numbers along the top of their respective timie zones, which are and :

The Azores is five hours ahead of Winnipeg, so when the flight takes off, since

,

it is 10:00 PM in the Azores.

Add the seven hours flight time, and take the result modulo 12:

The time is 5:00 AM in the Azores when the plane lands there.

The only way to get a positive product from multiplication is to multiply two positive numbers together or two negative numbers together.

If the first number was negative, the other number will also have to be negative.

The square root of a number is the number which, when squared - multiplied by itself - yields that number as its result. Recall that when two negative numbers are multiplied together they result in a positive numbers.

Therefore, negative 37 is the square root of

(I) and (II) are both negative, since the product or quotient of a negative number and a positive number is negative.

The sum of a negative number and a positive number assumes the sign of the number with the greater absolute value. Since in (III), the negative number has the higher absolute value (200 versus 180), the sign of the sum is negative.

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:

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

Multiplying a negative and a positive number creates a negative product: