Arrange the fractions 16/19, 11/14, and 17/22 in ascending (increasing) order.

Introduction / Context:
Ordering fractions requires comparing their sizes. You can convert to decimals or use cross-multiplication to avoid approximate arithmetic. The goal is to find the correct increasing order among the three given fractions.

Given Data / Assumptions:

• Fractions: 16/19, 11/14, 17/22.
• We want ascending order (smallest to largest).

Concept / Approach:
Two common methods: (1) Convert each fraction to a decimal; (2) Cross-multiply for pairwise comparisons without computing decimals. We will use decimals for clarity and then confirm with cross-multiplication.

Step-by-Step Solution:
Compute approximate decimals: 16/19 ≈ 0.8421, 11/14 ≈ 0.7857, 17/22 ≈ 0.7727.Order by value: 0.7727 < 0.7857 < 0.8421.Thus, ascending order: 17/22, 11/14, 16/19.Cross-check (pairwise): Compare 17/22 vs 11/14: 17*14 = 238, 11*22 = 242 → 238 < 242 → 17/22 < 11/14 (consistent).Compare 11/14 vs 16/19: 11*19 = 209, 16*14 = 224 → 209 < 224 → 11/14 < 16/19 (consistent).

Verification / Alternative check:
Both decimal and cross-multiplication methods agree on the same order, ensuring correctness.

Why Other Options Are Wrong:
Any order placing 16/19 before either fraction or 11/14 after 16/19 contradicts the computed comparisons.

Common Pitfalls:
Rounding too aggressively when using decimals; misreading ascending vs descending; arithmetic errors in cross-multiplication.

Final Answer:
17/22, 11/14, 16/19