







A puzzling equation 
20181204 

From Manny: Hello,
Can you explain why this is wrong:
1 = (1)^3 = (1)^{6/2} = ((1)^6)^{1/2} = (1)^{1/2} = 1 ??
Thank you Answered by Penny Nom. 





Adding two negatives 
20180204 

From Pinasshakoane: (23)+(3) Answered by Penny Nom. 





Positive and negative values of a function 
20180130 

From Grayson: f(x)=x^6x^4
Interval: ( negative infinity, negative one )
Test Value: negative two
Function Value f(x): positive forty eight
Interval: ( negative one, zero )
Test Value: negative one
Function Value f(x): zero
Interval: ( zero, positive one )
Test Value: positive one
Function Value f(x): zero
Interval: ( positive one, positive infinity )
Test Value: positive two
Function Value f(x): positive forty eight
What is the sign of f(x) for each Interval? Answered by Penny Nom. 





A fraction with a negative exponent in the denominator 
20150430 

From ellen: 7/ab to the 4 power Answered by Penny Nom. 





What is 3 squared? 
20141112 

From Christine: On a math test, it said "What is 3 squared?" It did NOT say "What's is (3)squared"
The teacher's explanation is that if there are no brackets or parenthesis, you ALWAYS square the number first then do the negative, so the answer should be 9, but I can't find anywhere that confirms this.
Help please. Answered by Robert Dawson. 





Changing the sign of an inequality 
20120919 

From Bryauna: Why do you change the signs in inequalities?! Answered by Penny Nom. 





Exponential form 
20120904 

From angie: How do i write 9^5 in exponential form? Answered by Penny Nom. 





Exponential form 
20120115 

From Helen: How do you write (1/x) in exponential form? Answered by Penny Nom. 





(27^r^1)^2/3 
20110424 

From YungJu: (27^r^1)^2/3 Answered by Penny Nom. 





A Squared Number That's Negative 
20100922 

From David: What is the only number that when it's squared becomes negative? Answered by Stephen La Rocque. 





What is 2^2? 
20100825 

From alex: I know that (2)^2 is 4 but what is 2^2? Answered by Robert Dawson and Penny Nom. 





A negative times a negative 
20100325 

From priya: why is minus into minus plus? Answered by Harley Weston. 





The test for some disease is 99% accurate 
20100224 

From baaba: Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease? Answered by Chris Fisher. 





Percentage increase from a negative to a positive 
20100112 

From Greg: If a company had a net lost in 2005 of $11,234 and net income of $3231 in 2006, what is the percentage annual growth in income between the two years? Answered by Robert Dawson. 





The intervals where the function is positive and negative 
20100110 

From Ron: Hello
I'm trying to find out the intervals where the function is positive and negative.
It's for a polynomial function y= (x+2)^2 (x2) and y= (x+1)(x+4)(x3)
I have tried the right and left side of each xintercepts, but I still don't understand the
results
thank you for your help Answered by Penny Nom. 





A number base that's not a positive integer 
20091211 

From Nick: Is it possible for a number to have a base that's not a positive integer?
Base 1 gives a result that's meaningless but possible. I have no concept of a base 0, a negative base, or a fractional base, never mind any other base. I think there isn't any base that's not a positive integer, but, knowing that math keeps jumping ahead and sometimes has inventions before anyone knows how to exploit them, I think I'd better ask.
Thank you.
Nick Answered by Robert Dawson and Claude Tardif. 





The maximum number of right angles in a polygon 
20091005 

From Bruce: Is there way other than by trial and error drawing to determine the maximum number of right angles in a polygon? Secondary question would be maximum number of right angles in a CONVEX polygon. Is there a mathematical way to look at this for both convex and concave polygons? Or are we limited to trial and error drawing? Answered by Chris Fisher. 





Percent increase from a negative number to a positive number 
20090421 

From Brian: I have no problem calculating year over year net profits but am having trouble when it comes to a negative.
2007 Net Profit = 110,333.00
2008 Net Profit = 66,054.00
Brian Answered by Harley Weston. 





Comparing positive and negative fractions 
20090324 

From Christyrose: Hello. I am a sixth grade math student and i need help on how to compare negative and positive fractions.
Here is is:
3/4 2/3 7/10 5/6
I'm not sure how to do the negative parts because i was absent for a couple days. Thank you!
Christyrose Answered by Penny Nom. 





