m:n = $2\frac{1}{3} : 1\frac{1}{5}$ and n : q = $1\frac{1}{2} : 1\frac{1}{3}$, find q : m.

Step 1: Convert to improper fractions

• m : n = 7/3 : 6/5
• n : q = 3/2 : 4/3

Step 2: Simplify each ratio to whole numbers

• m : n = 7/3 : 6/5. Multiply both sides by 15: 35 : 18.
• n : q = 3/2 : 4/3. Multiply both sides by 6: 9 : 8.

Step 3: Make n the same in both ratios

n is 18 in the first ratio and 9 in the second. Multiply the second ratio by 2: n : q = 18 : 16.

So m : n : q = 35 : 18 : 16.

Step 4: Find q : m

q : m = 16 : 35

Check: m/n = 35/18 and n/q = 9/8. Then m/q = (35/18)(9/8) = 315/144 = 35/16, so q/m = 16/35. ✓

Answer: B (16 : 35)

Tip: When chaining ratios, clear the fractions first. Then scale the shared term (here n) so it matches in both ratios, and join them into one ratio such as m : n : q. Read off the pair you need, and watch the order, since the question asks for q : m, not m : q.