HSPT Math : Problem Solving
Study concepts, example questions & explanations for HSPT Math
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Example Questions
Example Question #581 : Problem Solving
Which of the following operations always gives a negative result?
A negative number taken to the power of a positive integer
A negative number divided by a negative number
A negative number subtracted from a negative number
A negative number multipled by a negative number
A negative number added to a negative number
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. 
The difference of negative numbers can be either negative, positive, or zero:
Example Question #1 : Negative Numbers
If 
Because 
Because 
To check you answer, you can try plugging in any negative number for
Example Question #582 : Problem Solving
If x is a negative integer, what else must be a negative integer?
x – (–x)
x² – x
x – x
x²
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 #583 : Problem Solving
–7 – 7= x
–7 – (–7) = y
what are x and y, respectively
x = –14, y = 0
x = 0, y = 0
x = –14, y = 14
x = 14, y = –14
y = 0, x = 14
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 #2 : How To Divide Negative Numbers
Solve for 
Begin by isolating your variable.
Subtract 
Next, subtract 
Then, divide both sides by 
Recall that division of a negative by a negative gives you a positive, therefore:
Example Question #1 : How To Divide Negative Numbers
Solve the following equation:
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 : How To Divide Negative Numbers
Choose the answer which best solves the following equation:
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 #3 : Negative Numbers
Evaluate:
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 #583 : Hspt Mathematics
Subtract:
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:
Evaluate the inner term inside the parenthesis first. The expression can then be simplifed to an integer.
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