2. Write each of the following as a ratio in simplest form. (Hint: Convert to the same unit first.) \( \begin{array}{lll}\text { a. } 60 ¢: 6 & \text { b. } 75 ¢: 3.75 & \text { c. } 90 \mathrm{~cm}: 1.5 \mathrm{~m} \\ \text { d. } 0.6 \mathrm{~kg}: 900 \mathrm{~g} & \text { e. } 3.5 \mathrm{~kg}: 500 \mathrm{~g} & \text { f. } 40 \mathrm{~min}: 3 \mathrm{hours} \\ \text { g. } 20 \mathrm{~min}: 2 \text { hours } & \text { h. } 3 \text { hours }: 40 \mathrm{~min} & \text { i. } 50 \mathrm{~cm}: 3 \mathrm{~m}: 70 \mathrm{~cm} \\ \text { j. } 90 \mathrm{~cm}: 400 \mathrm{~mm}: 3 \mathrm{~m} & \text { k. } 3.5 \text { hours }: 2 \text { days } & \text { l. } 0.12 \mathrm{~km}: 400 \mathrm{~m}: 1.5 \mathrm{~km}\end{array} \)

We need to express each ratio using the same units and then simplify. Let’s work through parts (a) to (l) step‐by‐step. ────────────────────────── (a) 60¢ : 6 The money amounts are in cents and dollars. Convert 6 dollars to cents:   6 dollars = 6 × 100 = 600¢. Now, the ratio is 60¢ : 600¢. Divide both terms by 60:   60 ÷ 60 : 600 ÷ 60 = 1 : 10. ────────────────────────── (b) 75¢ : 3.75 Convert 3.75 dollars to cents:   3.75 dollars = 3.75 × 100 = 375¢. Now, the ratio is 75¢ : 375¢. Divide both terms by 75:   75 ÷ 75 : 375 ÷ 75 = 1 : 5. ────────────────────────── (c) 90 cm : 1.5 m Convert 1.5 meters to centimeters (1 m = 100 cm):   1.5 m = 150 cm. So the ratio is 90 cm : 150 cm. Divide both terms by 30:   90 ÷ 30 : 150 ÷ 30 = 3 : 5. ────────────────────────── (d) 0.6 kg : 900 g Convert 0.6 kg to grams (1 kg = 1000 g):   0.6 kg = 600 g. Thus, the ratio is 600 g : 900 g. Divide both by 300:   600 ÷ 300 : 900 ÷ 300 = 2 : 3. ────────────────────────── (e) 3.5 kg : 500 g Convert 3.5 kg to grams:   3.5 kg = 3500 g. The ratio is 3500 g : 500 g. Divide both terms by 500:   3500 ÷ 500 : 500 ÷ 500 = 7 : 1. ────────────────────────── (f) 40 min : 3 hours Convert 3 hours to minutes (1 hr = 60 min):   3 hrs = 3 × 60 = 180 min. The ratio is 40 : 180. Divide both by 10 first: 4 : 18, then by 2:   4 ÷ 2 : 18 ÷ 2 = 2 : 9. ────────────────────────── (g) 20 min : 2 hours Convert 2 hours to minutes:   2 hrs = 2 × 60 = 120 min. So the ratio is 20 : 120. Divide both by 20:   20 ÷ 20 : 120 ÷ 20 = 1 : 6. ────────────────────────── (h) 3 hours : 40 min Convert 3 hours to minutes:   3 hrs = 3 × 60 = 180 min. Now the ratio is 180 : 40. Divide both by 10: 18 : 4. Then divide by 2: 9 : 2. ────────────────────────── (i) 50 cm : 3 m : 70 cm Convert 3 m to centimeters:   3 m = 3 × 100 = 300 cm. So the ratio is 50 : 300 : 70. Divide each term by 10:   5 : 30 : 7. No further common factor exists among 5, 30, and 7, so the simplest form is 5 : 30 : 7. ────────────────────────── (j) 90 cm : 400 mm : 3 m It is easiest to convert everything to millimeters (1 cm = 10 mm, 1 m = 1000 mm). • 90 cm = 90 × 10 = 900 mm. • 400 mm remains 400 mm. • 3 m = 3 × 1000 = 3000 mm. Now the ratio is 900 : 400 : 3000. Divide each term by 100:   9 : 4 : 30. This is the simplified ratio. ────────────────────────── (k) 3.5 hours : 2 days Convert 2 days to hours (1 day = 24 hours):   2 days = 2 × 24 = 48 hours. So the ratio is 3.5 : 48. To eliminate the decimal multiply both terms by 2:   3.5 × 2 = 7 and 48 × 2 = 96. Thus, the ratio becomes 7 : 96. ────────────────────────── (l) 0.12 km : 400 m : 1.5 km Convert all distances to meters (1 km = 1000 m): • 0.12 km = 0.12 × 1000 = 120 m. • 400 m remains 400 m. • 1.5 km = 1.5 × 1000 = 1500 m. Now the ratio is 120 : 400 : 1500. Divide each term by 10:   12 : 40 : 150. The greatest common factor of 12, 40, and 150 is 2. Divide each term by 2:   12 ÷ 2 = 6, 40 ÷ 2 = 20, 150 ÷ 2 = 75. Thus, the simplest form is 6 : 20 : 75. ────────────────────────── Final Answers a. 1 : 10 b. 1 : 5 c. 3 : 5 d. 2 : 3 e. 7 : 1 f. 2 : 9 g. 1 : 6 h. 9 : 2 i. 5 : 30 : 7 j. 9 : 4 : 30 k. 7 : 96 l. 6 : 20 : 75 Any answer equivalent to these is correct.