Rational Properties Worksheets Grade 7

1. A rectangular swimming pool is drawn on a coordinate plane with corners at (0, 0), (20, 0), (20, 12), and (0, 12). A triangular safety zone is marked off inside the pool with vertices at (0, 0), (20, 0), and (10, 8). What is the area of the pool that remains available for swimming after excluding the safety zone?
2. (-3/4) × (2/3) + (5/6) ÷ (1/4) = ?
3. Olivia is tracking the temperature changes in her city for a science project. At 6:00 AM, the temperature was -8.5°C. By noon, the temperature had increased by 15.75°C. Then, from noon to 6:00 PM, the temperature decreased by 10.25°C. Olivia wants to use the associative property of addition to verify that she can group the temperature changes differently and still get the same final temperature. What is the final temperature at 6:00 PM?

…and 4 more problems

1. Tane is tracking the total profit from his online store over four weeks. In week 1, he makes a profit of $315. In week 2, he has a loss of $189 (shown as -189). In week 3, he makes a profit of $427. In week 4, he has a loss of $273 (shown as -273). Tane writes the expression 315 + (-189) + 427 + (-273). He wants to use the commutative and associative properties of addition to reorder and group the numbers to make the calculation easier. Show how Tane can use these properties to simplify the expression, then find his total profit for the four weeks.
2. A rectangular swimming pool is drawn on a coordinate plane with vertices at (0, 0), (20, 0), (20, 12), and (0, 12). A triangular diving area is marked off inside the pool with vertices at (0, 0), (20, 0), and (10, 8). What is the area of the remaining pool space that is not part of the diving area?
3. (-14) × [(-28) + 42] = ?

…and 4 more problems

1. Emma is planning a road trip from her home to her grandmother's house, which is 420 miles away. Her car's fuel efficiency is 28 miles per gallon, and gasoline costs $3.75 per gallon. If she wants to budget for the round trip, how much money should Emma set aside for gasoline?
2. Noah is managing his online store's inventory and finances. He starts the month with $12,500 in his business account. He then spends $3,200 on new inventory, receives a payment of $8,750 from a customer, pays a shipping fee of $1,500, and finally gets a refund of $600 for a returned item. Noah wants to use the commutative and associative properties of addition to verify his ending balance. He writes the expression: 12500 + (-3200) + 8750 + (-1500) + 600. Show how to use the commutative property to reorder the numbers and the associative property to group them in a way that makes the calculation easier, then find Noah's ending balance.
3. A rectangular swimming pool is drawn on a coordinate plane with corners at (0, 0), (20, 0), (20, 12), and (0, 12). A triangular shallow end is marked off with vertices at (0, 0), (8, 0), and (0, 6). What is the area of the deep end section of the pool?

…and 3 more problems