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Evaluate:
(i) $4 \times 6 \times 8$
(ii) $\left( { - 4} \right) \times 6 \times 8$
(iii) $\left( { - 4} \right) \times 6 \times \left( { - 8} \right)$

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Last updated date: 25th Jun 2024
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Answer
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Hint: Here, we will evaluate the given integers. We will use the properties of integers and then the given arithmetic operation of multiplication to evaluate for the given integers. Multiplication is the process of repeated addition.

Complete Step by Step Solution:
We are given the following to evaluate the given integers.
(i) $4 \times 6 \times 8$
We know that the product of two positive integers is a positive integer.
Now, by multiplying the first two integers, we get
$ \Rightarrow 4 \times 6 \times 8 = 24 \times 8$
We know that the product of two positive integers is a positive integer.
Now, by multiplying the integers, we get
$ \Rightarrow 24 \times 8 = 192$
Thus, the product of 4, 6, 8 is 192.

(ii) $\left( { - 4} \right) \times 6 \times 8$
We know that the product of a negative integer and a positive integer is a negative integer.
 Now, by multiplying the first two integers, we get
$ \Rightarrow \left( { - 4} \right) \times 6 \times 8 = \left( { - 24} \right) \times 8$
We know that the product of a negative integer and a positive integer is a negative integer.
Now, by multiplying the integers, we get
$ \Rightarrow \left( { - 24} \right) \times 8 = \left( { - 192} \right)$
Thus, the product of $ - 4$ , 6, 8 is $ - 192$.

(iii) $\left( { - 4} \right) \times 6 \times \left( { - 8} \right)$
We know that the product of a negative integer and a positive integer is a negative integer.
 Now, by multiplying the first two integers, we get
$ \Rightarrow \left( { - 4} \right) \times 6 \times \left( { - 8} \right) = \left( { - 24} \right) \times \left( { - 8} \right)$
We know that the product of a negative integer and a negative integer is a positive integer. Now, by multiplying the integers, we get
$ \Rightarrow \left( { - 24} \right) \times \left( { - 8} \right) = 192$
Thus, the product of $ - 4$ , 6, $ - 8$ is 192.

Therefore, the product of 4, 6, 8 is 192, the product of $ - 4$ , 6, 8 is $ - 192$ and the product of $ - 4$ , 6, $ - 8$ is 192.

Note:
We know that the arithmetic operation of Multiplication is the repeated addition of equal groups. The properties of integers is that the product of two positive integers is always a positive integer, the product of two negative integers is always a positive integer and the product of a positive integer and a negative integer is always a negative integer. Thus the properties of integers is always used in finding the product of two integers with the like signs or unlike signs.