Evaluate 1/2 x 3/7 x 14/15 and reduce to lowest terms.

To solve the expression ( \frac{1}{2} \times \frac{3}{7} \times \frac{14}{15} ) and reduce it to lowest terms, we follow these steps:

First, multiply the numerators together and the denominators together:

[

\text{Numerator: } 1 \times 3 \times 14 = 42

]

[

\text{Denominator: } 2 \times 7 \times 15 = 210

]

This results in the fraction ( \frac{42}{210} ).

Next, we need to simplify ( \frac{42}{210} ) by finding the greatest common divisor (GCD) of 42 and 210.

The prime factorization of each number helps us:

• ( 42 = 2 \times 3 \times 7 )

• ( 210 = 2 \times 3 \times 5 \times 7 )

The common factors are ( 2 ), ( 3 ), and ( 7 ). Therefore, the GCD is ( 42 ).

Now, divide both the numerator and denominator by their GCD:

[