







An arithmetic sequence 
20190131 

From sara: if the 6th term of an arithmetic sequence is 8 and the 11th term is 2, what is the first term? Answered by Penny Nom. 





Converting decimals to common fractions 
20180508 

From Ruth: what does the 0 represent in .018 versus the decimal .180? As in, changing these to fractions? Thank you. Answered by Penny Nom. 





A parallelogram, a rhombus and a rectangle 
20180207 

From Sambo: what do parallelogram, rhombus and rectangle have in common? Answered by Penny Nom. 





An arithmetic sequence 
20171130 

From yo: x; 2x+1; 11 are three consecutive terms of an arithmetic sequence.calculate x Answered by Penny Nom. 





GCD 
20171125 

From A student: Suppose a,b, c are integers such that gcd(a,b)=gcd(a,c)=1. Show that gcd(a,bc)=1. Answered by Penny Nom. 





Abstract algebra 
20171125 

From A student: Suppose a,b, c are integers such that gcd(a,b)=gcd(a,c)=1. Show that gcd(a,bc)=1. Answered by Penny Nom. 





An arithmetic sequence 
20170717 

From abbi: hi there im a student in 11 grade
ive been trying to do this task but i have no idea how to do it
the question is
Find the common difference and the n^th term of the arithmetic sequence if the first term is 4 and the twentieth sum of the terms is 1030 Answered by Penny Nom. 





Baseball Cards 
20170420 

From Raquel: A minor league baseball team gave away baseball cards to each person entering the stadium. One group receives 28 baseball cards. A second group received 68 baseball card. If each person entering the stadium receive the same number of cards, what was the greatest possible number of baseball cards that each person could have received? Answered by Penny Nom. 





Two boys on the same route 
20161206 

From Abbey: Starting from the same spot, one boy completed a route in 9 minutes and another boy completed it in 15 minutes. When will both boys be at the same starting point at the same time again? Answered by Penny Nom. 





An airplane schedule 
20161014 

From Stephanie: Starting at 8:00a.m., a passenger plane leaves from an airport every 6 minutes and a cargo plane leaves every 7 minutes. When is the next time these kinds of planes will leave at the same time? Answered by Penny Nom. 





An equation with fractions 
20160309 

From Ed: 7/10___ +3/2=6/5 Answered by Penny Nom. 





A common tangent to two general parabolas 
20151115 

From Kind: Hi,
I want to find the common tangent of two general parabolas, but i don't know if it's possible or not.
If it's possible, please make a tutorial.
The first parabola equation : Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
The second parabola equation : Gx^2 + Hxy + Iy^2 + Jx + Ky + L = 0.
I need this because i want to find the equation of Beloch fold. (Huzita  Hatori 6th axiom)
However if you know any other method to find Beloch folds equation, I am open for any suggestions. Answered by Chris Fisher. 





Factorise 15x + 15y 
20141120 

From Jordan: hi i saw a question in class today that i didn't understand and i didn't really understand what my teacher was going on about so how do you factorise 15x + 15y Answered by Robert Dawson and Penny Nom. 





A factoring problem 
20141005 

From Gina: 3x^2+6x+3 Answered by Penny Nom. 





An arithmetic sequence 
20140320 

From Xabiso: The 10th term of an arithmetic sequence is 28 and the 7th term is 19. Calculate the common difference and the first term of the sequence. Answered by Penny Nom. 





The greatest common divider of n^23n1 and 3 
20140309 

From Rimoshika: determine the greatest common divider (n^23n1,3) Answered by Penny Nom. 





Adding mixed numbers 
20131120 

From Kathy: 1 3/4 + 1 2/3= ?
5 1/2  2 5/6= ? Answered by Penny Nom. 





An Arithmetic Progression 
20131008 

From collins: In an A.P. the difference between the 8th and 4th term is 20 and the 8th is one and half times the 4th term... what is the common difference and the first term Answered by Penny Nom. 





{(1+x)^1/31/3X(1+x)^2/3}/(1+x)^2/3 
20130617 

From STEPHEN: {(1+x)^1/31/3X(1+x)^2/3}/(1+x)^2/3 Answered by Penny Nom. 





Factoring 
20120426 

From Amanda: y=x^29x Answered by Penny Nom. 





A common chord to two circles 
20120422 

From Nicole: What is a common chord between two circles and how is it found in the problem: Two circles intersect and have a common chord, the radii of the circles are 13 and 15, the distance between the circle's centers is 14, find the common chord. Answered by Penny Nom. 





