Compare the following:
5:12 and 3:8

Answer

To compare the ratios 5:12 and 3:8, we can convert them into fractions and then compare their values. Here’s the step-by-step solution:

### Step 1: Write the ratios as fractions
We can express the ratios as fractions:
- The first ratio, 5:12, can be written as \( \frac{5}{12} \).
- The second ratio, 3:8, can be written as \( \frac{3}{8} \).

### Step 2: Find a common denominator
To compare the two fractions, we need to find a common denominator. The denominators are 12 and 8. The least common multiple (LCM) of 12 and 8 is 24.

### Step 3: Convert the fractions to have the same denominator
Now we will convert both fractions to have the common denominator of 24:
- For \( \frac{5}{12} \):
\[ \frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24} \]
- For \( \frac{3}{8} \):
\[ \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \]

### Step 4: Compare the numerators
Now that both fractions have the same denominator, we can compare their numerators:
- The numerator of \( \frac{10}{24} \) is 10.
- The numerator of \( \frac{9}{24} \) is 9.

Since \( 10 > 9 \), we conclude that:
\[ \frac{5}{12} > \frac{3}{8} \]

### Step 5: State the final comparison
Thus, we can say that:
\[ 5:12 > 3:8 \]