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Four multiples of 10 2017-09-23
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 2017-07-22
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 2016-12-06
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 2016-11-23
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 2-D figure(actually,quadrilateral) having length consisting of 2 boxes of 1-by-1 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 2-3rd,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?

Answered by Penny Nom.
An airplane schedule 2016-10-14
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 2016-06-09
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.


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 2016-05-21
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 2016-04-03
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 2015-03-30
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 2014-10-14
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 2014-08-07
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?


Answered by Penny Nom.
60% as much as $30. 2014-07-18
From Kenneth:
Question from Kenneth:


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 2013-12-03
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 2013-11-27
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.
Six-digit passwords 2013-03-19
From Judy:
Can you please explain why the answer to the following question is 10^6? What is the number of possible six-digit passwords when using the digits 0 through 9, with repetition allowed.
Thank you.

Answered by Penny Nom.
Multiplication in base two 2013-02-01
From Michael:
multiply in the indicated base


Answered by Penny Nom.
The multiplication table for the different bases 2013-02-01
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 2012-10-29
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 2012-09-19
From Bryauna:
Why do you change the signs in inequalities?!
Answered by Penny Nom.
Multiples 2012-05-28
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 2012-05-14
From Jordan:
How do I solve the equation:

Answered by Penny Nom.
Building a tipi 2012-01-29
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 2011-11-14
From anonymous:
I started with Euler's identity and manipulated it
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 2011-08-30
From Lucjan:
how to sketch a diagram that shows 4x2 expression?
Answered by Penny Nom.
3.8 x 2.2 2011-08-18
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) 2011-02-15
From Janet:
Prove sin x = sin (pi - x)
Answered by Penny Nom.
Multiplication and order 2011-01-21
From Janet:
Answered by Robert Dawson.
Convert to multiplication 2010-10-23
From angelina:
how to covert 5+5+5=15 to multiplication
Answered by Penny Nom.
Geocaching 2010-10-15
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 2010-10-08
From Ashishthombre:
step by step LCM of x/200+x/400+x/600+x/800
Answered by Penny Nom.
Constructing a tipi 2010-09-20
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 2010-08-30
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 2010-05-27
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 six-digit 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) 2010-04-28
From alex:
In the equation cos x = sin x-1 for -pi/2 A: solve for x graphically
B: solve algebraically and prove the solution is correct.


Answered by Penny Nom.
1/6 x 5 x 12 = what 2010-02-19
From dana:
1/6 x 5 x 12 = what
Answered by Lorraine Dame.
Two bus routes 2010-02-03
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 2010-01-06
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 2009-09-15
From Kamaldeep:
Find the first 2 common multiples of 36 and 48.
Answered by Penny Nom.
Jogging and swimming 2009-09-11
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 2009-07-09
From Jessica:
What is 12 billion X 6 trillion?
Answered by Janice Cotcher.
Multiplying Large Numbers 2009-07-09
From Jessica:
What is 12 billion X 6 trillion?
Answered by Janice Cotcher.
Investing in multiple accounts 2009-06-26
From Kenneth:

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%.

Answered by Robert Dawson.
Fraction Word Problem 2009-05-13
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 2009-05-11
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 2009-04-23
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 2009-04-13
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  

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

Answered by Robert Dawson, Stephen La Rocque and Claude Tardif.

2sinB=3tanA 2009-04-10
From Xanathax:
ABC is a right-angled triangle. 2sinB=3tanA. Calculate the measure of angle A.
Answered by Penny Nom.
Multiplication of polynomials 2009-04-07
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 2009-03-21
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 2009-02-25
From Susan:
11 base 2 X 22 base 3 + 33 base 4 = _________ base 5
Answered by Robert Dawson.
mutiplying decimals 2009-02-24
From telly:
how to do this sum0.24*0.398
Answered by Robert Dawson and Penny Nom.
Multiplying negative numbers 2009-01-15
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 2008-11-14
From natalie:
what is 8 times 30
Answered by Penny Nom.
Confusion in a multiple choice question 2008-11-14
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: 4525-2221= 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 2008-09-13
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 2008-07-15
From chaleen:
multiply = 3a - 3b by a+b
Answered by Penny Nom.
sin(2x)/sin(3x) 2008-06-19
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? 2008-04-30
From Jonathon:
How do you reduce an equation with multiple variables?