Simplify the expression 
20120212 

From Christy: Hi guys, ok so I'm having problems with solving this equation since it's been so long I've done precal.
I have to find critical points so I have to find the derivative first. This is what I've done so far
s(t)= (t6)^4 * (t+1)^2
t'= 4(t6)^3*(1)*(t+1)^2+ 2(t+1)(1)*(t6)^4
so this is where I got stuck, which is the algebra part. How can I simplify this to get the answer to figure out the critical points. Answered by Penny Nom. 





8 3/8  6 1/4 
20110321 

From lenora: explain an error pattern in each of the following. 8 3/8  6 1/4 = 2 2/4 Answered by Penny Nom. 





1/a^2 + 1/b^2 
20110119 

From robert: If (a + b)^2 = 81 and ab = 18, find the value of 1/a^2 + 1/b^2 ? Answered by Penny Nom. 





A geometric progression 
20101215 

From Abeth: find the value of x so that 2(x1), x+3, x will be a geometric progression. Answered by Penny Nom. 





x/200+x/400+x/600+x/800 
20101008 

From Ashishthombre: step by step LCM of x/200+x/400+x/600+x/800 Answered by Penny Nom. 





Three cars 
20100830 

From Anil: 3 cars are moving at speed of 4 kmph,5.5 kmph and 8 kmph in a circular track.The circular track has
a distance of 11 km. What is the time taken for all the 3 cars to meet at the starting point ? Answered by Stephen La Rocque. 





Algebraic fractions 
20100422 

From rory: 3x/(x²64)+4/(x²6x16)= Answered by Robert Dawson and Harley Weston. 





A geometric sequence 
20100413 

From glen: A geometric sequence has a first term of 0.1024, a second term of 0.256,
and a middle term of 156.25. how many terms are there in the whole
sequence?
i know that r=2.5 but i dont know how to find how many terms there are. Answered by Penny Nom. 





A geometric sequence 
20100222 

From Kelsey: _, 2, _, _, 250, _
i don't know how to fill in the missing terms Answered by Penny Nom. 





Least common denominator 
20100213 

From Priscila: 3/8 + 4/5 + 7/3 + 9/10 = ?
Thank you for your assistance.
Priscila Answered by Penny Nom. 





Combining fractions 
20100210 

From Nick: Combine the fractions
2m/t + 5/mt Answered by Penny Nom. 





Two bus routes 
20100203 

From kiyah: from 4:30 pm to 6:30 pm the route 1 bus stops every 12 min at the gym's bus stop. the route 2 bus stops there every 15 min. if both buses are now at the stop and schedule is kept, how long will it be before both buses will be at the stop again? Answered by Penny Nom. 





Common multiples of 36 and 48 
20090915 

From Kamaldeep: Find the first 2 common multiples of 36 and 48. Answered by Penny Nom. 





Jogging and swimming 
20090911 

From Brandon: Trevor swims jogs 3 days and swims every 4 days. How often does he jog and swim on the same day Answered by Leeanne Boehm. 





HCF 
20090803 

From Nazrul: If (x+ a) be the H,C.F. of x^2+px+q and x^2+mx+n, prove that (pm)a=qn Answered by Stephen La Rocque. 





Highest Common Factor of Two Polynomials 
20090728 

From Nazrul: If x+a be the h.c.f. of x^2+px+q and x^2+mx+n, how can I prove that (pm)a=qn. Answered by Robert J. Dawson & Janice Cotcher. 





how do I factor 45  5x^2 
20090531 

From tracey: how do I factor 45  5x^2 Answered by Penny Nom. 





A geometric progression 
20090516 

From sweta: find the ratio of GP if the first term is 1 and the sum of third and fifth term is 90. Answered by Penny Nom. 





Common multiples of 2 and 5 
20090423 

From pat: what are the common multiples of 2 and 5, through 30, because i been working on it for hours Answered by Robert Dawson and Stephen La Rocque. 





Factor x squared(x3)+(x3) 
20090419 

From Victor: How do I factor x squared(x3)+(x3) ? Answered by Harley Weston. 





A common tangent to two curves 
20090302 

From Jay: For what values of a and b will the parabola y = x^2 + ax + b be tangent to the curve y = x^3 at (1,1)? Answered by Penny Nom. 





