Answer :
Alright, let's tackle each expression step-by-step using appropriate mathematical properties.
1. (ii) [tex]\( 21 \times 38 \times (-25) \)[/tex]:
The properties involved here are the commutative and associative properties of multiplication, indicating that the order of multiplying numbers doesn't change the result. This expression simplifies directly to:
[tex]\[ 21 \times 38 \times (-25) = -19950 \][/tex]
2. (i) [tex]\( 46 \times (-38) + (-38) \times (-36) \)[/tex]:
Here, we can factor out [tex]\((-38)\)[/tex] since it is common in both terms:
[tex]\[ 46 \times (-38) + (-38) \times (-36) = (-38) \times (46 - (-36)) = (-38) \times 82 = -380 \][/tex]
3. (iv) [tex]\( 25 \times (-35) \times (-4) \times 0 \)[/tex]:
Any number multiplied by zero equals zero, so this expression simplifies quickly:
[tex]\[ 25 \times (-35) \times (-4) \times 0 = 0 \][/tex]
4. (iii) [tex]\( 25 \times (-6) \times (-4) \)[/tex]:
Using the associative property:
[tex]\[ 25 \times (-6) \times (-4) = 25 \times 24 = 600 \][/tex]
5. (xivi) [tex]\( 625 \times (-55) + (-625) \times 65 \)[/tex]:
Here, we can factor out [tex]\( 625 \)[/tex] (with appropriate signs):
[tex]\[ 625 \times (-55) + (-625) \times 65 = 625 \times (-55 - 65) = 625 \times (-120) = -75000 \][/tex]
6. (v) [tex]\( -36 \times 102 \)[/tex]:
This is a straightforward multiplication:
[tex]\[ -36 \times 102 = -3672 \][/tex]
7. (viii) [tex]\( (-57) \times (-19) + 57 \)[/tex]:
First, handle the multiplication, and then the addition:
[tex]\[ (-57) \times (-19) + 57 = 1083 + 57 = 1140 \][/tex]
8. (vii) [tex]\( 17 \times [100 - 2] \)[/tex]:
Simplify the expression inside the brackets first:
[tex]\[ 17 \times (100 - 2) = 17 \times 98 = 1666 \][/tex]
Thus, the final results for each of the expressions are:
[tex]\[ \begin{align*} (ii) & : -19950 \\ (i) & : -380 \\ (iv) & : 0 \\ (iii) & : 600 \\ (xivi) & : -75000 \\ (v) & : -3672 \\ (viii) & : 1140 \\ (vii) & : 1666 \\ \end{align*} \][/tex]
1. (ii) [tex]\( 21 \times 38 \times (-25) \)[/tex]:
The properties involved here are the commutative and associative properties of multiplication, indicating that the order of multiplying numbers doesn't change the result. This expression simplifies directly to:
[tex]\[ 21 \times 38 \times (-25) = -19950 \][/tex]
2. (i) [tex]\( 46 \times (-38) + (-38) \times (-36) \)[/tex]:
Here, we can factor out [tex]\((-38)\)[/tex] since it is common in both terms:
[tex]\[ 46 \times (-38) + (-38) \times (-36) = (-38) \times (46 - (-36)) = (-38) \times 82 = -380 \][/tex]
3. (iv) [tex]\( 25 \times (-35) \times (-4) \times 0 \)[/tex]:
Any number multiplied by zero equals zero, so this expression simplifies quickly:
[tex]\[ 25 \times (-35) \times (-4) \times 0 = 0 \][/tex]
4. (iii) [tex]\( 25 \times (-6) \times (-4) \)[/tex]:
Using the associative property:
[tex]\[ 25 \times (-6) \times (-4) = 25 \times 24 = 600 \][/tex]
5. (xivi) [tex]\( 625 \times (-55) + (-625) \times 65 \)[/tex]:
Here, we can factor out [tex]\( 625 \)[/tex] (with appropriate signs):
[tex]\[ 625 \times (-55) + (-625) \times 65 = 625 \times (-55 - 65) = 625 \times (-120) = -75000 \][/tex]
6. (v) [tex]\( -36 \times 102 \)[/tex]:
This is a straightforward multiplication:
[tex]\[ -36 \times 102 = -3672 \][/tex]
7. (viii) [tex]\( (-57) \times (-19) + 57 \)[/tex]:
First, handle the multiplication, and then the addition:
[tex]\[ (-57) \times (-19) + 57 = 1083 + 57 = 1140 \][/tex]
8. (vii) [tex]\( 17 \times [100 - 2] \)[/tex]:
Simplify the expression inside the brackets first:
[tex]\[ 17 \times (100 - 2) = 17 \times 98 = 1666 \][/tex]
Thus, the final results for each of the expressions are:
[tex]\[ \begin{align*} (ii) & : -19950 \\ (i) & : -380 \\ (iv) & : 0 \\ (iii) & : 600 \\ (xivi) & : -75000 \\ (v) & : -3672 \\ (viii) & : 1140 \\ (vii) & : 1666 \\ \end{align*} \][/tex]
