Answer :
Sure, let's go through each multiplication step-by-step to determine the correct answers:
1. [tex]\(3 \times (-1) = -3\)[/tex]
- Multiplying a positive number by a negative number results in a negative number.
2. [tex]\((-12) \times (-11) \times 10 = 1320\)[/tex]
- Multiplying two negative numbers gives a positive number: [tex]\((-12) \times (-11) = 132\)[/tex].
- Then, multiplying the positive result by a positive number retains the positivity: [tex]\(132 \times 10 = 1320\)[/tex].
3. [tex]\((-1) \times 225 = -225\)[/tex]
- Multiplying a negative number by a positive number results in a negative number.
4. [tex]\((-1) \times (-2) \times (-3) = -6\)[/tex]
- Multiplying two negative numbers gives a positive number: [tex]\((-1) \times (-2) = 2\)[/tex].
- Then, multiplying a positive number by a negative number results in a negative number: [tex]\(2 \times (-3) = -6\)[/tex].
5. [tex]\((-15) \times 0 = 0\)[/tex]
- Multiplying any number by zero results in zero.
6. [tex]\((-21) \times (-30) = 630\)[/tex]
- Multiplying two negative numbers gives a positive number.
7. [tex]\((-18) \times (-5) \times (-4) = -360\)[/tex]
- Multiplying two negative numbers gives a positive number: [tex]\((-18) \times (-5) = 90\)[/tex].
- Then, multiplying a positive number by a negative number results in a negative number: [tex]\(90 \times (-4) = -360\)[/tex].
8. [tex]\((-3) \times (-6) \times (-2) \times (-1) = 36\)[/tex]
- Multiplying two negative numbers gives a positive number: [tex]\((-3) \times (-6) = 18\)[/tex].
- Multiplying the positive result by another negative number results in a negative number: [tex]\(18 \times (-2) = -36\)[/tex].
- Finally, multiplying a negative number by a negative number gives a positive number: [tex]\(-36 \times (-1) = 36\)[/tex].
9. [tex]\((-316) \times (-1) = 316\)[/tex]
- Multiplying two negative numbers gives a positive number.
Thus, the results are:
[tex]\[ \begin{array}{l} 3 \times (-1) = -3 \\ (-12) \times (-11) \times 10 = 1320 \\ (-1) \times 225 = -225 \\ (-1) \times (-2) \times (-3) = -6 \\ (-15) \times 0 = 0 \\ (-21) \times (-30) = 630 \\ (-18) \times (-5) \times (-4) = -360 \\ (-3) \times (-6) \times (-2) \times (-1) = 36 \\ (-316) \times (-1) = 316 \\ \end{array} \][/tex]
1. [tex]\(3 \times (-1) = -3\)[/tex]
- Multiplying a positive number by a negative number results in a negative number.
2. [tex]\((-12) \times (-11) \times 10 = 1320\)[/tex]
- Multiplying two negative numbers gives a positive number: [tex]\((-12) \times (-11) = 132\)[/tex].
- Then, multiplying the positive result by a positive number retains the positivity: [tex]\(132 \times 10 = 1320\)[/tex].
3. [tex]\((-1) \times 225 = -225\)[/tex]
- Multiplying a negative number by a positive number results in a negative number.
4. [tex]\((-1) \times (-2) \times (-3) = -6\)[/tex]
- Multiplying two negative numbers gives a positive number: [tex]\((-1) \times (-2) = 2\)[/tex].
- Then, multiplying a positive number by a negative number results in a negative number: [tex]\(2 \times (-3) = -6\)[/tex].
5. [tex]\((-15) \times 0 = 0\)[/tex]
- Multiplying any number by zero results in zero.
6. [tex]\((-21) \times (-30) = 630\)[/tex]
- Multiplying two negative numbers gives a positive number.
7. [tex]\((-18) \times (-5) \times (-4) = -360\)[/tex]
- Multiplying two negative numbers gives a positive number: [tex]\((-18) \times (-5) = 90\)[/tex].
- Then, multiplying a positive number by a negative number results in a negative number: [tex]\(90 \times (-4) = -360\)[/tex].
8. [tex]\((-3) \times (-6) \times (-2) \times (-1) = 36\)[/tex]
- Multiplying two negative numbers gives a positive number: [tex]\((-3) \times (-6) = 18\)[/tex].
- Multiplying the positive result by another negative number results in a negative number: [tex]\(18 \times (-2) = -36\)[/tex].
- Finally, multiplying a negative number by a negative number gives a positive number: [tex]\(-36 \times (-1) = 36\)[/tex].
9. [tex]\((-316) \times (-1) = 316\)[/tex]
- Multiplying two negative numbers gives a positive number.
Thus, the results are:
[tex]\[ \begin{array}{l} 3 \times (-1) = -3 \\ (-12) \times (-11) \times 10 = 1320 \\ (-1) \times 225 = -225 \\ (-1) \times (-2) \times (-3) = -6 \\ (-15) \times 0 = 0 \\ (-21) \times (-30) = 630 \\ (-18) \times (-5) \times (-4) = -360 \\ (-3) \times (-6) \times (-2) \times (-1) = 36 \\ (-316) \times (-1) = 316 \\ \end{array} \][/tex]
