Equivalent Expressions Worksheets Grade 7

1. Rewrite 5(4x + 15) - 2(3x - 10) in simplest form.
2. A rectangular garden has a length that is 3 meters more than twice its width. If the perimeter of the garden is 42 meters, what is the width of the garden in meters?
3. Isabella draws a rectangular prism with a length of 14 units, a width of 9 units, and a height of 11 units. She then creates a net of the prism by flattening all its faces. The net consists of six rectangles arranged in a cross-like pattern. Write two equivalent expressions that represent the total surface area of the prism: one in expanded form (showing the sum of the areas of all six faces) and one in factored form. Then determine if these two expressions are equivalent.

…and 3 more problems

1. Charlotte is designing a rectangular mural for her school's art show. The length of the mural is 14 meters more than 5 times its width. She needs to write two equivalent expressions for the area of the mural in expanded form and factored form to help calculate the amount of paint needed. If the width is w meters, write two equivalent expressions for the area. Then, find the area of the mural when the width is 11 meters using both expressions to verify they are equivalent.
2. Liam is designing a rectangular garden for his school's science project. The garden's length is 12.5 meters and its width is 8.4 meters. He needs to calculate the total area to determine how much soil to buy. What is the area of Liam's garden in square meters?
3. Rewrite 9(2x + 7) - 5x in simplest form.

…and 3 more problems

1. Emma is organizing a charity run and needs to calculate the total distance covered by all participants. There are 245 runners, and each runner completes 3.2 kilometers. If the charity donates $1.50 for every kilometer run, how much money will be raised in total?
2. (3/4 × 8/9) ÷ (2/3) = ?
3. Mere draws a rectangle on a coordinate plane with corners at (2, 2), (10, 2), (10, 6), and (2, 6). She then draws a second rectangle that has the same area but a different shape. The second rectangle has a length of 16 units. What is the width of the second rectangle? Show that the two rectangles are equivalent by writing an expression for the area of each rectangle in expanded and simplified form.

…and 5 more problems