Understanding and Matching Fractions

This question asks us to match fractions and their descriptions from Column I with the correct types or equivalent fractions in Column II. Let's analyze each point:

Analyzing Each Match

a. Equivalent fraction of \( \frac{7}{12} \)

An equivalent fraction is found by multiplying or dividing both the numerator and the denominator by the same non-zero number. Let's check option (iii) from Column II, which is \( \frac{21}{36} \).

We can see that \( 21 = 7 \times 3 \) and \( 36 = 12 \times 3 \). So, \( \frac{7}{12} \) multiplied by \( \frac{3}{3} \) gives \( \frac{21}{36} \).

\( \frac{7}{12} = \frac{7 \times 3}{12 \times 3} = \frac{21}{36} \)

Therefore, \( \frac{21}{36} \) is an equivalent fraction of \( \frac{7}{12} \).

• Match: a - iii

b. Equivalent fraction of \( \frac{9}{15} \)

Let's look at option (iv) from Column II, which is \( \frac{3}{5} \). We can simplify the fraction \( \frac{9}{15} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

\( \frac{9}{15} = \frac{9 \div 3}{15 \div 3} = \frac{3}{5} \)

Therefore, \( \frac{3}{5} \) is an equivalent fraction of \( \frac{9}{15} \).

• Match: b - iv

c. \( \frac{7}{11} \) is

We need to identify the type of fraction \( \frac{7}{11} \). A proper fraction is a fraction where the numerator is less than the denominator. In \( \frac{7}{11} \), the numerator (7) is less than the denominator (11).

\( 7 < 11 \)

This fits the definition of a proper fraction, which is option (i) in Column II.

• Match: c - i

d. \( \frac{19}{5} \) is

Finally, let's identify the type of fraction \( \frac{19}{5} \). An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In \( \frac{19}{5} \), the numerator (19) is greater than the denominator (5).

\( 19 > 5 \)

This fits the definition of an improper fraction, which is option (ii) in Column II.

• Match: d - ii

Summary of Matches

Based on our analysis, the correct matches are:

• a - iii
• b - iv
• c - i
• d - ii

This combination corresponds to one of the given options.