







A times table in base 5 
20200311 

From Felix: Design a time table for numbers 110 in base 5 Answered by Penny Nom. 





Multiplication base 8 
20200219 

From Tamesha: Let’s count with the symbols 0,1,2,3,4,5,6,7 (base 8)
A). Create a multiplication table for this base
B). Compute the following products using the multiplication algorithm
I). 7605 times 3713
II). 63725 times 40627 Answered by Penny Nom. 





Dividing the tips 
20200102 

From Pat: trying to figure out division of tips I have 3 full time employees 40 hrs a week and 1 part time worker 12 hours a week what percentages do i give them to give them appropriate tips :) Answered by Harley Weston. 





Two people are clapping their hands 
20191206 

From Yukti: Two people are clapping their hands, but with different frequencies. Ramya claps her hands
17 times per 3 minutes, and Kumar claps his hands 31 times per 5 minutes. They start
clapping at the same time. How many times does each one clap before they clap together at
the same time again? Answered by Penny Nom. 





Packing chocolates in boxes 
20190722 

From CHESKA: 1.levy can pack the chocolate bars either with 35 bars in a box,with 42 in a box, or with 49 in a box. what is the least number of chocolate bars that he has?
2. the blue light of a Christmas light blinks every 2 second. the red light blinks every 3 second and the yellow light blinks every 5 second. how many times will the three lights blink at the same tims in one hour?
3.a wooden straightedge can exactly measure an 825 cm rope, a675 cm rope, and 375 cm rope. what is the least possible length of the straightedge? how many times will it measure each rope? Answered by Penny Nom. 





Multiplies and factors 
20180224 

From Lil: Is a multiple the same as a factor? Answered by Penny Nom. 





3 yards 6 inches times 7 
20180208 

From Tamara: 3 yards 6 inches × 7 Answered by Penny Nom. 





Four multiples of 10 
20170923 

From Laudacir: Four multiples of 10 are added together.the total is a 3 digit number with three consecutive digits. What could the four number be? Answered by Penny Nom. 





3 consecutive multiples of 11 
20170722 

From nisha: using the multiples formula shown at ypur site how can we solve finding 3 consecutive multiples of 11 whose sum is 363 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. 





Multiplication and repeated addition 
20161123 

From Anandmay: Hello
I was looking closely at early arithmetic where I found how we discovered properties of Arithmetic.
Like:2 x 3 = 3 x 2.
This can be proved by considering a 2D figure(actually,quadrilateral) having length consisting of 2 boxes of
1by1 dimensions and breadth of 3 boxes of the same dimensions.
Now,consider it again,but,this time,length of 3,and breadth of 2 of such 1 by 1 boxes.
We now notice that we can fit the 2 types of rectangles formed on each other precisely.
So the multiplicative property of commutativity is true for all natural numbers as we can generalize the result(in our mind,for self satisfaction).
Now,can you find me a nice satisfactory reason of why a fraction times a natural number equals the number times the fraction?
I mean, for example,i can understand the meaning of 3 x 2/3 to be three times 23rd,that is, 2/3+2/3+2/3.Fair enough.
But here is the problem:By definition and actual meaning of multiplication, a x b means the repeated sum of b,done 'a' times.
So what is the meaning of doing 2/3 x 3?The repeated addition of 3 how many times??2/3 times??Not making sense,right?And even
we have not proved yet the commutative property of numbers INCLUDING fractions.So how can we resolve this problem and make these things meaningful?
Thanks 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. 





The difference between the ares of two rectangles 
20160609 

From Ingrid: I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.
Question:
Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?
I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?
Thanks for your help Answered by Chris Fisher and Harley Weston. 





Two pieces of rope 
20160521 

From Render: Fred cuts a 12 inch piece of rope. Then he cuts a second piece of rope that is 3/2 longer than the first piece. Is the second piece shorter or longer than the first piece? Explain. Answered by Penny Nom. 





