Simplify the ratio 7200 cents : R16 8

To simplify the ratio \( 7200 \) cents : \( R16.8 \), we first need to convert both quantities to the same unit. 1. **Convert R16.8 to cents:** Since \( 1 \) Rand (R) is equal to \( 100 \) cents, we can convert \( R16.8 \) to cents: \[ R16.8 = 16.8 \times 100 = 1680 \text{ cents} \] 2. **Now we have the ratio:** \[ 7200 \text{ cents} : 1680 \text{ cents} \] 3. **Simplify the ratio:** To simplify the ratio, we divide both sides by the greatest common divisor (GCD) of \( 7200 \) and \( 1680 \). First, we can find the GCD of \( 7200 \) and \( 1680 \). Let's calculate the GCD. - The prime factorization of \( 7200 \) is: \[ 7200 = 2^4 \times 3^2 \times 5^2 \] - The prime factorization of \( 1680 \) is: \[ 1680 = 2^4 \times 3^1 \times 5^1 \times 7^1 \] The GCD is obtained by taking the lowest power of each prime factor present in both factorizations: - For \( 2 \): \( 2^4 \) - For \( 3 \): \( 3^1 \) - For \( 5 \): \( 5^1 \) Thus, the GCD is: \[ GCD = 2^4 \times 3^1 \times 5^1 = 16 \times 3 \times 5 = 240 \] 4. **Now divide both sides of the ratio by the GCD:** \[ \frac{7200}{240} : \frac{1680}{240} \] Calculating these values: \[ \frac{7200}{240} = 30 \quad \text{and} \quad \frac{1680}{240} = 7 \] 5. **Final simplified ratio:** The simplified ratio is: \[ 30 : 7 \] Thus, the simplified ratio of \( 7200 \) cents to \( R16.8 \) is \( 30 : 7 \).