For example, if 3x + y = k(x-3), what would x be equal to?

Answered by Penny Nom.
Matrix multiplication 2008-04-08
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? 2008-04-06
From Scott:
45 x fraction? = 10
Answered by Penny Nom.
2 times 0 times 0 times 4 2008-03-30
From ben:
what is 2 times 0 times 0 times 4?
Answered by Penny Nom.
Multiplying decimal numbers 2008-02-05
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 2008-01-16
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 2008-01-08
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 2007-12-09
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 2007-11-11
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 open-ended cone 2007-10-16
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? 2007-10-14
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 2007-10-12
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 2007-09-30
From John:
y squared over 3 times 8 over y
Answered by Stephen La Rocque.
Least Common Multiples 2007-09-20
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 2007-07-26
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 real-world 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

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

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 2007-07-24
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 2007-07-18
From Bridget:
Sam and Mary each owned one-half 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 2007-05-31
From devin:
x^3-8 , x^3-4, x^2+4x+4
Answered by Penny Nom.
Triple angle tangent formula 2007-03-15
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 2007-02-05
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? 2007-01-20
From Kathy:
Which lets you put equal groups together? division, multiplication, subtraction, estimation
Answered by Stephen La Rocque.
Comparing two fractions 2007-01-18
From Kayla:
Why does eight over twelve compared to one half work when you use cross multiplication.
Answered by Penny Nom.
Products with symbols 2007-01-09
From Jennifer:
Find the product of each

Answered by Penny Nom.
A 15% tip 2006-12-06
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 2006-11-08
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 2006-10-31
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 2006-10-16
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 2006-09-25
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 2006-09-10
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 2006-04-16
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? 2006-04-07
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 2006-04-04
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) 2006-03-29
From Joshua:
I'm having trouble proving that cos(3X)=cos3X -(cosX)(sin2 X)
Answered by Penny Nom.
A bill with a 15% tip and a 10% discount 2006-03-20
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 2006-02-21
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 2006-01-07
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 2005-12-12
From Alex:
what is the LCM of 210 and 54 and the LCM of 42 and 126
Answered by Penny Nom.
Least common multiple 2005-10-22
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 2004-11-05
From Christine:
what is the lcm of 5,3,4,7,2
Answered by Penny Nom.
The lcm of 1 and -1 2004-11-03
From Nayiyan:
I would like to know what is the LCM of (-1) and (+1) is.
Answered by Penny Nom.
Multiplying two algebraic fractions 2004-10-31
From A parent:

x+2 x²-4
----- x -------
x-2 x²+x-2

Answered by Harley Weston.
GCD and LCM 2004-10-31
From Cartalina:
how do you calculate the "positive difference between the GCF and LCM of two numbers"?
Answered by Penny Nom.
sin(3A) 2004-10-20
From A student:
Express sin3A in terms of sinA and cosA.
Answered by Penny Nom.
The Parliament of the land of Achronia 2004-05-29
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) 2004-01-28
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 cos4x- sin4x is the same as cos2x. Is cos8x-sin8x = cos2x also true? Thank you.s
Answered by Chris Fisher.
Multiplier and multiplicand 2003-12-17
From Karen:
The K-5 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 2003-02-11
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 2003-01-21
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


Answered by Penny Nom.
Why is 5 divided by 1/7 greater than 5 divided by 2/3? 2002-11-19
From Elizabeth:
  1. Without performing the division, explain why 5 divided by 1/7 is a number greater than 5 divided by 2/3.
  2. 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 2002-07-07
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 2002-03-10
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 2002-02-25
From Allan:

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 2001-12-12
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 2001-11-06
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 eight-hour 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 2001-10-26
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? 2001-10-26
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 2001-10-22
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 2001-10-08
From A parent:
Answered by Leeanne Boehm.
GCD and LCM 2001-09-24
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


2 to power q, 3 to power r, 7 to power p

Answered by Penny Nom.
Multiplying binomials 2001-09-08
From A student:
please tell me this question!!

