Question

Column A: \(\frac{0.3}{1.5}\)
Column B: \(\frac{2}{10}\)

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

Hint:

When dealing with fractions involving decimals, the easiest first step is often to multiply the numerator and denominator by a power of 10 to convert them into integers. This makes simplification much easier.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question involves comparing two simple fractions, one expressed with decimals and the other with integers. The goal is to simplify both fractions to their simplest form to compare them.
Step 2: Detailed Explanation:
Simplifying Column A:
The expression is \(\frac{0.3}{1.5}\).
To eliminate the decimals, we can multiply both the numerator and the denominator by 10.
\[ \frac{0.3 \times 10}{1.5 \times 10} = \frac{3}{15} \] Now, we can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
\[ \frac{3 \div 3}{15 \div 3} = \frac{1}{5} \] So, the value of Column A is \(\frac{1}{5}\).
Simplifying Column B:
The expression is \(\frac{2}{10}\).
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
\[ \frac{2 \div 2}{10 \div 2} = \frac{1}{5} \] So, the value of Column B is \(\frac{1}{5}\).
Step 3: Comparing the Quantities:
Column A: \(\frac{1}{5}\)
Column B: \(\frac{1}{5}\)
The values are identical.
Step 4: Final Answer:
Since both quantities simplify to \(\frac{1}{5}\), the two quantities are equal.