1. **State the problem:** Rita and Fred share sweets in the ratio 2 : 3. We have two scenarios: - Scenario 1: Altogether they have 90 sweets. - Scenario 2: Rita has 90 sweets. We want to match the bar models to these worded ratio questions. 2. **Recall the ratio concept:** The ratio 2 : 3 means for every 2 parts Rita has, Fred has 3 parts. 3. **Scenario 1: Total sweets = 90** - Total parts = 2 + 3 = 5 parts. - Each part = $\frac{90}{5} = 18$ sweets. - Rita's sweets = $2 \times 18 = 36$ sweets. - Fred's sweets = $3 \times 18 = 54$ sweets. 4. **Scenario 2: Rita has 90 sweets** - Rita's 2 parts = 90 sweets. - Each part = $\frac{90}{2} = 45$ sweets. - Fred's sweets = $3 \times 45 = 135$ sweets. - Total sweets = $90 + 135 = 225$ sweets. 5. **Match with bar models:** - Bar model with segments labeled 18 corresponds to Scenario 1 (total 90 sweets). - Bar model with segments labeled 45 corresponds to Scenario 2 (Rita has 90 sweets). **Final answer:** - Bar model with 18 per segment matches "Altogether they have 90 sweets." - Bar model with 45 per segment matches "Rita has 90 sweets."