Pizza delivery 
20160403 

From Andrew: Suppose you own a local pizza restaurant, Pizza with Pizzazz, and in order to compete with the big pizza chains in your area you are considering an advertising campaign offering customers a free pizza if their pizza is not delivered in 30 minutes or less. Even though your pizza restaurant is known for its fast and friendly delivery service, you are not sure if you can afford to give away too many pizzas for free. Looking over your past 12,421 pizza deliveries you find out 97% of the pizzas were delivered in 30 minutes or less.
Calculate the probability that all 100 randomly selected pizza deliveries will have been made in 30 minutes or less? Hint: Use the multiplication rule. (Round 4 decimals)
I'm really stumped on how exactly to do this problem. I don't need the answer just the steps broken down to show me how to get it!
It would be gladly appreciated if you could help! Answered by Penny Nom. 





n^2 is a multiple of 100 
20150330 

From Rahul: I have to prove that n^2 is a multiple of 100 is necessary or
Sufficient condition (or both) for n being multiple of 10 Answered by Penny Nom. 





A fact family containing 4, 4 and 16 
20141014 

From Leslie: I am helping my son and the question is 4,4,16 in fact family what does that mean Answered by Penny Nom. 





Multiplication in base five 
20140807 

From Alise: Hi Maths Central!
I was wondering if you could help me with multiplying in base 5. I have read a question previously answered by you in regards to this but got fairly confused by it and was hoping you could help me with my question.
My question is: Multiply 1422 base 5 by 21 base 5 keeping these numbers and answer in base 5.
Would you also be able to explain how to get to the answer?
Thanks! Answered by Penny Nom. 





60% as much as $30. 
20140718 

From Kenneth: Question from Kenneth:
Hello:
Do you know why some "as...as" phrases indicate multiplication?
For example, ? is 60% as much as $30. This is equivalent to 60% X $30 = $18. How does this make sense?
I saw this example in an old textbook on business mathematics, but the author did not explain why it is equivalent
to multiplication.
I thank you for your reply. Answered by Robert Dawson. 





Problem solving with fractions 
20131203 

From Jennie: Paul has 2/3 as many postcards as Shawn. Shawn has 3/5 as many postcards as Tim.
If the 3 boys have 280 postcards, how many more postcards does Tim have than Paul? Answered by Penny Nom. 





Base 5 arithmetic 
20131127 

From samuel: Good day sir, please i don't understand when you say 4x4=13 in base five? In fact, am always having difficulties in addition, subtraction, division and multiplication of number in the same base other than base ten. Please can you give me one example each with details explainations? Answered by Penny Nom. 





Sixdigit passwords 
20130319 

From Judy: Hello:
Can you please explain why the answer to the following question is 10^6?
What is the number of possible sixdigit passwords when using the digits 0 through 9, with repetition allowed.
Thank you. Answered by Penny Nom. 





Multiplication in base two 
20130201 

From Michael: multiply in the indicated base
110two*11two Answered by Penny Nom. 





The multiplication table for the different bases 
20130201 

From sylvia: I am having a difficult time trying to figure out how to fill in the multiplication table for the different bases. i don't know how to get the numbers. Answered by Penny Nom. 





birdhouse in the shape of a rectangular prism 
20121029 

From Tiffany: Hello, I am Tiff M. from NYC.
I was solving a math problem about adding,subtracting,multiplying
or dividing fractions and mixed numbers. I am not getting this
question below.
* Laura is building a birdhouse in the shape of a rectangular prism.
The base of the birdhouse has an area of 5 square inches. The
height of the birdhouse is 2 7/12 inches. Laura calculated the
volume of the bird house to be 10 7/12in. Is she correct?
If not, what did she do wrong? 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. 





Multiples 
20120528 

From Kenneth: If I understand correctly , a multiple is a product of two numbers. For example some of the multiples of 6 are 6, 12, 18, 24, 30, etc. I just multiplied 6 by 1, 2, 3, 4, 5, etc.
Are the multiples of a fraction, for example, 2/3, determined in the same way? Are they 2/3, 4/3, 6/3, 8/3, 10/3, etc., or are they instead, 2/3, 4/6, 6/9, 8/12, 10/15, etc.?
Or do fractions have no multiples? Answered by Penny Nom. 





Multiplying binomials 
20120514 

From Jordan: How do I solve the equation:
3(x+4)(x6) Answered by Penny Nom. 





Building a tipi 
20120129 

From Lacy: Hi there!
We are building a tipi for our children. We want to build a large one about 15ft tall with a base of about 15 feet diameter. I am trying to figure out how much canvas we need to accomplish this. I graduated about 20 years ago and am struggling. Please help if you can. Answered by Penny Nom. 





