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

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

• A. 1/5
• B. 2/5
• C. 1/4
• D. 3/5

Answer: (A)

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: \[

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:

[