Certainly! Let's go through each of the operations step by step.
1. Evaluate each of the following:
(i) [tex]\(5 \times (-2)\)[/tex]
To multiply 5 and -2:
[tex]\[
5 \times (-2) = -10
\][/tex]
The result is [tex]\(-10\)[/tex].
(ii) [tex]\((-3) \times (-125)\)[/tex]
To multiply -3 and -125:
[tex]\[
(-3) \times (-125) = 375
\][/tex]
When you multiply two negative numbers, the result is positive. So, the result is [tex]\(375\)[/tex].
(iii) [tex]\(333 \times (-1)\)[/tex]
To multiply 333 and -1:
[tex]\[
333 \times (-1) = -333
\][/tex]
The result is [tex]\(-333\)[/tex].
(iv) [tex]\((-40) \div (-5)\)[/tex]
To divide -40 by -5:
[tex]\[
(-40) \div (-5) = 8.0
\][/tex]
When you divide two negative numbers, the result is positive. So, the result is [tex]\(8.0\)[/tex].
(v) [tex]\(60 \div (-12)\)[/tex]
To divide 60 by -12:
[tex]\[
60 \div (-12) = -5.0
\][/tex]
The result is [tex]\(-5.0\)[/tex].
(vi) [tex]\(10 \times (-5) \times (-8)\)[/tex]
To multiply 10, -5, and -8 step by step:
[tex]\[
10 \times (-5) = -50
\][/tex]
Then multiply by -8:
[tex]\[
-50 \times (-8) = 400
\][/tex]
So, the result is [tex]\(400\)[/tex].
(vii) [tex]\((-2) \times (-4) \times (-6) \times (-8)\)[/tex]
To multiply -2, -4, -6, and -8 step by step:
[tex]\[
(-2) \times (-4) = 8
\][/tex]
Then multiply by -6:
[tex]\[
8 \times (-6) = -48
\][/tex]
Finally, multiply by -8:
[tex]\[
-48 \times (-8) = 384
\][/tex]
So, the result is [tex]\(384\)[/tex].
(viii) [tex]\((-21) \times 0 \times 42\)[/tex]
To multiply -21, 0, and 42:
[tex]\[
(-21) \times 0 \times 42 = 0
\][/tex]
Any number multiplied by 0 is 0. So, the result is [tex]\(0\)[/tex].
(ix) [tex]\(0 \div (-15)\)[/tex]
To divide 0 by -15:
[tex]\[
0 \div (-15) = -0.0
\][/tex]
Any number (including zero) divided by a non-zero number results in zero. The results may reflect a negative sign due to division direction, but mathematically it is [tex]\(0\)[/tex].
So, the comprehensive results are:
[tex]\[
[-10, 375, -333, 8.0, -5.0, 400, 384, 0, -0.0]
\][/tex]