A fraction with negative exponents 
20090214 

From Gabriel: What does the line seperating the top from the bottom mean? what does it tell you to do and what is the answer to the question?
Question 3
Simplify. Write the answer using only positive exponents. Assume all variables represent nonzero numbers.
(x^5)^4(x^1y)^3
________________
(xy^4)^3 Answered by Penny Nom. 





Multiplying negative numbers 
20090115 

From stephanie: hi, I'm currently working in a grade 8 class where the students are
learning about integers. the students were asked to find examples of how
integers are applied in real life. they were able to find aplications for:
adding and subtracting both positive and negative integers. however,
we could not find an example of where two negative integers would be
either divided or multiplied together in real life. For example: (2)(4)= +8.
please help. Answered by Harley Weston. 





Negative rate of change 
20090112 

From hemanshu: when i have to find rate of change of decrease in any value my ans comes in negative why?????????? Answered by Penny Nom. 





A product of positive and negative numbers 
20081003 

From kaylou: Suppose you were given 13 numbers and asked to find their product.
Seven of the numbers were positive, and the rest were negative.
Would your product be positive or negative? Why? Answered by Penny Nom. 





Negative Exponents 
20080129 

From Bill: t to the negative fourth power inside parenthesis to the ninth power
OVER
t to the negative fourth power inside parenthesis to the third power
I am confused on how to start the problem. What I did was invert the Ts to make them positive and I then multiplied the powers. I am not sure if this is the correct process. Answered by Harley Weston. 





x^3 y^(6) 
20080124 

From Bill: I need help completing this negative exponents problem:
x to the power of 3 multiplied by y to the power of negative 6.
What would the process to solving this problem be? Answered by Penny Nom. 





Negative numbers 
20071214 

From mannal: what negative integers do we use in the real world? like 30 temperature? Answered by Penny Nom. 





Multiplying an inequality by a negative number 
20071127 

From Lisa: Why is it that you have to switch the sign of the inequality when you divide or multiply by an negative number to solve for a variable? Answered by Penny Nom and Walter Whiteley. 





Multiplcation of two negative numbers 
20070726 

From Brett: Someone asked a question about multiplication and division of two negative numbers yielding a positive result here:
http://mathcentral.uregina.ca/qq/database/QQ.09.99/butler1.html I was not fully happy with the explanation b/c I want to give me daughter a realworld example and I can't seem to find one.
The following illustrates why multiplying negative numbers has become difficult to explain:
2 X 2 = 4
(4)(2)024
In this example we start with 2 and then want 2 more of them.
When we move across the number line from 2 to our answer, which is four, we have moved only 2 units to the right.
2 X 2 = 4
(4)(2)024
In this example we start with 2 and then want 2 more of them.
When we move across the number line from 2 to our answer, which is four, we have moved 6 units to the right.
How can the phenomenon of multiplying two negative numbers being more powerful than multiplying two positive numbers be explained?
Brett Answered by Stephen La Rocque and Harley Weston. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





Limits as x approaches a constant 
20070625 

From Mac: can you please tell me what is the reason they say "denominator is a negative quantity"
in the solution 11 and "denominator is a positive quantity" solution 10 ??
If i guess correctly, for solution 10, its because of x^2 in the denominator. Answered by Penny Nom. 





A subtraction problem with negative numbers 
20070412 

From Bridget: my daughter has to change a subtraction problem with negative numbers in it to an addition problem with negative numbers and then solve the problem such as:
4(2)=? Answered by Penny Nom. 





What is the difference between (3) and (3)? 
20070211 

From Mckaylla: What is the difference between (3) and (3)? Answered by Melanie Tyrer. 





Negative exponents 
20070111 

From Bob: I have to write this "Y7" (but the 7 is an exponent) as a positive exponent. How? Answered by Penny Nom. 





2 to the 5th power 
20060619 

From Murray: Is 2 to the 5th power = 32? Answered by Penny Nom. 





Simplifying with negative exponents 
20060502 

From Kristine:
I am having a hard time understanding factoring and multiplying
polynomials. I have a couple of problems I just can't get, can you
please help me?
Simplify, do not use negatives in the answer:
(5a^{1}b^{7})(2a^{4}b^{2})
and:
(5x^{2}y^{7}z)(4xy^{3}z^{4})
Answered by Stephen La Rocque. 





3^4 and (3)^4 
20051217 

From Brad: What is the answer to
3^{4} = ?
(3)^{4} = ?
(3)^{4} = ? Answered by Penny Nom. 