I started with Euler's identity and manipulated it 
20111114 

From anonymous: I started with Euler's identity and manipulated it
e^i*pi=1
e^i*pi=(1)^1
e^i*pi=1
e^i*i*pi=(1)^i
e^pi=(1)^i
e^pi=(1)^i
type it in in a calculator and you get e^pi=23.1406926... and
(1)^i=0.0432139183... What did I do wrong? Answered by Robert Dawson. 





4 x 2 
20110830 

From Lucjan: how to sketch a diagram that shows 4x2 expression? Answered by Penny Nom. 





3.8 x 2.2 
20110818 

From Isaac: Question from isaac, a student: I am struggling in math & I need help on multiplying 3.8 x 2.2. Can you helpme Answered by Melanie Tyrer and Harley Weston. 





Prove sin x = sin (pi  x) 
20110215 

From Janet: Prove sin x = sin (pi  x) Answered by Penny Nom. 





Multiplication and order 
20110121 

From Janet: IN A MULTIPLICATION SENTENCE BASED ON A DRAWING..IS THERE ANY ORDER FOR THE MULTIPLICAND ANG MULTIPLIER FOR THE ANSWER TO RIGHT? Answered by Robert Dawson. 





Convert to multiplication 
20101023 

From angelina: how to covert 5+5+5=15 to multiplication Answered by Penny Nom. 





Geocaching 
20101015 

From Clint: I am stuck on a puzzle for Geocaching which is a GPS game.
I know it is a number matrix but don't know how to start.
[1 7 16 3 9; 1 3 18 20 33] x [1 8 9 3 5; 0 1 0 4 2; 0 0 1 2 1; 0 0 0 1 1; 0 0 0 0 1] = ? Answered by Stephen La Rocque. 





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. 





Constructing a tipi 
20100920 

From mike: we are thinking about making a lightweight tipi tent but we need to know what the angles and lengths of each side that we will need to cut. The height of the tipi wants to be about 2.2m span at the widest point wants to be about 3.2m we want to make it based upon a 6 sided(hexagon) shape thanks for your help Answered by Harley Weston. 





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. 





Two problems 
20100527 

From debbie:
Question from debbie, a parent:
hi, i have a daughter and she asked me a maths question I cannot solve. I was just wondering if you can give me the answers plus the working out so I could explain to my daughter,
1. The leftmost digit of a sixdigit number N is 1. If this digit is removed and then written as a rightmost digit, the number thus obtained is three times N .Find N.
2. Four friends are racing together down a flight of stairs. A goes 2 steps at a time, B 3 steps at a time. C 4 steps at a time and D 5 steps at a time. The only steps which all four tread on are the top one and the bottom one. How many stairs in the flight were stepped on exactly once? Answered by Penny Nom. 





cos(x) = sin(x  1) 
20100428 

From alex: In the equation cos x = sin x1 for pi/2
A: solve for x graphically
B: solve algebraically and prove the solution is correct.
Alex Answered by Penny Nom. 





1/6 x 5 x 12 = what 
20100219 

From dana: 1/6 x 5 x 12 = what Answered by Lorraine Dame. 





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. 





Dividing seashells among girls 
20100106 

From Eileen: A group of girls collected some seashells from the beach. They tried to divided these seashells equally among them. If each girl received 8 seashells, they would need 5 more seashells. If each girl received 7 seashells, they would have 3 seashells extra. How many seashells did they collect from the beach altogether? Answered by Robert Dawson and 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. 





Multiplying Large Numbers 
20090709 

From Jessica: What is 12 billion X 6 trillion? Answered by Janice Cotcher. 





Multiplying Large Numbers 
20090709 

From Jessica: What is 12 billion X 6 trillion? Answered by Janice Cotcher. 





Investing in multiple accounts 
20090626 

From Kenneth: Hello:
If an investor has $1000.00 to invest in multiple accounts, and he
wants a total return of 4%, is there one calculation that can be used
to determine what these amounts could be even though there may be
numerous amounts used as answers for most of the following examples?
For example,
Invest $1000.00 @ 2% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, 4% and 5% for total return of 4%.
etc. Answered by Robert Dawson. 





Fraction Word Problem 
20090513 

From Sonya: Debbie wants to eat 1/6 of her 12 pieces of candy. How many pieces did she eat ? Answered by Janice Cotcher. 





A six sided pyramid 
20090511 

From Karen: I am going to make my kids a six sided tipi (pyramid) I have a 5 foot tall central pole, and I would like the floor area to be 6 feet across. How do I work out what size to cut each fabric panel to make this happen? Answered by Harley Weston. 