Two tangent circles and common tangents 
20081201 

From Alan: Radius of big circle 30cm, radius of small circle 10 cm. From the diagram, the radius from the tangent do not form a semicircle but at an angle. Find the perimeter of the band around both the circle. May need to use trigonometry to find reflex angle AOB, CMD and get the major arc length AB and minor arc length CD Answered by Penny. 





How would put .12 with 2 repeating into a fraction? 
20080909 

From Savanna: How would put .12 with 2 repeating in fraction?
Savanna! Answered by Penny Nom. 





Two tangent circles 
20080822 

From Michele: A circle of radius 2 is externally tangent to a circle of radius 8,
How do you find the length of their common tangent. Answered by Penny Nom. 





Geometric sequences 
20080608 

From Rita: A geometric sequence is given. Find the common ratio and write out the first four terms.
(1) {(5)^n}
(2) {(2^n)/(3^(n  1)} Answered by Penny Nom. 





Lowest common denominator 
20080531 

From marlene: cant get the common lowest denominator of 10,46,64 Answered by Janice Cotcher. 





x/4 = 3 1/2 
20080530 

From Kelsey: How do you solve for "X" in the problem below?
X
 = 3 1/2
4
Kelsey Answered by Victoria West. 





Converting a decimal to a fraction 
20080519 

From judy: please explain how to get from the decimal number .3437 to the fraction 11/32 Answered by Leeanne Boehm. 





Two overlapping circles 
20080426 

From Michelle: Two overlapping circles O and Q have the common chord AB (vertical line between the overlapping circles). If AB is 6 and circle O has a radius of length 4 (horizontal line going through the overlapping circles and touching the side of the circle) and circle Q has a radius of length 6, how long is OQ. Answered by Penny Nom and Walter Whiteley. 





The zeros of a cubic 
20080409 

From Ryan: what are all the zeros of f(x)= x^31/2x^2+1/3x1/6 Answered by Penny Nom. 





Common fraction to decimal fraction 
20080401 

From chadwick: how do I turn 3/32 into a decimal Answered by Penny Nom. 





Repeating decimals 
20080310 

From Blaine: Is it possible to put a repeating decimal number into a calculator to solve a problem?
EX: Write 39.3939... as a fraction. Answered by Penny Nom. 





A common chord to two circles 
20080309 

From shubha: please help me out with this problem.
find the length of the common chord of the intersecting circles x2+y24x5=0
and x2+y22x+8y+9=0 Answered by Stephen La Rocque. 





1.2 as a fraction 
20080112 

From Confused: i have confused my brain and its driving me crazy i am trying to write 1.2 as a fraction but each time i do it i come out with a different number please help Answered by Penny Nom. 





LCM over 100 
20071209 

From Aris: A teacher has more than 100 sweets. She thinks that if she give 6, 8 or 9
sweets to her students she will have no remaining in the case. What is the
smallest number of sweets in the bag? Answered by Stephen La Rocque. 





A percent as a fraction 
20071124 

From Abby: write 43.75% as a fraction or mixed number in lowest terms. Answered by Penny Nom. 





Ordering fractions 
20071115 

From DEL: Hi. I feel really stupid ! I'm a mature student and i have completely forgotten
How to find out the order of fractions from largest to smallest. I
Have been put this poser;
7/4...1/6....7/2
Can you please tell me what is the largest and lowest?
Will be very grateful....thank you Answered by Gabe Potter. 





How do you convert eleven fifteenths into a decimal? 
20071114 

From Lauren: How do you convert eleven fifteenths into a decimal? Answered by Penny Nom and Stephen La Rocque. 





I need to order 3/11, 1/8, 2/9 from least to greatest 
20071019 

From Andrew: I need to order 3/11, 1/8, 2/9 in least to greatest. Answered by Penny Nom. 





13 year and 17 year locusts 
20071012 

From stefan: how many years pass between the years when both 13 year and 17 year locusts are out at the same time? Answered by Penny Nom. 





Least Common Multiples 
20070920 

From Aiyanna: What is The Lcm Of 3,7,and 8 Because my Teacher gave me That and he didnt even know the answer....
I Worked and worked but I Couldnt Find It..... Answered by Penny Nom and Victoria West. 





Converting a repeating decimal to a common fraction 
20070822 

From isabelle: how do you turn 6.333... into a fraction in simplest form? Answered by Stephen La Rocque and Penny Nom. 





Common factors 
20070819 

From John: I have problem factorising 2p^3  34p. Please advise me. Answered by Leeanne Boehm, Steve La Rocque and Penny Nom. 





