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Use the tables to help you compare the two ratios.

\begin{tabular}{|c|c|c|}
\hline
3 & 6 & 9 \\
\hline
10 & 20 & 30 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|c|}
\hline
1 & 2 & 3 \\
\hline
5 & 10 & 15 \\
\hline
\end{tabular}

Compare the ratios [tex]1: 5[/tex] and [tex]3: 10[/tex].

A. The ratio [tex]1: 5[/tex] is less than [tex]3: 10[/tex].

B. The ratio [tex]1: 5[/tex] is greater than [tex]3: 10[/tex].

C. The ratio [tex]1: 5[/tex] is equal to [tex]3: 10[/tex].

D. The ratios cannot be compared.


Sagot :

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].