Question

Compare the ratios $7:9and6:5$.

Answer 1

Comparison of ratios:

Step 1: Express the given ratios as fractions in their simplest form:

$\Rightarrow \frac{7}{9}and\frac{6}{5}$

Step 2: Find the LCM of the denominators of the fractions:

$$\begin{gathered} 9=3\times 3 \\ 5=5 \end{gathered}$$

LCM of $9$ and $5=45$.

Step 3: Convert the fractions into like fractions with the LCM as their denominators:

$$\begin{gathered} \Rightarrow \frac{7\times 5}{9\times 5}=\frac{35}{45} \\ \Rightarrow \frac{6\times 9}{5\times 9}=\frac{54}{45} \end{gathered}$$

Step 4: Now, compare the numerators of the like fractions:

The fractions with the greater numerator will be greater

$$\begin{gathered} \Rightarrow \frac{35}{45}<\frac{54}{45} \\ \Rightarrow \frac{7}{9}<\frac{6}{5} \end{gathered}$$

Thus,$7:9<6:5$.