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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.
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.
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.
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.
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.
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.
1/6 x 5 x 12 = what 2010-02-19
From dana:
1/6 x 5 x 12 = what
Answered by Lorraine Dame.
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.
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.
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.

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.
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.
multiply = 3a - 3b by a+b 2008-07-15
From chaleen:
multiply = 3a - 3b by a+b
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Cross multiplication 2000-02-16
From J E Swinton:
Why does cross multiplication work?

How come canceling work?

Answered by Penny Nom.
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.
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.

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.

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.
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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