A fraction \( \frac{a}{b} \) can be written in simplest terms (that is, as \( \frac{c}{d} \), where \( c \) and \( d \) have no common factor other than 1\( ) \) by dividing both a and \( b \) by \( G C D(a, b) \). (a) Compute \( G C D(30,228) \). (b) Determine a fraction in simplest terms equivalent to \( \frac{30}{228} \). (a) \( G C D(30,228)=\square \)

1. We compute \( GCD(30,228) \) using the Euclidean algorithm. - First, divide \( 228 \) by \( 30 \): \[ 228 = 30 \times 7 + 18 \] So, \( GCD(30,228) = GCD(30,18) \). 2. Next, divide \( 30 \) by \( 18 \): \[ 30 = 18 \times 1 + 12 \] So, \( GCD(30,18) = GCD(18,12) \). 3. Then, divide \( 18 \) by \( 12 \): \[ 18 = 12 \times 1 + 6 \] So, \( GCD(18,12) = GCD(12,6) \). 4. Finally, divide \( 12 \) by \( 6 \): \[ 12 = 6 \times 2 + 0 \] Since the remainder is \( 0 \), we have \( GCD(12,6)=6 \). Thus, \[ GCD(30,228)=6. \] 5. To express the fraction \( \frac{30}{228} \) in simplest terms, divide both the numerator and the denominator by \( 6 \): \[ \frac{30 \div 6}{228 \div 6} = \frac{5}{38}. \] (a) \( GCD(30,228)=\boxed{6} \).