To Be Or Not To Be Proportional” Worksheet - Free Printable

1] Dylan makes $10.50 per hour. Angela makes $10.00 per hour.

2] No, Dylan’s wage for 25 hours is not proportional to Angela’s wage for 42 hours. Dylan’s hourly rate is $10.50 and Angela’s is $10.00. Since their hourly rates are different, the ratios of their wages to hours worked are not equal. For proportionality, the unit rates must be identical.

Conclusion: To determine proportionality between two ratios or rates, compare their unit rates (simplify each ratio to a value per one unit); if the unit rates are equal, the ratios are proportional.

Table 1 Ratios:
- 1 hour: $75 → 75/1 = 75
- 2 hours: $120 → 120/2 = 60
- 3 hours: $165 → 165/3 = 55
- 4 hours: $210 → 210/4 = 52.5
- 5 hours: $255 → 255/5 = 51

Table 2 Ratios:
- 1 hour: $45 → 45/1 = 45
- 2 hours: $90 → 90/2 = 45
- 3 hours: $135 → 135/3 = 45
- 4 hours: $180 → 180/4 = 45
- 5 hours: $225 → 225/5 = 45

3] Table 2 shows a proportional relationship.

4] It is proportional because the ratio of total cost to number of hours (y/x) is constant (always 45) across all entries.

Conclusion: To determine proportionality from a table, calculate the ratio y/x for each row; if all ratios are equal, the relationship is proportional.