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. 





Choices at a restaurant 
20090413 

From Rob: There is a restaurant you get:
Rice/Noodles (1) 
Main Ingredient (any) 
Sauce (1) 
1 
1 
1 
2 
2 
2 
3 
3 
3 
4 
4 
4 
5 
5 
5 
6 
6 
6 
7 
7 


8 


9 


10 


11 


12 

So the question is how many different combinations are there. You can only have 1 rice/noodles in a selection and only 1 sauce in a selection but you can have between 1 and all twelve mains in a selection. there are 7 rice/noodles , 12 mains and 6 sauces. How many possibilies. I did it mentally in the restuarant, no pen, paper or calculater and i got 3276..i think thats wrong. please help
Rob Answered by Robert Dawson, Stephen La Rocque and Claude Tardif. 





2sinB=3tanA 
20090410 

From Xanathax: ABC is a rightangled triangle. 2sinB=3tanA.
Calculate the measure of angle A. Answered by Penny Nom. 





Multiplication of polynomials 
20090407 

From Carla: I am struggling to understand Multiplication of Polynomials. No matter how hard I try to understand Multiplication of Polynomials, I just can't get it!
The problem that I am trying to solve is this :
3x^3y(y + 2 x^2 + x) Answered by Robert Dawson. 





A rectangular open box 
20090321 

From tina: An open box is to be made from a rectangular piece of tin by cutting two inches squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin. Answered by Stephen La Rocque. 





Multiplying in different bases 
20090225 

From Susan: 11 base 2 X 22 base 3 + 33 base 4 = _________ base 5 Answered by Robert Dawson. 





mutiplying decimals 
20090224 

From telly: how to do this sum0.24*0.398 Answered by Robert Dawson and 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. 





Multiplication 
20081114 

From natalie: what is 8 times 30 Answered by Penny Nom. 





Confusion in a multiple choice question 
20081114 

From BJ: My son got this math problem which he could mostly solve. Here it is:
The highest location in a certain country is 4525 m above sea level. The lowest point in the same country is 192 m below sea level.
a) Find the difference of the two elevations. His answer: a(b)= a+b or 4525(192)= 4525+192=4717 m. No problem.
b) A city is 2221 m above sea level. Is this elevation closer to the highest point or the lowest point?
His answer: highest point because: 45252221= 2304 m (closest to the highest point) and 2221(192)=2221+192= 2413 m. (farthest to the lowest point). OK so far.
But then he was given 4 choices for this question with no other information:
a) 4717 m; lowest b) 4333 m; lowest c) 4333 m; highest d) 4717 m; highest
What does it mean? What's the connection with the rest of the problem? Answered by Harley Weston. 





A multiple choice exam 
20080913 

From Phalange: A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if:
a. You go into the exam without knowing a thing, and have to resort to pure guessing?
b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.
c. You have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing. Answered by Harley Weston. 





multiply = 3a  3b by a+b 
20080715 

From chaleen: multiply = 3a  3b by a+b Answered by Penny Nom. 





sin(2x)/sin(3x) 
20080619 

From matt: how does sin2x break down (not with identities) and how would sin3x be created. My
prob. is sin 2x/ sin 3x and I want to know how the double(or triple angle) would break
down. I want to be able to cancel out sins. Thanks! Answered by Harley Weston. 





How do you reduce an equation with multiple variables? 
20080430 

From Jonathon: How do you reduce an equation with multiple variables?
For example, if 3x + y = k(x3), what would x be equal to? Answered by Penny Nom. 





Matrix multiplication 
20080408 

From manashi: i. why matrix division is not possible?
ii.when we add or subtract two matrix , getting the result by addind or subtracting correspondind elements....but in case of multiplication it is not but why? Answered by Harley Weston. 





What fraction of 45 is 10? 
20080406 

From Scott: 45 x fraction? = 10 Answered by Penny Nom. 





2 times 0 times 0 times 4 
20080330 

From ben: what is 2 times 0 times 0 times 4? Answered by Penny Nom. 





Multiplying decimal numbers 
20080205 

From alwyn: Why should when you Multiplying Decimal numbers is value becoming less and less? don't you think even decimal number is a quantity and in no chance when it multiplies its should become less or nil !!!
In fact all Multiplying and or adding the value will go up and only when you subtract and divide it should become less !! Answered by Stephen La Rocque and Penny Nom. 





