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Sagot :
Alright, let's break down each part of the given problem step-by-step.
### Part 1: Find the Products
(a) [tex]\( 15 \times (-16) \)[/tex]
The product of a positive number and a negative number is negative. So, multiplying:
[tex]\[ 15 \times (-16) = -240 \][/tex]
(b) [tex]\( 21 \times (-32) \)[/tex]
Similarly, the product of a positive number and a negative number is negative. So, multiplying:
[tex]\[ 21 \times (-32) = -672 \][/tex]
(c) [tex]\( (-42) \times 12 \)[/tex]
In this case, the product of a negative number and a positive number is also negative. So, multiplying:
[tex]\[ (-42) \times 12 = -504 \][/tex]
(d) [tex]\( -55 \times 15 \)[/tex]
Again, the product of a negative number and a positive number is negative. So, multiplying:
[tex]\[ -55 \times 15 = -825 \][/tex]
### Part 2: Check if the expressions are equal
(a) [tex]\( 25 \times (-21) = (-25) \times 21 \)[/tex]
First calculate both sides:
- [tex]\( 25 \times (-21) = -525 \)[/tex]
- [tex]\( (-25) \times 21 = -525 \)[/tex]
So, [tex]\( 25 \times (-21) = (-25) \times 21 \)[/tex] is indeed True.
(b) [tex]\( (-23) \times 20 = 23 \times (-20) \)[/tex]
First calculate both sides:
- [tex]\( (-23) \times 20 = -460 \)[/tex]
- [tex]\( 23 \times (-20) = -460 \)[/tex]
Thus, [tex]\( (-23) \times 20 = 23 \times (-20) \)[/tex] is again True.
### Five More Examples
1. [tex]\( (-10) \times 3 = 10 \times (-3) \)[/tex]
First calculate both sides:
- [tex]\( (-10) \times 3 = -30 \)[/tex]
- [tex]\( 10 \times (-3) = -30 \)[/tex]
Thus, [tex]\( (-10) \times 3 = 10 \times (-3) \)[/tex] is True.
2. [tex]\( 7 \times (-2) = (-7) \times 2 \)[/tex]
First calculate both sides:
- [tex]\( 7 \times (-2) = -14 \)[/tex]
- [tex]\( (-7) \times 2 = -14 \)[/tex]
So, [tex]\( 7 \times (-2) = (-7) \times 2 \)[/tex] is True.
3. [tex]\( (-5) \times 9 = 5 \times (-9) \)[/tex]
First calculate both sides:
- [tex]\( (-5) \times 9 = -45 \)[/tex]
- [tex]\( 5 \times (-9) = -45 \)[/tex]
Thus, [tex]\( (-5) \times 9 = 5 \times (-9) \)[/tex] is True.
4. [tex]\( 14 \times (-8) = (-14) \times 8 \)[/tex]
First calculate both sides:
- [tex]\( 14 \times (-8) = -112 \)[/tex]
- [tex]\( (-14) \times 8 = -112 \)[/tex]
Therefore, [tex]\( 14 \times (-8) = (-14) \times 8 \)[/tex] is True.
5. [tex]\( (-3) \times 11 = 3 \times (-11) \)[/tex]
First calculate both sides:
- [tex]\( (-3) \times 11 = -33 \)[/tex]
- [tex]\( 3 \times (-11) = -33 \)[/tex]
So, [tex]\( (-3) \times 11 = 3 \times (-11) \)[/tex] is True.
To summarize, all given relations and additional examples hold true as their respective products are equal when considering the sign changes.
### Part 1: Find the Products
(a) [tex]\( 15 \times (-16) \)[/tex]
The product of a positive number and a negative number is negative. So, multiplying:
[tex]\[ 15 \times (-16) = -240 \][/tex]
(b) [tex]\( 21 \times (-32) \)[/tex]
Similarly, the product of a positive number and a negative number is negative. So, multiplying:
[tex]\[ 21 \times (-32) = -672 \][/tex]
(c) [tex]\( (-42) \times 12 \)[/tex]
In this case, the product of a negative number and a positive number is also negative. So, multiplying:
[tex]\[ (-42) \times 12 = -504 \][/tex]
(d) [tex]\( -55 \times 15 \)[/tex]
Again, the product of a negative number and a positive number is negative. So, multiplying:
[tex]\[ -55 \times 15 = -825 \][/tex]
### Part 2: Check if the expressions are equal
(a) [tex]\( 25 \times (-21) = (-25) \times 21 \)[/tex]
First calculate both sides:
- [tex]\( 25 \times (-21) = -525 \)[/tex]
- [tex]\( (-25) \times 21 = -525 \)[/tex]
So, [tex]\( 25 \times (-21) = (-25) \times 21 \)[/tex] is indeed True.
(b) [tex]\( (-23) \times 20 = 23 \times (-20) \)[/tex]
First calculate both sides:
- [tex]\( (-23) \times 20 = -460 \)[/tex]
- [tex]\( 23 \times (-20) = -460 \)[/tex]
Thus, [tex]\( (-23) \times 20 = 23 \times (-20) \)[/tex] is again True.
### Five More Examples
1. [tex]\( (-10) \times 3 = 10 \times (-3) \)[/tex]
First calculate both sides:
- [tex]\( (-10) \times 3 = -30 \)[/tex]
- [tex]\( 10 \times (-3) = -30 \)[/tex]
Thus, [tex]\( (-10) \times 3 = 10 \times (-3) \)[/tex] is True.
2. [tex]\( 7 \times (-2) = (-7) \times 2 \)[/tex]
First calculate both sides:
- [tex]\( 7 \times (-2) = -14 \)[/tex]
- [tex]\( (-7) \times 2 = -14 \)[/tex]
So, [tex]\( 7 \times (-2) = (-7) \times 2 \)[/tex] is True.
3. [tex]\( (-5) \times 9 = 5 \times (-9) \)[/tex]
First calculate both sides:
- [tex]\( (-5) \times 9 = -45 \)[/tex]
- [tex]\( 5 \times (-9) = -45 \)[/tex]
Thus, [tex]\( (-5) \times 9 = 5 \times (-9) \)[/tex] is True.
4. [tex]\( 14 \times (-8) = (-14) \times 8 \)[/tex]
First calculate both sides:
- [tex]\( 14 \times (-8) = -112 \)[/tex]
- [tex]\( (-14) \times 8 = -112 \)[/tex]
Therefore, [tex]\( 14 \times (-8) = (-14) \times 8 \)[/tex] is True.
5. [tex]\( (-3) \times 11 = 3 \times (-11) \)[/tex]
First calculate both sides:
- [tex]\( (-3) \times 11 = -33 \)[/tex]
- [tex]\( 3 \times (-11) = -33 \)[/tex]
So, [tex]\( (-3) \times 11 = 3 \times (-11) \)[/tex] is True.
To summarize, all given relations and additional examples hold true as their respective products are equal when considering the sign changes.
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