Question

COLUMN A: \(\frac{16}{35}\)
COLUMN B: \(\frac{4}{9}\)

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

Cross-multiplication is usually the fastest and most accurate way to compare two simple fractions without a calculator. Just remember to multiply the numerator of one fraction by the denominator of the other.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a question about comparing two fractions.
Step 2: Key Formula or Approach:
There are several methods to compare fractions: 1. Cross-multiplication: To compare \( \frac{a}{b} \) and \( \frac{c}{d} \), compare \( ad \) and \( bc \). If \( ad>bc \), then \( \frac{a}{b}>\frac{c}{d} \). 2. Common denominator: Convert both fractions to have the same denominator and then compare the numerators. 3. Decimal conversion: Convert both fractions to decimals and compare them. Step 3: Detailed Explanation:
Method 1: Cross-multiplication
We are comparing \( \frac{16}{35} \) (Column A) and \( \frac{4}{9} \) (Column B). Let's cross-multiply: - For Column A, we calculate \( 16 \times 9 \). \( 16 \times 9 = 144 \). - For Column B, we calculate \( 35 \times 4 \). \( 35 \times 4 = 140 \). Since \( 144>140 \), the fraction corresponding to the 144 product is greater. Therefore, \( \frac{16}{35}>\frac{4}{9} \). Method 2: Decimal conversion
Column A: \( \frac{16}{35} \). Let's estimate. \( 16/32 = 0.5 \). Since the denominator is larger, the fraction will be a bit smaller. \( 16 \div 35 \approx 0.457 \). Column B: \( \frac{4}{9} \). This is a repeating decimal: \( 4 \div 9 = 0.444... \) Comparing the decimals, \( 0.457>0.444... \). So Column A is greater. Step 4: Final Answer:
Both cross-multiplication (\(144>140\)) and decimal conversion (\(0.457>0.444\)) show that the quantity in Column A is greater.