6/7 × 7/12× 5/3

To solve the expression \( \frac{6}{7} \times \frac{7}{12} \times \frac{5}{3} \), we can multiply the numerators together and the denominators together.

1. Multiply the numerators: \( 6 \times 7 \times 5 = 210 \)

2. Multiply the denominators: \( 7 \times 12 \times 3 = 252 \)

Now, we have:

\[ \frac{210}{252} \]

Next, we'll simplify this fraction. We can find the greatest common divisor (GCD) of 210 and 252 to simplify.

The prime factorizations are:

• \( 210 = 2 \times 3 \times 5 \times 7 \)
• \( 252 = 2^2 \times 3^2 \times 7 \)

The GCD is:

• The lowest powers of the common primes: \( 2^1 \), \( 3^1 \), and \( 7^1 \), which gives us \( 2 \times 3 \times 7 = 42 \).

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

\[ \frac{210 \div 42}{252 \div 42} = \frac{5}{6} \]

Thus, the simplified result of \( \frac{6}{7} \times \frac{7}{12} \times \frac{5}{3} \) is \( \frac{5}{6} \).