Verification of the Property x×(y z) = x×y x z

To verify the given property, we need to substitute the given values of x, y, and z into both sides of the equation and check if they are equivalent. Let's evaluate each side step by step.

Given values:
x = 1/3
y = 1/5
z = 1/7

Left-hand side (LHS) of the equation:
LHS = x × (y z)

Substituting the given values:
LHS = (1/3) × ((1/5) × (1/7))

Now, let's simplify the expression inside the parentheses first:
(1/5) × (1/7) = 1/35

Substituting back into the LHS:
LHS = (1/3) × (1/35)

To multiply fractions, we multiply the numerators and denominators:
LHS = (1 × 1) / (3 × 35) = 1/105

Right-hand side (RHS) of the equation:
RHS = x × y × z

Substituting the given values:
RHS = (1/3) × (1/5) × (1/7)

Let's multiply the fractions step by step:
(1/3) × (1/5) = 1/15
(1/15) × (1/7) = 1/105

Therefore, RHS = 1/105

Conclusion:
After evaluating both sides of the equation, we find that the LHS is equal to the RHS.
LHS = 1/105 = RHS

Hence, the property x × (y z) = x × y × z is verified using the given values of x = 1/3, y = 1/5, and z = 1/7.

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