HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

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Example Questions

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

y = 0, x = 14

x = –14, y = 14

x = –14, y = 0

Correct answer:

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 #2 : Negative Numbers

Solve for :

Possible Answers:

Correct answer:

Explanation:

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 Add / Subtract / Multiply / Divide Negative Numbers

Solve the following equation:

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

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 #2 : Negative Numbers

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

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 #3 : Negative Numbers

Subtract:  

Possible Answers:

Correct answer:

Explanation:

It is possible to rewrite the expression as:

Take the negative of the difference of 47 and 23.

The answer is .

Example Question #1 : How To Add / Subtract / Multiply / Divide Negative Numbers

Solve:  

Possible Answers:

Correct answer:

Explanation:

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

Example Question #111 : Arithmetic

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #11 : Negative Numbers

Flight map

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?

Possible Answers:

Correct answer:

Explanation:

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 .

Example Question #591 : Problem Solving

Flight map

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?

Possible Answers:

5:00 PM

7:00 PM

5:00 AM

7:00 AM

Correct answer:

5:00 AM

Explanation:

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.

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