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 Fundamentals of mathematics
 Multiplication and division of
 Properties of multiplication
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses properties of multiplication of whole numbers. By the end of the module students should be able to understand and appreciate the commutative and associative properties of multiplication and understand why 1 is the multiplicative identity.
Section overview
 The Commutative Property of Multiplication
 The Associative Property of Multiplication
 The Multiplicative Identity
We will now examine three simple but very important properties of multiplication.
The commutative property of multiplication
Commutative property of multiplication
The product of two whole numbers is the same regardless of the order of the factors.
Sample set a
Multiply the two whole numbers.
$6\cdot 7=\text{42}$
$7\cdot 6=\text{42}$
The numbers 6 and 7 can be multiplied in any order. Regardless of the order they are multiplied, the product is 42.
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Practice set a
Use the commutative property of multiplication to find the products in two ways.
The associative property of multiplication
Associative property of multiplication
If three whole numbers are multiplied, the product will be the same if the first two are multiplied first and then that product is multiplied by the third, or if the second two are multiplied first and that product is multiplied by the first. Note that the order of the factors is maintained.
It is a common mathematical practice to
use parentheses to show which pair of numbers is to be combined first.
Sample set b
Practice set b
Use the associative property of multiplication to find the products in two ways.
The multiplicative identity
The multiplicative identity is 1
The whole number 1 is called the
multiplicative identity , since any whole number multiplied by 1 is not changed.
Sample set c
Practice set c
Multiply the whole numbers.
Exercises
For the following problems, multiply the numbers.
For the following 4 problems, show that the quantities yield the same products by performing the multiplications.
$\text{23}\cdot (\text{11}\cdot \text{106})$ and
$(\text{23}\cdot \text{11})\cdot \text{106}$
$\text{23}\cdot \mathrm{1,}\text{166}=\text{26},\text{818}=\text{253}\cdot \text{106}$
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The fact that
$(\text{a first number}\cdot \text{a second number})\cdot \text{a third number}=\text{a first number}\cdot (\text{a second number}\cdot \text{a third number})$ is an example of the
property of multiplication.
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Exercises for review
Questions & Answers
show that the set of all natural number form semi group under the composition of addition
what is the meaning
Dominic
explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the
fraction, the value of the fraction becomes 2/3. Find the original fraction.
2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2
 = _
x + 9 + 6 3
x + 6 3
 x  (cross multiply)
x + 15 2
3(x + 6) = 2(x + 15)
3x + 18 = 2x + 30 (2x from both)
x + 18 = 30 (18 from both)
x = 12
Test:
12 + 6 18 2
 =  = 
12 + 9 + 6 27 3
Pawel
2.
(x) + (x + 2) = 60
2x + 2 = 60
2x = 58
x = 29
29, 30, & 31
Pawel
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Q2
x+(x+2)+(x+4)=60
3x+6=60
3x+66=606
3x=54
3x/3=54/3
x=18
:. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1
x + 3x + 1 = 113
4x = 112, x = 28
Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
divide by 2 on each side of the equal sign to solve for x
corri
Want to review on complex number
1.What are complex number
2.How to solve complex number problems.
Beyan
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Mark
use the y intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
please help me prove quadratic formula
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you
help me with how to prove the quadratic equation
Seidu
may God blessed u for that.
Please I want u to help me in sets.
Opoku
x2y+3z=3
2xy+z=7
x+3yz=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point For:
(6111,4111,−411)(6111,4111,411)
Equation Form:
x=6111,y=4111,z=−411x=6111,y=4111,z=411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11
y=41/11
z=−4/11
x=61/11
y=41/11
z=4/11
Brenna
Need help solving this problem (2/7)^2
what is the coefficient of 4×
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)1/7 (x1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
In the number 779,844,205 how many ten millions are there?
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scientists to 52,000. How many were there in 1973?
7hours 36 min  4hours 50 min
Source:
OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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