Fact families with multiplication and division 
20080116 

From Donna: I am trying to help my granddaughter with some math homework. I
looked at what you have on fact families. Am I correct to assume that
the same process applies to multiplication and division as well? Her question
asks for fact families for 2, 8, & 16. Answered by Penny Nom. 





Multiplying numbers in bases other than 10 
20080108 

From Imaiya: In class we've been learning about numbers with a base other than ten. For example, base 7, base 5,
and base 6. What's really stumping me is how to multiply these numbers, when they aren't a base of 10.
I've had it explained to me once, but don't seem to understand it. Here are the equations, and I've listed the first few numbers for that particular base.
Base 5: 0,1,2,3,4,10,11,12,13,14,20 etc... The Equation: 34 x 42
Base 9: 1,2,3,4,5,6,7,8,10,11,12,13,14, etc... The Equation: 56 x 78
If you could explain to me how to multiply numbers with any type of base, I'd really appreaciate it. Also
if you could show me how to do one of the questions that I listed, that would really help me =) Thanks so much,
and once again, thank you for your great site! Answered by Stephen La Rocque. 





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. 





6 consecutive multiples of 6 
20071111 

From jeff: find 6 consecutive multiples of 6 whose sum is the least common multiple of 13 and 18 Answered by Penny Nom. 





Surface area of an openended cone 
20071016 

From Lorne: What is the surface area of an open ended cone? Measured at 10' high,
16' diameter on the bottom and 2' diameter at the top. Answered by Stephen La Rocque. 





How much can Daisy spend? 
20071014 

From Math: Daisy has $25.00 to spend on dinner. Her sister tells her to leave 18% of the bill as a tip and
the sales tax is 8% of the bill. What is the maximum amount she can spend on dinner in order to cover
the meal, sales tax, and the tip? 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. 





y squared over 3 times 8 over y 
20070930 

From John: y squared over 3 times 8 over y Answered by Stephen La Rocque. 





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. 





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. 





Guessing multiple choice answers 
20070724 

From carla: You are taking a multiple choice quiz that consist in 3 questions, each question has
3 possible answers only one is correct. To complete the quiz you randomly guess the answer
to each question . Find the probability of guessing exactly 2 answer correctly. b) at least to answer correctly . c)less than two answer correctly Answered by Stephen La Rocque. 





Fractions of fractions 
20070718 

From Bridget: Sam and Mary each owned onehalf stock in a printing company. Sam sold 2/3 of his stock to Mary. What fractional part of the printing business does Mary now own? Answered by Penny Nom. 





The lcm of polynomials 
20070531 

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





Triple angle tangent formula 
20070315 

From sam: Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks Answered by Penny Nom. 





Multiplying and dividing by zero 
20070205 

From colin: i would like to if u multiply 1,000,000 by 0 does it equal o or 1.
if you have a number eg 15689 and you divide by o what would the answer be is it 1 Answered by Penny Nom. 





Which lets you put equal groups together? 
20070120 

From Kathy: Which lets you put equal groups together? division, multiplication, subtraction, estimation Answered by Stephen La Rocque. 





Comparing two fractions 
20070118 

From Kayla: Why does eight over twelve compared to one half work when you use cross multiplication. Answered by Penny Nom. 





Products with symbols 
20070109 

From Jennifer: Find the product of each (8x)(4) (3x)(5y)(7z) (8x^3y)5X^2) (6a)(3a)(b^2) Answered by Penny Nom. 





A 15% tip 
20061206 

From Danielle: When she eats at a restaurant,Viviana like to leave a 15% tip,multiplying the price of the meal by 0.15. Franklin usually leaves a 20% tip,multiplying the price by 0.20.They both round up to the nearest $0.05. How much tip would Viviana leave for a $24.85 meal? Answered by 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. 





Induction 
20061031 

From Ross: Suppose that A and B are square matrices with the property AB= BA. Show that AB^n = B^n A for every positive integer n. Answered by Stephen La Rocque and Penny Nom. 





Lattice multiplication 
20061016 

From Patti: I am a parent of a 5 th grader, and am a bit loss in the "new" math. I know how to multiply using the "old fashion" method. But, could you please explain lattice multiplication. Answered by Diane Hanson. 





