Simplify the ratio 7200 cents : R16 8

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UpStudy AI · Accepted Answer

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 $$ 30 : 7 $$.
The simplified ratio of 7200 cents to R16.8 is 30:7.

Simplify the ratio 7200 cents : R16 8

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