Answered by Leeanne Boehm.
Conformable matrices 2001-08-05
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 2001-06-06
From Danielle:
How many boy-girl dancing couples could be formed if 85 boys and 102 girls attend a school dance?
Answered by Penny Nom.
Multiplication 2001-05-30
From Lindsay:
Who came up with multipling? its so easy
Answered by Claude Tardif and Penny Nom.
Your DJ Business 2001-05-30
From Linda:
Your DJ Business has 6 rap, 10 rock, 6 alternative, 8 oldies, and 5 country CD singles. How many different 10-song sets can the DJ play, if she plays 2 singles from each category? and How many different 10-song sets if she plays exactly 3 rap singles and 4 rock singles in each set?
Answered by Leeanne Boehm.
A four digit number 2001-02-17
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 2001-02-17
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 2001-02-11
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? 2001-02-09
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)(-b-1) 2001-02-06
From Melissa:
Alright, lets say you are multiplying (-2b+3)(-b-1) and you are using "FOIL" first you would get : 2b2+2b-3b-3 then you add like-terms. 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 2b3-3b-3 or would it be 2b2-b-3?

Answered by Penny Nom.
Two number theory questions 2001-01-30
From Richie:
i have two questions and they are:
  1. the product of three consecutive prime numbers is 7429. Find the product of the smallest and largest of these three integers.

  2. 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 2001-01-30
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 2001-01-23
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? 2001-01-10
From John:
Find all positive integers n so that n2 - 2 is a multiple of n - 4.
Answered by Sukanta Pati.
Multiplication of fractions 2001-01-08
From Angela:

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 2000-11-26
From Margaret Pratt:
My daughter has a math question and I am afraid I am of no help. Can you help? 2x5/2+1-5= 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 2000-11-24
From Angie:
Multiply (3-2i)2=32-2(3)(2i)+(2i)2
Answered by Penny Nom.
Dividing fractions 2000-10-18
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 2000-10-16
From Lily:
I need help with mutiplying decimals (example) 2.28*0.48( * = times).
Answered by Harley Weston.
Permutations and Multiplication Principle 2000-09-22
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? 2000-05-24
From Salil Dave:
Addition, subtraction and multiplications start with right most digit and proceed left, but division starts from left-most digits and goes right ... why?
Answered by Harley Weston.
Multiplying fractions 2000-05-14
From A student:
75/2 x 1/100 = 3/8

Please show how to came up with the answer?
Answered by Penny Nom.

Star-multiplication 2000-04-07
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 2000-02-27
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 2-3 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 2000-02-23
From Sara:
Can one derive a triple angle formula for sine and cosine? If so, how?
Answered by Chris Fisher.
Cross multiplication 2000-02-16
From J E Swinton:
Why does cross multiplication work?

How come canceling work?

Answered by Penny Nom.
Least Common Multiple 2000-02-16
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 1999-12-22
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 1999-12-06
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 1999-10-05
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.
  1. Investigate how many different arrangements there are of 4 cubes on top of 5 cubes on a two by three grid

  2. investigate the number of different arrangements of six cubes on top of seven cubes on a two by four grid

  3. 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 1999-09-26
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 1999-08-31
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 1999-08-28
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 1999-06-22
From Ryan Cochrane:
If sinA = 4/5, and A is a first quadrant angle, find sin4A
Answered by Harley Weston.
Roman Numerals 1999-04-29
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. 1999-03-06
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

Answered by Denis Hanson.
The Board Problem 1999-02-15
From Avery:
Mr. Avery has 3-foot boards and 4-foot boards. If he puts the 3-foot boards in a line, they have the same length as the 4-foot boards put in a line. Altogether he has between 16 and 25 boards. How many 3-foot boards does he have?
Answered by Jack LeSage and Penny Nom.
Duplation method of multiplication 1998-11-26
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 1998-10-26
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.

x 8


x 13

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 1998-04-27
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. 1998-01-09
From Percy Stribling:
how do you figure out what the greater common factor is?
Answered by Penny Nom.
Roman Numerals 1997-10-31
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 1997-08-28
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 1996-11-04
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? 1996-10-07
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) 1995-10-25
From Azmat:
Why is (-3)x(-2) = 6?
Answered by Herley Weston and Ed Giesbrecht.
Une multiplication 2009-04-03
From josee:

le x est une multiplication et il n'y as pas de parenthèses.

Merci Josée

Answered by Antoine Letarte and Claude Tardif.



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