







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. 





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. 





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. 





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. 





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. 





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. 





1/6 x 5 x 12 = what 
20100219 

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





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. 





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. 





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. 





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. 





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. 





multiply = 3a  3b by a+b 
20080715 

From chaleen: multiply = 3a  3b by a+b 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. 





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. 





y squared over 3 times 8 over y 
20070930 

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





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





Cross multiplication 
20000216 

From J E Swinton: Why does cross multiplication work? How come canceling work? Answered by Penny Nom. 





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. 





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. 





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. 





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. 





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. 

