Which of the following two ratios is greater 17:18 and 10:11?

Options

A. a. 17:18
B. b. 10:11
C. c. Both are same
D. d. Cannot determine

Answer

To determine which of the two ratios, 17:18 and 10:11, is greater, we will follow these steps:

### Step 1: Convert the Ratios to Fractions
We can express the ratios as fractions:
- \( \frac{17}{18} \) for the ratio 17:18
- \( \frac{10}{11} \) for the ratio 10:11

### Step 2: Find a Common Denominator
To compare the two fractions, we need a common denominator. The denominators are 18 and 11. The least common multiple (LCM) of 18 and 11 is 198.

### Step 3: Convert Each Fraction to Have the Common Denominator
Now we will convert each fraction to have a denominator of 198:
- For \( \frac{17}{18} \):
\[ \frac{17}{18} = \frac{17 \times 11}{18 \times 11} = \frac{187}{198} \]
- For \( \frac{10}{11} \):
\[ \frac{10}{11} = \frac{10 \times 18}{11 \times 18} = \frac{180}{198} \]

### Step 4: Compare the Numerators
Now that both fractions have the same denominator, we can compare their numerators:
- \( 187 \) (from \( \frac{187}{198} \))
- \( 180 \) (from \( \frac{180}{198} \))

Since \( 187 > 180 \), we conclude that:
\[ \frac{187}{198} > \frac{180}{198} \]

### Step 5: Conclusion
Thus, we can conclude that:
\[ 17:18 > 10:11 \]

### Summary
The ratio 17:18 is greater than the ratio 10:11.

---