Least common multiple 
20060925 

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





What was the total cost of the dinners he served 
20060910 

From Connie: Walter is a waiter at the town diner. He earns a daily wage of $100 plus tips that equal to .15 of the total cost of the dinners he serves. What was the total cost of the dinners he served if he earned $170 on Tuesday? Answered by Stephen La Rocque. 





Mayan multiplication 
20060416 

From Marca: I'm researching the Mayans, and my advisor, Dr. McDonald, stated that you may know whether the Mayans knew how to multiply. I'm finding conflicting information on the internet, and anything you could provide would be greatly appreciated. Answered by Chris Fisher. 





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. 





Mastering the multiplication tables 
20060404 

From Ellie: I need a detailed study plan fro helping my son master his multiplication tables.
Grade: 3 elementary Answered by Paul Betts. 





cos(3X) 
20060329 

From Joshua: I'm having trouble proving that cos(3X)=cos^{3}X (cosX)(sin^{2} X) Answered by Penny Nom. 





A bill with a 15% tip and a 10% discount 
20060320 

From Tracy: A $4500 bill is presented, without tax. 10% discount coupon. Add 15% tip with 3 people spitting for the sever. 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. 





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. 





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. 





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 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. 





Multiplying two algebraic fractions 
20041031 

From A parent: Multiply:
x+2 x²4
 x 
x2 x²+x2 Answered by Harley Weston. 





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. 





sin(3A) 
20041020 

From A student: Express sin3A in terms of sinA and cosA. 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. 





Sin(3x), cos(3x) and tan(3x) 
20040128 

From Jon: What is the identity for cos3x, sin3x, and tan3x? In class, we learned double angel identities and were asked to find out the identity to these three trig functions. If you can help, please do. Also, i know that the cos^{4}x sin^{4}x is the same as cos2x. Is cos^{8}xsin^{8}x = cos2x also true? Thank you.s Answered by Chris Fisher. 





Multiplier and multiplicand 
20031217 

From Karen: The K5 curriculum states that at a grade 5 level students should "understand and use the terms multiplier, multiplicand" The curriculum defines 'multiplicand' as " a number being multiplied by another number. A factor." There is no definition given for 'multiplier'
Question: Define these words are they just other words for 'factors'. If so, how important is it that students use these terms? It would seem like 'factors' would be the better choice of words to use. If multiplcand refers to eg. the first factor in the equation and the 'multiplier' the seond term, (if in fact it does) is this not confusing for students when we teach them that multiplication is commutative? 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. 





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. 





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. 





The base 10 multipliction table 
20020707 

From A student: These are two questions from Math for Elementary Teachers and they have me stumped. You have two coins that are worth 30 cents. One of the coins is not a nickel. What are the two coins? The product of the diagonals of any 2x2 matrix in the base 10 multiplication table are equal. Why? Answered by Penny Nom. 





Multiplying decimals 
20020310 

From Kaitlin: I just recently had a test on multiplying decimals and I did not do really well on it. Only 5 kids out of 19 got a passing grade. My teacher says that she will give us a different test and we can take it again, but I'm still not sure of it. My teacher has taught me a lot and she had done a wonderful job of it but I'm just confused with where to put the decimals and stuff like that. I have a math practice workbook that I do for fun and they have nothing on decimals in it. I have checked on websites to try to find worksheets but I really couldn't find a good one. Can you please help me either give me some tips or clues or send me a worksheet. Answered by Penny Nom. 





sin 2x = cos 3x 
20020225 

From Allan: solve: sin 2x = cos 3x Primary question: how do you handle the cos 3x? Answered by Paul Betts and Chris Fisher. 





For 7 the multiplicand is 143 
20011212 

From Cory: For 7 the multiplicand is 143 I am asked to solve this, if you could help me it would be greatly appreciated! Answered by Penny Nom. 





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. 





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. 





Multiplying vectors 
20011022 

From Murray: Could you please explain why a vector times a vector is a scalar and how to derive the formula vector a * vector b = ab cos(a,b) Answered by Harley Weston. 





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. 





Multiplying binomials 
20010908 

From A student: (x+1)(x+2)=? (2x1)(x4)=0 please tell me this question!! Answered by Leeanne Boehm. 





Conformable matrices 
20010805 

From Wayne: Can someone explain the concept of conformable matrices in a way that is easy to understand ? One definition says to multiply matrices rows and columns must conform, ie, 5 x 3 matrix times a 3 x 5 matrix. In the next example, however a 8 x 1 matrix and a 8 x 3 matrix are said to be conformable! Answered by Steve Kirkland. 





