To compare the ratios [tex]\(1: 5\)[/tex] and [tex]\(3: 10\)[/tex], let's first understand what these ratios represent.
### Step-by-Step Solution
#### Step 1: Express the Ratios as Fractions
- The ratio [tex]\(1: 5\)[/tex] can be expressed as the fraction [tex]\(\frac{1}{5}\)[/tex].
- The ratio [tex]\(3: 10\)[/tex] can be expressed as the fraction [tex]\(\frac{3}{10}\)[/tex].
#### Step 2: Convert the Ratios to Decimal Form
- To compare these ratios easily, we can convert them into decimal form:
- [tex]\(\frac{1}{5} = 0.2\)[/tex]
- [tex]\(\frac{3}{10} = 0.3\)[/tex]
#### Step 3: Compare the Decimal Values
- Now, we compare the decimal values [tex]\(0.2\)[/tex] and [tex]\(0.3\)[/tex].
### Step-By-Step Comparison
- [tex]\(0.2 < 0.3\)[/tex]
#### Conclusion
- Since [tex]\(0.2\)[/tex] (which is [tex]\(\frac{1}{5}\)[/tex]) is less than [tex]\(0.3\)[/tex] (which is [tex]\(\frac{3}{10}\)[/tex]), we conclude that:
- The ratio [tex]\(1: 5\)[/tex] is less than the ratio [tex]\(3: 10\)[/tex].
Thus, the correct comparison and conclusion is:
- The ratio [tex]\(1: 5\)[/tex] is less than [tex]\(3: 10\)[/tex].