Adding algebraic fractions 
20070814 

From John: Ive completely forgot anything to do with the subject mentioned, so my question is straight to the point..
I need to know how to do the following problem (Preferably do not give me an answer though)
(k/3k8)  (4/k+2) Answered by Penny Nom. 





Simplifying an algebraic fraction expression 
20070725 

From Jessica: How do I simplify b/(b^{2}25) + 5/(b+5)  6/b? Answered by Stephen La Rocque. 





The lcm of polynomials 
20070531 

From devin: x^38 , x^34, x^2+4x+4 Answered by Penny Nom. 





Students in rows 
20070517 

From Ashi: the student of three classescan be made to stand into rows having same number of students. there are 24,36 and 60 students in the classes. how many maximum number of student will stand in each row. Answered by Stephen La Rocque. 





Greatest common divisor 
20070314 

From Marie: How do I prove this?
Let h be the greatest common divisor of the positive integers a and b.
Show that there exist integers p and q (not necessarily positive) such that
pa + qb = h.
Thanks Answered by Penny Nom. 





A common tangent line 
20070220 

From chris: I have this problem I have been working on for days and cannot figure it out. it states: Find the two points on the curve y=x^4  2x^2  x that have a common tangent line.
I know you use the first derivative to find the tangent line so if it is a common tangent line should you find two of the exact same tangent line equations at two coordinate points? Answered by Chris Fisher. 





Greatest common factor 
20070126 

From Alexis: What is the greatest common factor of 52,and 100? Answered by Penny Nom. 





Common denominator 
20070110 

From A parent: what is the common denominator of 3/5, 2/7 and 4/8? Answered by Stephen La Rocque. 





Order the fractions from least to greatest 
20070104 

From Justin: I am a sixth grader, and I am having trouble with the last question in my homework assisgnment. 1/6, 2/5, 3/7, 3/5! Answered by Stephen La Rocque and Penny Nom. 





Least common multiple 
20061108 

From Melenie: I have a daughter in 5th grade she can't seem to grasp the concept of finding LCM's does anyone have a quick easy way for her to learn????? Answered by Stephen La Rocque. 





The greatest common factor 
20061017 

From Myrna: What is the greatest common factor of 49,164 and 80,860 Answered by Stephen La Rocque. 





Least common denominator 
20061004 

From Paulette: Why is the LCD of 3/4 and 4/8 not the product of 4 and 8? Answered by Penny Nom. 





What is 1.7142857143 as a fraction? 
20061001 

From Lizzy: What is 1.7142857143 as a fraction? Answered by Stephen La Rocque and Penny Nom. 





Least common multiple 
20060925 

From A student: What is the LCM of 10,45 and 38? Answered by Stephen La Rocque. 





1/x + 1/y 
20060811 

From Sonya: what is 1/x+1/y = ? is it equal to 1/x+y or what? Answered by Penny Nom. 





The greatest common factor of two numbers 
20060716 

From Fadwa: What is the greatest common factor(GCF) of the following algebraic expressions? 1680 and 6048
Answered by Stephen La Rocque. 





The lowest denominator 
20060702 

From Lisa:
What is the lowest denominator for the following numbers:
a) 26
b) 21
c) 47
Answered by Stephen La Rocque. 





How many people are in the race? 
20060407 

From Marty: You're in a race with 1/5 of the racers ahead of you and 5/6 of them behind you. How many people are in the race? Answered by Penny Nom. 





Adding with mixed fractions 
20060330 

From Becca:
can anyone help with how we change to get the same denominator with adding whole number.
example:8+7 3/8
6 1/2 + 2 5/6
Answered by Stephen La Rocque. 





Adding fractions 
20060326 

From Barbara: I know that to subtract 1/4 from 2/3 I must find a common denom. Now the 2/3 becomes 8/12.....i understand the 12, but where does the 8 come from? Answered by Penny Nom. 





GCD 
20060320 

From Jana: How can i prove:
if gcd(a,b)=1 then gcd(a+b,ab)=1 Answered by Penny Nom. 





The Least Common Multiple of two primes 
20060221 

From Kristine: Is the Least Common Multiple to two prime numbers always their product? Why or Why not? Answered by Stephen La Rocque. 