Danging couples 
20010606 

From Danielle: How many boygirl dancing couples could be formed if 85 boys and 102 girls attend a school dance? Answered by Penny Nom. 





Multiplication 
20010530 

From Lindsay: Who came up with multipling? its so easy Answered by Claude Tardif and Penny Nom. 





Your DJ Business 
20010530 

From Linda: Your DJ Business has 6 rap, 10 rock, 6 alternative, 8 oldies, and 5 country CD singles. How many different 10song sets can the DJ play, if she plays 2 singles from each category? and How many different 10song sets if she plays exactly 3 rap singles and 4 rock singles in each set? Answered by Leeanne Boehm. 





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. 





Triakis 
20010217 

From Anne Grant: I am a grade 8 teacher and have come across the term "Triakis" used with Tetrahedron, octahedron, and hexahedron. What does this term refer to, and what's the difference between a triakis polyhedron and one that is not? I'd also like to know what is meant by the term antiprism, as opposed to prism. Answered by Penny Nom. 





Multiplying one and two digit numbers 
20010211 

From Marty: When multiplying do you put the number you are multiplying by on the top or the bottom. Example if you are multiplying by 6's would you write the problem 6 x 2 or 2 x 6 Maybe it just doesn't matter. But when you get to double digits, the double digit always goes on the top? Answered by Penny Nom. 





What is wrong with these probelms? 
20010209 

From Cindy: Hi, I am a planning on becomming a teacher and i am asked to find out what is wrong with these probelms and how i would go about showing a student what is wrong with them!! Error in patterns: 13/35=1/5; 27/73=2/3; 16/64=1/4 4/5+2/3=6/8; 2/5+3/4=5/9; 7/8+1/3=8/11 2/3*3=6/9; 1/4*6=6/24; 4/5*2=8/10 Answered by Leeanne Boehm and Penny Nom. 





(2b+3)(b1) 
20010206 

From Melissa: Alright, lets say you are multiplying (2b+3)(b1) and you are using "FOIL" first you would get : 2b^{2}+2b3b3 then you add liketerms. when multiplying,if the bases are the same, add the exponents...does the same thing apply when you are adding the results of the multiplication even though it's addition? would the answer be 2b^{3}3b3 or would it be 2b^{2}b3? 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. 





Fractions of fractions 
20010130 

From Katie: When you multiply two positive fractions less than 1, how does the answer compare to the size of the fraction? Why? Answered by Penny Nom. 





7x6 by doubling 
20010123 

From A student: Can you think of a way to use doubling to multiply 6x7? Answered by Allen Herman. 





Is n^2  2 a multiple of n  4? 
20010110 

From John: Find all positive integers n so that n^{2}  2 is a multiple of n  4. Answered by Sukanta Pati. 





Multiplication of fractions 
20010108 

From Angela: Questions:
1. represent multiplication of fractions via an area model 2. describe why, not just how, to round decimals Answered by Penny Nom. 





Order of operations 
20001126 

From Margaret Pratt: My daughter has a math question and I am afraid I am of no help. Can you help? 2x5/2+15= She arrives at 8 as the answer and has been told this is incorrect. Any help you can give would be appreciated. Answered by Penny Nom. 





A complex calculation 
20001124 

From Angie: Multiply (32i)^{2}=3^{2}2(3)(2i)+(2i)^{2} Answered by Penny Nom. 





Dividing fractions 
20001018 

From Paula: Why do you have to change the division sign to a multiplication sign and invert the fraction that follows the division sign in order to get the answer to a division problem when you're working with fractions? Answered by Penny Nom. 





Multiplying decimals 
20001016 

From Lily: I need help with mutiplying decimals (example) 2.28*0.48( * = times). Answered by Harley Weston. 





Permutations and Multiplication Principle 
20000922 

From Candice: A forester selects 4 pink and 4 white dogwoods. The trees are to be planted in row. If a tree is distinguished by color only, in how many ways can the eight dogwoods be planted? How many of these arrangements have at least two trees of the same color side by side? Answered by Denis Hanson and Claude Tardif. 





Why does division start from the left? 
20000524 

From Salil Dave: Addition, subtraction and multiplications start with right most digit and proceed left, but division starts from leftmost digits and goes right ... why? Answered by Harley Weston. 





