Arrange the following fractions in increasing order:

A. 14/17
B. 11/13
C. 7/9
D. 16/19
Choose the correct answer from the options given below:

The correct answer is C, A, D, B, which means the fractions arranged in increasing order are:

$\frac{7}{9}$ < $\frac{14}{17}$ < $\frac{16}{19}$ < $\frac{11}{13}$

The most reliable way to compare fractions with different numerators and denominators is to convert each one into its decimal equivalent. This allows us to place them on a common number line and compare directly.

Step 1: Convert each fraction to a decimal.

Fraction C: 7/9
$\frac{7}{9}=7÷9=0.7778$ (approximately)

Fraction A: 14/17
$\frac{14}{17}=14÷17=0.8235$ (approximately)

Fraction D: 16/19
$\frac{16}{19}=16÷19=0.8421$ (approximately)

Fraction B: 11/13
$\frac{11}{13}=11÷13=0.8462$ (approximately)

Step 2: Summarise the decimal values in a table for clarity.

Step 3: Arrange the decimal values in increasing (ascending) order.

$0.7778$ < $0.8235$ < $0.8421$ < $0.8462$

Mapping these back to the original fraction labels:

$\text{C}$ < $\text{A}$ < $\text{D}$ < $\text{B}$

Key Insight (a useful shortcut): Notice that all four fractions are "close to 1" — each has a numerator just slightly less than its denominator. A useful trick: the fraction whose numerator-to-denominator gap (i.e., denominator - numerator) is largest relative to its denominator is actually the smallest fraction. For example, C = 7/9 has a gap of 2 out of 9, which is relatively the largest gap, making it the smallest fraction. This confirms our decimal calculation.

Therefore, the correct increasing order is C, A, D, B.