Highest common factor 
20060206 

From Sajid:
1.A rectangular field has dimensions 156 m and 84 m. It is to be fenced with wire netting supported by stakes, equally spaced, a stake being placed at each corner of the field. What is the greatest possible distance between any two stakes, given that it should be more than 2 m and less than 8 m?
2. What is the length of the side of the largest square tile which can be used to cover a floor 525 cm long by 275 cm wide without leaving a gap?
3. Find the greatest number which will divide 140 and 249 to leave remainders 8 and 18 respectively?
4. Find the greatest number which will divide 304 and 298 so as to leave remainder 4 in each case.
Answered by Penny Nom. 





GCF, LCM, primes and the ladder method 
20060107 

From Linda: How would I teach both finding the GCF and LCM with prime factors...I recall the ladder method vaguely.??? Answered by Penny Nom. 





LCM 
20051212 

From Alex: what is the LCM of 210 and 54 and the LCM of 42 and 126 Answered by Penny Nom. 





Common fractions to decimals 
20051125 

From A student: how do u turn 8 over23 into a decimal and how do u turn 8 over 29 into a decimal Answered by Penny Nom. 





Adding improper fractions 
20051125 

From Paula: I would like a simple step by step explanation on how to add improper fractions. Answered by Penny Nom. 





Rational expressions 
20051115 

From Zach: I can solve easy problems such as (x/2)+3=2+(3x/4). That is easy because the Lowest Common Denominator is 4. But what really gets me stuck is a problem like this one.
(6/x2) = ( 21/(x2)(x+2) )+ 1. Answered by Penny Nom. 





Factoring 
20051030 

From A student: Factor 18x^{3} y^{3} + 12xy^{2} Answered by Penny Nom. 





Least common multiple 
20051022 

From Dayna: I'm stumped! I can't seem to come up with a least common multiple of 22 and 25. Is there one? Answered by Penny Nom. 





Isn't 1/3 written as a decimal .33? 
20050921 

From Lisa: Isn't 1/3 written as a decimal .33? My son informs me I'm wrong, but doesn't know the answer
Answered by Chris Fisher and Penny Nom. 





A geometric sequence 
20050621 

From A student:
The first three terms of a geometric series are 3(q+5), 3(q+3), (q+7) respectively.
Calulate the value of q. Answered by Penny Nom. 





The lcm of 5, 3, 4, 7 and 2 
20041105 

From Christine: what is the lcm of 5,3,4,7,2 Answered by Penny Nom. 





The least common denominator 
20041103 

From A student: Write the LCD for each pair of fractions.
13. 1/3,1/5
14. 2/7,1/4
15. 3/4,3/5 Answered by Penny Nom. 





The lcm of 1 and 1 
20041103 

From Nayiyan: I would like to know what is the LCM of (1) and (+1) is. Answered by Penny Nom. 





GCD and LCM 
20041031 

From Cartalina: how do you calculate the "positive difference between the GCF and LCM of two numbers"? Answered by Penny Nom. 





A common tangent line 
20041005 

From Shanup: The xaxis is a common tangent of y = x^2 and y = x^3. Find the equation of another common tangent. Answered by Penny Nom. 





Rational expressions 
20040924 

From A student: In general, I understand rational expressions except when it comes to solving problems such as:
x+y/2xy  2x/y2x or m4/3m4 + 3m+2/43m
I am confounded by the issue of having to find a common denominator. For example, if I tried to solve these problems by multiplying both denominators they would still be uncommon. Answered by Claude Tardif. 





GCD (a + b , a^2  ab + b^2) 
20040827 

From Carol: Let a and b integer and relatively prime. Proof that:
GCD (a + b , a^2  ab + b^2) = 1 or 3 Answered by Penny Nom. 





The Parliament of the land of Achronia 
20040529 

From Christine: The Parliament of the land of Achronia consists of two houses. The parliament was elected in 2003 for a period of six years beginning on Thursday, the 1st of January 2004, when the two houses had their first sessions. According to the rules, the meetings of the first house must occur every twelve days for the duration of the term, and the meetings of the second house must occur every eighteen days. For example, the second meetings of the first and the second houses were held on the 13th and 19th of January respectively. A new law can be passed on any day when both houses meet, except on a Thursday. On how many days can the parliament members pass new laws during this six year term? Answered by Penny Nom. 





Subtracting fractions 
20040511 

From Filipe: Question:
_5_  __7__
6ab 8a Answered by Penny Nom. 





Common fractions to decimals 
20040212 

From A parent: I'm trying to help my son work with turning fractions into decimals and this seems foreigh to me after 20 years of not being in school. Can you give me a few illustrations and/or examples of how to do that?? Answered by Penny Nom. 





