Rational Properties Worksheets Grade 7

1. Sophia is tracking the temperature changes in her city over a weekend. On Saturday morning, the temperature was -6°C. By noon, it increased by 11°C, but then dropped by 7°C by evening. On Sunday morning, the temperature was 4°C higher than Saturday evening. By Sunday afternoon, it increased by 5°C, then decreased by 9°C by night. What was the temperature on Sunday night? Use the associative property of addition to verify your answer by grouping the changes differently.
2. 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 by connecting points (0, 0), (8, 0), and (0, 6). What is the area of the deep end section of the pool?
3. Liam is designing a rectangular garden with a perimeter of 48 meters. The length of the garden is 2 meters more than twice its width. What are the dimensions of Liam's garden?

…and 5 more problems

1. 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?
2. Charlotte is tracking the temperature changes in her science experiment. The temperature started at -12 degrees Celsius. She added a chemical that caused the temperature to rise by 8 degrees, then another chemical that caused it to fall by 15 degrees, and finally a third chemical that caused it to rise by 22 degrees. Use the associative property of addition to show that the final temperature is the same regardless of how the temperature changes are grouped. What is the final temperature?
3. A rectangular swimming pool is drawn on a coordinate plane with vertices at (0, 0), (20, 0), (20, 12), and (0, 12). A triangular shallow end is marked off by connecting points (0, 0), (8, 0), and (0, 6). What is the area of the deep end section of the pool?

…and 4 more problems

1. Kaia is calculating her monthly budget. She has a part-time job that pays her $1,250 per month, but she also has expenses: rent of $450, groceries of $275, and transportation costs of $120. Additionally, she receives a monthly allowance of $150 from her parents. To simplify her calculations, Kaia writes the expression: 1250 + 150 - 450 - 275 - 120. She decides to rearrange it as 1250 - 450 + 150 - 275 - 120. Which property of operations with rational numbers allows Kaia to rearrange the terms in the expression? Verify that both expressions are equal.
2. Liam is designing a rectangular garden with a length-to-width ratio of 5:3. He wants to plant flowers along the entire perimeter, which measures 128 meters. What is the area of Liam's garden in square meters?
3. Aroha is tracking her savings for a school trip. She starts with $125 in her account. On Monday, she withdraws $37 to buy supplies. On Tuesday, she deposits $48 from a babysitting job. On Wednesday, she withdraws $15 for a movie ticket. Aroha wants to verify her balance using the commutative property of addition to add the transactions in a different order. Show that the sum of the transactions (including the starting balance as a positive number) is the same when added in two different orders, and then calculate her final balance.

…and 4 more problems