Multiplying fractions 
20000514 

From A student: 75/2 x 1/100 = 3/8 Please show how to came up with the answer? Answered by Penny Nom. 





Starmultiplication 
20000407 

From Greg Potts: I have this question to answer and I don't know where to start. 1*9=0, 9*8=72 and 2*8=9, then 9*9 =? Answered by Penny Nom. 





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. 





Triple angle formula 
20000223 

From Sara: Can one derive a triple angle formula for sine and cosine? If so, how? Answered by Chris Fisher. 





Cross multiplication 
20000216 

From J E Swinton: Why does cross multiplication work? How come canceling work? 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. 





order 4+ determinants 
19991206 

From Joe Kron: Why is it never shown how to calculate the value of 4x4 (or larger size) deteminants by the diagonal multiply methods that are generally shown for 2x2 and 3x3 determinants? The method I'm talking about is called Cramer's Rule??? Is this method not extensible to order 4+ and if not why not? Anyway the method always shown for order 4+ is called "reduction by minors" which is not the answer to this question. Answered by Walter Whiteley. 





towers of cubes 
19991005 

From Sanker: I need help to solve this Rules for bulding towers of cubes rule 1  The number of cubes on the bottom layer is always one less than the number of squares on the grid  rule 2  Each new layer is made with one cube less than the layer underneath it.   Investigate how many different arrangements there are of 4 cubes on top of 5 cubes on a two by three grid
 investigate the number of different arrangements of six cubes on top of seven cubes on a two by four grid
 investigate the relation between the number of arrangements of cubes and the size of the grid
 when there are two layers of cubes
 when there are more than two layers of cubes
Answered by Walter Whiteley. 





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. 





A Multiple Choice Test 
19990831 

From Cintra Ramnarine: I have ten questions. There are two multiple choice answers to each question. What are the chances of answering all questions correctly. Answered by Harley Weston. 





Invert and multiply 
19990828 

From Debbie Walter: I have another question please, WHY do we invert and multiply when dividing fractions? I know that's what we do but WHY? What is the reasoning behind it? Answered by Penny Nom. 





Sin 4A 
19990622 

From Ryan Cochrane: If sinA = 4/5, and A is a first quadrant angle, find sin4A Answered by Harley Weston. 





Roman Numerals 
19990429 

From Michelle Jenkinson: Someone proposed this question to me and I do not know the answer, so I was wondering if you could help. How, using Roman Numeral, did people add, subtract, multiply, and divide with no zero or negative numbers? 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. 





Duplation method of multiplication 
19981126 

From Sara Whitford: I am wondering why 16 and multiples of 16 do not work in the ancient duplation method of multiplication used by the Egyptians. I discovered the method in the Journeys math text gr 7 level. Just curious. Am I doing something wrong?? Answered by Jack LeSage and Harley Weston. 





A Number Trick 
19981026 

From Brenda Meagher: I'm a 37 year old mother and i have returned to school for personal reasons. I was faced with this question. Choose any number less than 10, multiply it by 8547, then take your answer and multiply it by 13. I chose the number 8. 8547 x 8  68376 and 68376 x 13  205128 68376  888888 Any number chosen from 1 to 9 will result in the same form of answer.If the number two is used you will end up with 222,222.etc So my question is, is there another number that will results in the answers. Answered by Harley Weston. 





Multiplying by Nine  Chismbop Style 
19980427 

From Noria Jones: About a year ago a grade 5 teacher at my son's school taught the children how to multiply the 9 times table on their fingers quickly. It was part of a kind of finger math kind of thing... Answered by Patrick Maidorn. 





Greatest Common Factor. 
19980109 

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





Roman Numerals 
19971031 

From Mark Curts: I am looking for some resources for teaching Roman Numerals. I would like to expand upon the basic concepts, by locating some addition, subtraction, multiplication or division problems written with Roman Numerals.  Mark Curts 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. 





Priority of operations 
19961104 

From Wallace: What is the answer to this problem? Let x=2 and y=3. Evaluate 12x / 2y (if the old division sign is used). Answered by Chris Fisher. 





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. 





(3)x(2) 
19951025 

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





Une multiplication 
20090403 

From josee: 24/6x5+4010=
le x est une multiplication et il n'y as pas de parenthèses.
Merci
Josée Answered by Antoine Letarte and Claude Tardif. 