A/30 + B/105 = (7A + 2B)/x 
20040205 

From Jim: If A/30 + B/105 = (7A + 2B)/x and A, B, and x are integers greater than 1, what must x equal? Answered by Penny Nom. 





Adding fractions 
20031116 

From Ken: My name is Ken and I am taking my GED course for my High School and have not been in a class for 35 years. I am doing this for retraining. I am at the part about fractions. Here is an example that I am having trouble with.
1 3/7 + 4 2/3 + 11/21
They have no common denominators. Could you PLEASE help me. If you could send me a step by step explanation it would be greatly appreciated. Answered by Penny Nom. 





Greatest Common Factor 
20031108 

From Beth: How do you use the Greatest Common Factor in addtion and subtraction of fraction? Answered by Penny Nom. 





Subtracting rational expressions 
20030510 

From Simone: hi, i'm totally lost. i understand that you need to find a lowest common denominator to subtract two fractions (rational expressions) with different denominators. but what if the denominators are "x1" and "x". is x the common denominator? if so what happens to the "1"? do you know of any live online help i can get with the following: 3/(x1)  (12x)/x i've looked through my notes and have no examples that quite match that i can follow to get through it. please help! Answered by Penny Nom. 





Multiples of all four of the numbers 2, 3, 4, and 5 
20030211 

From Stephanie: How many of the first 1000 positive integers are multiples of all four of the numbers 2, 3, 4, and 5? Answered by Penny Nom. 





Some 5th grade problems 
20030124 

From Sabrina:
[What is the greatest common factor of 20,28, and 36?] next problem is [5k+7(k+8)= ] next problem [Curtis simplified 0.8 divided by 0.2 x 0.04 and got 10. Latoya Simplified and got 1.6. is either correct? Can you explaine how you got the answer please.] Answered by Penny Nom. 





The least common denominator 
20030121 

From Brittan: Hi there I need help! My name is Brittany and i am in the 6th grade. I need help finding the least common denominator(LCD), and the book says Find the LCM of the denominators and i've done that and then it says write equivalent fractions,using the LCM as the least commonn denominator.The directions say Use the LCD to write each pair as like fractions. and the problem is 1/8 and 5/40. Could u explain how in the word u do this? Thanks a lot Brittany Answered by Penny Nom. 





Composites, primes, factors and common factors 
20021120 

From Connie: My son can't remember what a composite number is, what a prime number is and the explaination of factors and common factors. Help! Answered by Penny Nom. 





Why is 5 divided by 1/7 greater than 5 divided by 2/3? 
20021119 

From Elizabeth:
 Without performing the division, explain why 5 divided by 1/7 is a number greater than 5 divided by 2/3.
 Is the least common multiple of two prime numbers always their product? Why or why not?
Answered by Diane Hanson and Penny Nom. 





Rational expressions 
20021003 

From Ashley: 1/x(squared) + 5/xy Answered by Penny Nom. 





Common Denominator 
20020826 

From Slobodanka: What is a Common Denominator? Answered by Penny Nom. 





Factor 12x^2  20x  8 
20020430 

From Crystal: Factor Completely: 12x^{2}  20x  8 Answered by Penny Nom. 





Common fractions to decimal fractions 
20020402 

From Natalie: My questions are: "how can I change 23/60 into a decimal. and give my answer to 2dp."?????????? 2nd question:for each of these pairs, which is bigger?
4/7 or 36%____________ 3/11or 0.29____________ 14/24 or 0.57___________ Answered by Penny Nom. 





The reciprocal of a decimal mixed number 
20020329 

From A student: How do I find the reciprocal of a decimal mixed number? Answered by Penny Nom. 





24x^4 + 3x 
20020318 

From gary: 24x^{ 4} + 3x Answered by Penny Nom. 





Factor completely 
20020307 

From Taylor: I'm supposed to completely factor this but I don't know what to do with all the variables. a^{3}b^{5}  a^{2}b^{5}  12ab^{5}. Does it have anything to do with b^{5} being a common factor or am I completely off? Answered by Penny Nom. 





Reduce 79,537/3,623,420 
20011213 

From Eliana: How do you reduce 79,537/3,623,420. Answered by Claude Tardif. 





Manufactures golf balls 
20011106 

From Kevin: A company manufactures golf balls. Golf balls are each numbered consecutively 0 to 4, and then the numbering starts over with zero again. Every 12th golf ball is yellow. Every 8th golf ball is tested for defects. The company produces 120,000 golf balls in an eighthour shift. A. How many yellow golf balls are tested for defects during the day? Explain your reasoning. B. How many of these yellow balls that are tested are imprinted with the numeral 2? Explain your reasoning. Answered by Penny Nom. 





