Certainly! Let's go through each operation step-by-step to understand the calculations involved.
e) [tex]\( 3(2 + 4) = 3 \cdot 2 + 3 \cdot 4 \)[/tex]
1. Evaluate the left-hand side:
[tex]\[ 3(2 + 4) \][/tex]
Simplify inside the parentheses first:
[tex]\[ 3(6) \][/tex]
Multiply:
[tex]\[ 18 \][/tex]
2. Evaluate the right-hand side:
[tex]\[ 3 \cdot 2 + 3 \cdot 4 \][/tex]
Calculate each multiplication separately:
[tex]\[ 6 + 12 \][/tex]
Add the results:
[tex]\[ 18 \][/tex]
So, [tex]\( 3(2 + 4) = 3 \cdot 2 + 3 \cdot 4 \)[/tex] both equal to 18.
f) [tex]\( 5 + 0 = 0 + 5 = 5 \)[/tex]
1. Evaluate the left-hand side:
[tex]\[ 5 + 0 \][/tex]
Add:
[tex]\[ 5 \][/tex]
2. Evaluate the right-hand side:
[tex]\[ 0 + 5 \][/tex]
Add:
[tex]\[ 5 \][/tex]
So, both [tex]\( 5 + 0 \)[/tex] and [tex]\( 0 + 5 \)[/tex] result in 5.
g) [tex]\( 3 \cdot 1 = (1) \cdot 3 = 3 \)[/tex]
1. Evaluate the left-hand side:
[tex]\[ 3 \cdot 1 \][/tex]
Multiply:
[tex]\[ 3 \][/tex]
2. Evaluate the right-hand side:
[tex]\[ 1 \cdot 3 \][/tex]
Multiply:
[tex]\[ 3 \][/tex]
So, both [tex]\( 3 \cdot 1 \)[/tex] and [tex]\( (1) \cdot 3 \)[/tex] result in 3.
h) [tex]\( 4 + (-4) = 0 \)[/tex]
1. Evaluate the expression:
[tex]\[ 4 + (-4) \][/tex]
Add:
[tex]\[ 0 \][/tex]
So, [tex]\( 4 + (-4) \)[/tex] equals 0.
In summary:
- For part e), both sides equal 18.
- For part f), both expressions equal 5.
- For part g), both expressions equal 3.
- For part h), the result is 0.
These results show that the properties of arithmetic operations (distributive, identity, and inverse) hold true for the given equations.
