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We will now examine three simple but very important properties of multiplication.
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.
Use the commutative property of multiplication to find the products in two ways.
$\mathrm{15}\cdot 6=\mathrm{90}$ and $6\cdot \mathrm{15}=\mathrm{90}$
$\mathrm{432}\cdot \mathrm{428}=\mathrm{184,896}$ and $\mathrm{428}\cdot \mathrm{432}=\mathrm{184,896}$
It is a common mathematical practice to use parentheses to show which pair of numbers is to be combined first.
Multiply the whole numbers.
$(8\cdot 3)\cdot \text{14}=\text{24}\cdot \text{14}=\text{336}$
$8\cdot (3\cdot \text{14})=8\cdot \text{42}=\text{336}$
Use the associative property of multiplication to find the products in two ways.
Multiply the whole numbers.
$\text{12}\cdot 1=\text{12}$
$1\cdot \text{12}=\text{12}$
Multiply the whole numbers.
For the following problems, multiply the numbers.
For the following 4 problems, show that the quantities yield the same products by performing the multiplications.
$(4\cdot 8)\cdot 2$ and $4\cdot (8\cdot 2)$
$\text{32}\cdot 2=\text{64}=4\cdot \text{16}$
$(\text{100}\cdot \text{62})\cdot 4$ and $\text{100}\cdot (\text{62}\cdot 4)$
$\text{23}\cdot (\text{11}\cdot \text{106})$ and $(\text{23}\cdot \text{11})\cdot \text{106}$
$\text{23}\cdot \mathrm{1,}\text{166}=\text{26},\text{818}=\text{253}\cdot \text{106}$
$1\cdot (5\cdot 2)$ and $(1\cdot 5)\cdot 2$
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
associative
The fact that
$\text{1}\cdot \text{any number}=\text{that particular number}$ is an example of the
Use the numbers 7 and 9 to illustrate the commutative property of multiplication.
$\text{7}\cdot \text{9}=\text{63}=\text{9}\cdot \text{7}$
Use the numbers 6, 4, and 7 to illustrate the associative property of multiplication.
( [link] ) In the number 84,526,098,441, how many millions are there?
6
( [link] ) Replace the letter m with the whole number that makes the addition true. $\begin{array}{c}\hfill \text{85}\\ \hfill \underline{+m}\\ \hfill \text{97}\end{array}$
( [link] ) Use the numbers 4 and 15 to illustrate the commutative property of addition.
$\text{4}+\text{15}=\text{19}$
$\text{15}+\text{4}=\text{19}$
( [link] ) Find the product. $\mathrm{8,}\text{000},\text{000}\times \mathrm{1,}\text{000}$ .
( [link] ) Specify which of the digits 2, 3, 4, 5, 6, 8,10 are divisors of the number 2,244.
2, 3, 4, 6
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