Locusts 
20011008 

From A parent: JOHN CONJECTURED THAT BOTH 13YR.&17YR. LOCUSTS CAME OUT THE SAME YEAR. ASSUME IT IS CORRECT. HOW MANY YEARS PASS BETWEEN THE YRS. WHEN BOTH 13 YR. & 17YR. LOCUSTS ARE OUT AT THE SAME TIME? EXPLAIN. NEXT, SUPPOSE THERE WERE 12YR.,14 YR.,& 16YR. LO CUSTS,& THEY ALL COME OUT THIS YR. HOW MANY YRS. WILL IT BE BEFORE THEY ALL COME OUT TOGETHER AGAIN? Answered by Leeanne Boehm. 





GCD and LCM 
20010924 

From David: Find the GCD adn LCM of the following numbers. Assume p 2 to the power p, 3 to power q, 5 to power r and 2 to power q, 3 to power r, 7 to power p Answered by Penny Nom. 





4x(2x1)+(2x1)^{2} 
20010917 

From Nick: how do u solve 4x(2x1)+(2x1)^{2} Answered by Penny Nom. 





Common solution 
20010602 

From Samantha:
 Solve for common solution: x+y=6 2x3y=2
 Solve for y in terms of x: 3xy=4
Answered by Penny Nom. 





Greatest Common Factor 
20010509 

From Nicole: What is the Greatest Common Facter for:
126,261 1008,1080 546,1995 128,256 and 255,256 Answered by Penny Nom. 





Adding and subtracting rational expressions 
20010503 

From Donna: Adding and subtracting Rational expressions. I am in grade 10 and I am a student here is an example of the questions: 1/(x+1)  1/(x1) = ? Answered by Penny Nom. 





Common tangents 
20010408 

From Anne: I have been working on this problem for a while but I'm not sure I'm getting the right answer: Find the common tangents of 2y=x^{2} and 2y=x^{2}16 Thanks for the help. :) Answered by Harley Weston`. 





A four digit number 
20010217 

From Dean: Need to find a 4 digit number that can be divided by 2, 3, 4, 5, 6, 7, 8, 9, and will always have a remainder of 1 in the answer. Answered by Penny Nom. 





Two number theory questions 
20010130 

From Richie: i have two questions and they are:  the product of three consecutive prime numbers is 7429. Find the product of the smallest and largest of these three integers.
 the least common multiple of two relatively prime positive integers, a and b, is 144. if a (a>or=2) is as small as possible, compute the value of b.
Answered by Penny Nom. 





Factoring a trinomial 
20010124 

From Kyle: I am an eighth grade student.I can not figure out the following problem. 4x^{2} + 2x  20 Answered by Leeanne Boehm. 





Greatest common factor 
20010117 

From A teacher: I'm a teacher at a local Middle School and I would like the answers for the following questions. What is the greatest common factor for.. 546 and 780 156 and 732 . . . Answered by Leeanne Boehm and Penny Nom. 





A pair of numbers whose GCF is 28 
20001227 

From John: Name 2 different pairs of numbers whose GCF is 28. Answered by Penny Nom. 





Factoring (uv)^{3}+vu 
20001215 

From A parent: I am a middle school teacher and a parent. I am snowed in and trying to help my 9th grader get ready for 9 weeks exams. I have tried to factor this problem to no avail. (uv)^3+vu. I have the answer but I need to know how it is done. Answered by Penny Nom. 





Factoring a cubic 
20001031 

From A student: Factor Completely 18p^{3}  51p^{2}  135p Answered by Paul Betts and Penny Nom. 





LOG(LN(x)) = 1 
20000728 

From An algebra student: LET F(x)=LOG X AND G(x)= LN X. SOLVE (f *G)(x)= 1 SHOW COMPOSITION AND USE DEFINITION OF LOGS. Answered by Harley Weston. 





Factoring, primes, GCF and LCM 
20000227 

From Ruth Kroek: My son is in grade seven, he has to do a Factoring Booklet the areas covered are:  Prime #'s
 Composite #'s
 Rainbow Factoring
 Finding Multiples (consecutive multiples)
 Finding GCF of 23 numbers uning Rainbow factoring
 Finding LCM of 2 numbers using consecutive multiples
 prime factor trees
 prime factor ladders
 finding GCF of 2 numbers using Prime number Method
Although his text 'Math Power' gives some information, we are at a loss .. Answered by Penny Nom. 





