Negative numbers - HSPT Math

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Question

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

Answer

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.

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Question

–7 – 7= x

–7 – (–7) = y

what are x and y, respectively

Answer

x: –7 – 7= –7 + –7 = –14

y: –7 – (–7) = –7 + 7 = 0

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

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Question

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

Answer

Because $\dpi{100} \small -3b$ is positive, $\dpi{100} \small b$ must be negative since the product of two negative numbers is positive.

Because $\dpi{100} \small ab$ is also positive, $\dpi{100} \small a$ must also be negative in order to produce a prositive product.

To check you answer, you can try plugging in any negative number for $\dpi{100} \small a$ .

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Question

Which of the following operations always gives a negative result?

Answer

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. $(-2) ^{2} = 4$ , which is positive, and $(-2) ^{3} = -8$ , which is negative.

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

, but

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Question

Solve for :

Answer

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

$x=\frac{-10}{-5}$

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

$x=\frac{10}{5}$ or

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Question

Solve the following equation:

$\frac{-288}{-16} =$

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:

$\frac{-288}{-16} = 18$

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Question

Choose the answer which best solves the following equation:

$-\frac{396}{x} = 12$

Answer

To solve, first put the equation in terms of :

$-\frac{396}{x} = 12$

First multiply the x to both sides.

Now divide by 12 to solve for x.

$x = -\frac{396}{12}$

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

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Question

Evaluate:

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.

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Question

Subtract:

Answer

It is possible to rewrite the expression as:

Take the negative of the difference of 47 and 23.

The answer is .

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Question

Solve:

Answer

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

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Question

Evaluate:

Answer

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:

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Question

Note: Public domain map from CIA World Factbook.

Refer to the above time zone map. The numbers along the top represent the difference, in hours, between the given time zone and Greenwich Mean Time (the time zone for the United Kingdom).

Which of the following expressions gives the time difference, in hours, between Paris and Dallas?

Answer

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 .

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Question

Note: Public domain map from CIA World Factbook.

Refer to the above time zone map. The numbers along the top represent the difference, in hours, between the given time zone and Greenwich Mean Time (the time zone for the United Kingdom).

A flight took off from Winnipeg, Canada at 5:00 PM and took 7 hours to get to the Azores. What time was it in the Azores when it landed there?

Answer

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:

$17 \div 12 = 1\textup{ R }5$

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

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Question

If you have a negative number and multiply it by another, the final answer is positive. What sign did the other number have?

Answer

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.

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Question

Evaluate 3x3 + x2 if x = _–_2

Answer

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

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Question

Simplify the following expression: (–4)(2)(–1)(–3)

Answer

First, we multiply –4 and 2. A negative and a positive number multiplied together give us a negative number, so (–4)(2) = –8. A negative times a negative is a positive so (–8)(–1) = 8. (8)(–3) = –24.

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Question

If a = –2 and b = –3, then evaluate a3 + b2

Answer

When multiplying negative numbers, we get a negative answer if there are an odd number of negative numbers being multiplied. We get a positive answer if there are an even number of negative numbers being multiplied.

a3 + b2 becomes (–2)3 + (–3)2 which equals –8 + 9 = 1

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Question

What is 1 + (–1) – (–3) + 4 ?

Answer

You simplify the expression to be 1 – 1 + 3 + 4 = 7

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Question

Evaluate:

–3 * –7

Answer

Multiplying a negative number and another negative number makes the product positive.

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Question

Evaluate.

$\dpi{100} \small (-8\times 6) - (5\times -3)$

Answer

$\dpi{100} \small (-8\times 6) - (5\times -3)$

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

$\dpi{100} \small (-48)-(-15)$

$\dpi{100} \small -48+15$

$\dpi{100} \small -33$

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