How do you simplify a fraction if one of the numbers is negative? 
20051205 

From Stephanie:
Question: How do you simplify a fraction if one of the numbers is negative?
Ex. 32/40
Answered by Penny Nom. 





120 divided by 15 
20051109 

From Joshua: how do you evaluate 120 divided by (15) Answered by Penny Nom. 





Adding positive and negative numbers 
20050903 

From Billy: 46 + 24 =
38 + 22 =
19  20 = Answered by Penny Nom. 





1242, 826, 1034, 930, 1658 
20050831 

From Elizabeth: here is a math question my niece gave me, grade 7
1242, 826, 1034, 930, 1658
first day of school and this is what they give her no explanation Answered by Harley Weston. 





Strategies for teaching operations with positive and negative decimal numbers 
20050202 

From Erin: I am wondering if you can suggest any strategies for teaching operations with positive and negative decimal numbers that do not rely on rules that must be memorized? Answered by Diane Hanson. 





Two consecutive negative integers 
20040117 

From Amanda: Find two consecutive negative intergers whose product is 182. Answered by Penny Nom. 





Positive, negative and zero 
20030904 

From Brian: Can the Value of zero be positive or can it be negative or can it be both. Answered by Penny Nom. 





The sum of two numbers is 5 and their difference is 
20030616 

From Akhil: The sum of two numbers is 5 and their difference is 11. What is the product of the two numbers? Answered by Penny Nom. 





F = 3 + 3 
20020319 

From Jessica: F= 3 + 3 WHAT IS F????? Answered by Penny Nom. 





Negative exponents 
20020116 

From Julie: If z to the power of 4= 1/z4 then how would you solve 1/t2? Answered by Penny Nom. 





Negative numbers 
20011115 

From Jewel: If zero means nothing or an empty set, then how can a number be less than zero, as in negative number? My understanding of negative numbers is distance from a set point in a given direction. Thus having a negative and positive side of a line is arbritary and is related to displacement rather than value. Am I in error? Answered by Penny Nom. 





Squares of negative numbers 
20011103 

From Susana: I wanted to know if I can square a negative number..? Answered by Leeanne Boehm. 





(3)to the power 2, divided by 3 
20011031 

From Raz: what is (3)to the power 2, divided by 3= Answered by Penny Nom. 





Negative times negative is positive 
20011026 

From Mary: I have a question about adding and multiplying positive and negative numbers. When we add two negative numbers the answer is negative BUT when we multiply two negative numbers the answer is positive. I don't understand. Why? Answered by Penny Nom. 





Why do you flip the inequality sign? 
20011026 

From Sean: I have a question about an inequality problem. Here it is: Solve and graph 5  3x => 17. (=> is greater than or equal). Please tell me why you flip the inequality sign when divinding by a negative number. Answered by Penny Nom. 





Integers 
20010909 

From A student: I am a Grade 9 student from Ontario Canada who has never understood how to do integers very well. I was wondering if you would be able to either send me some sites that will tell me how to calculate them in a simple way or if you would be able to write me back and give me some pointers. Answered by Leeanne Boehm. 





A negative times a negative 
20000229 

From Michael J. Butler: I have reviewed the answer in relation to the question of why (3)x(2)=6; however, I am still not able to properly explain the reasoning to my son, Jonathan, who is in grade 7. I want him to understand the reason for the rule that the multiplication or division of two negative numbers equals a positive number. Can you help? Answered by Chris Fisher. 





log(a) 
19991022 

From Brenda Miskimmin: I need to know the mercury concentration in mg/L or ng/L for the following: log M (Hg) = 8.5 where mw of Hg=200.59 (it's the negative sign in front of log that confuses me). Answered by Harley Weston. 





Is zero positive? 
19990903 

From Shah: Is zero a positive integer? Answered by Penny Nom. 





A double negative 
19990901 

From Dennis: If b = 2 what does b = ? As in (a + 8.5)  [(b) + c] a = 1.5, c = 1.7 Answered by Penny Nom. 





Division by a negative 
19990819 

From Sangeeta B.: 56/8 Answered by Penny Nom. 





Negative Primes. 
19971110 

From Leah Zucker and Paul Michael: I have received the following question via email from my granddaughter: "Can negative numbers (like 7) be prime? If not, why not?" Answered by Chris Fisher. 





(3)x(2) 
19951025 

From Azmat: Why is (3)x(2) = 6? Answered by Herley Weston and Ed Giesbrecht. 