Least Common Multiple 
20000216 

From Kathy Heath: The way I understand it is for 2,3,9 the least common multiple is 18. Am I right? If so, I guess the least common multiple for 3,4,7 is 105. Please let me know if I'm right so I can tell my daughter. Answered by Denis Hanson. 





Climbing stairs 
19991222 

From Harman Chaudhry: Paul, Michelle and Michael all climb up 54 steps. Paul climbs the steps one at a time i.e. 1, 2, 3, etc. Michelle Climbs the stairs 2 at a time i.e. 2, 4, 6, etc. Michael climbs the stairs 3 at a time i.e. 3, 6, 9, etc. How many steps are used by exactly two people? Answered by Penny Nom. 





Common factors 
19991006 

From Tommygirl98: Ok I have a question about common factoring I'm not to sure if you could help me but it's worth a try here it goes. Ok I have a test on Friday and i'm having trouble understanding how to do it here's an example, Factor, 10 + 2b how do you do it and what do they mean by factor? Answered by Penny Nom. 





Jose and Arthur 
19990926 

From Joel Hammer: Jose can run around the track in 40 seconds. Arthur runs with Jose but in the opposite direction. They meet every 15 second. How long will it take Arthur to make one trip around the track? Answered by Denis Hanson. 





Repeating decimals 
19990918 

From Kavoos Bybordi: I dont know how to change a reccuring decimal to a fraction please could you tell me the method. Answered by Penny Nom. 





Where three sequences meet. 
19990306 

From Ali: My name is Ali and I am in the 5th grade. I have a math question: What is the least positive integer meeting each of the following conditions:  Dividing by 7 gives a remainder of 4
 Dividing by 8 gives a remainder of 5
 Dividing by 9 gives a remainder of 6
Help! Answered by Denis Hanson. 





The Board Problem 
19990215 

From Avery: Mr. Avery has 3foot boards and 4foot boards. If he puts the 3foot boards in a line, they have the same length as the 4foot boards put in a line. Altogether he has between 16 and 25 boards. How many 3foot boards does he have? Answered by Jack LeSage and Penny Nom. 





Adding Fractions 
19981003 

From Pam Bailey: Can you help me simplfy this? (1/2a + 1/3b)  (1/4a  1/5b) + (1/6a  1/7) thanx Answered by Harley Weston. 





Greatest Common Factor. 
19980109 

From Percy Stribling: how do you figure out what the greater common factor is? Answered by Penny Nom. 





Fractions 
19971020 

From Rebecca Henry: When we add fractions, we find a common denominator and add the numerators When we multiply fractions, we simply multiply both numerators and denominators with no regard to commonality.  Why do we not have to find a common denominator when multiplying?
 Why do we multiply both numerators and denominators?
Answered by Chris Fisher. 





Two Questions 
19970828 

From Faye Tan: I am a trainee teacher. I would appreciate it very much if you could help me solve the following two problems which I think are meant for students at middle grade. 1. If a hen and a half lays an egg and a half in a day and a half, how many hens are needed to lay a dozen eggs in one day? 2. There are fewer than 200 passengers on a train. If they get off in pairs, one passenger will be without a partner. If they get off in groups of 3 or 4, there will still be one passenger left by himself. However, if they get off in groups of 5, no one will be left by themselves. How many passengers are there on the train? Answered by Penny Nom. 





A Question About Pi. 
19970708 

From Mike Chan: I have read the section Repeating Decimals in your data base. It mention that 1/17 has at most only 16 repeating digits. But, why does "pi" have an infinite number of digits (and not repeating ). Answered by Penny Nom. 





How many digits are there in 2^2520? 
19961007 

From Rita Leung: A)The number 64 is a sq., a cube, and a sixth power because 64=8*8, 4*4*4, 2*2*2*2*2*2. Find the smallest integer greater than 1 that is a sq., a cube, a 4th, 5th, 6th, 7th, 8th, 9th and 10th power. I have found that the answer is 2 to the power 2520th. B) How many digits are in the correct answer to part A? The answer is uncertain. It is either 758 or 759. Can you give me any ideas? Answered by Penny Nom. 





quel sont les plus grands diviseurs communs? 
20050907 

From Sylvain: quel sont les plus grands diviseurs communs? Answered by Claude Tardif. 

