Reduce the ratio in simplest form
5 (1)/(3) : 2 (2)/(15)`

Answer

To reduce the ratio \( 5 \frac{1}{3} : 2 \frac{2}{15} \) in simplest form, we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

- For \( 5 \frac{1}{3} \):
\[ 5 \frac{1}{3} = 5 \times 3 + 1 = 15 + 1 = \frac{16}{3} \]

- For \( 2 \frac{2}{15} \):
\[ 2 \frac{2}{15} = 2 \times 15 + 2 = 30 + 2 = \frac{32}{15} \]

### Step 2: Write the Ratio with Improper Fractions
Now, we can write the ratio using the improper fractions:
\[ \frac{16}{3} : \frac{32}{15} \]

### Step 3: Simplify the Ratio
To simplify the ratio \( \frac{16}{3} : \frac{32}{15} \), we can express it as a single fraction:
\[ \frac{16}{3} \div \frac{32}{15} = \frac{16}{3} \times \frac{15}{32} \]

### Step 4: Multiply the Fractions
Now, we multiply the fractions:
\[ = \frac{16 \times 15}{3 \times 32} \]

### Step 5: Simplify the Numerator and Denominator
Now we can simplify:
- The numerator: \( 16 \times 15 = 240 \)
- The denominator: \( 3 \times 32 = 96 \)

So we have:
\[ \frac{240}{96} \]

### Step 6: Reduce the Fraction
Now we can reduce \( \frac{240}{96} \) to its simplest form:
- Divide both the numerator and denominator by their greatest common divisor (GCD), which is 48:
\[ \frac{240 \div 48}{96 \div 48} = \frac{5}{2} \]

### Step 7: Write the Final Ratio
Thus, the ratio in simplest form is:
\[ 5 : 2 \]