Formulas and Rearranging Equations
A free Algebra I lesson from the “Algebra Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Formulas are literal equations tied to real quantities. Algebra helps you rearrange a formula first, then substitute numbers with fewer steps and fewer errors. In Algebra Foundations, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.
What you'll learn
- Choose a useful formula for a context
- Substitute values carefully
- Rearrange formulas before calculating
Worked example
Problem. The formula d = rt gives distance. If d = 180 and t = 3, find r.
- Solve d = rt for r: r = d/t.
- Substitute d = 180 and t = 3.
- r = 180/3 = 60.
- Connect the result back to Formulas and Rearranging Equations so the method and meaning are both clear.
Answer: 60
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Use d = rt. If r = 55 and t = 2, what is d?
Show solution
- Multiply rate by time.
- 55 x 2 = 110.
Answer: 110
2. Use A = bh. If b = 9 and h = 4, what is A?
Show solution
- Multiply base by height.
- 9 x 4 = 36.
Answer: 36
3. Which formula gives speed from distance and time?
Choices: r = d/t · r = dt · r = t/d · r = d - t
Show solution
- Distance equals rate times time.
- Solve d = rt for r.
Answer: r = d/t
4. Use V = lwh. If l = 5, w = 4, and h = 3, what is V?
Show solution
- Multiply the three dimensions.
- 5 x 4 x 3 = 60.
Answer: 60
5. Use A = bh/2. If b = 12 and h = 7, what is A?
Show solution
- Multiply 12 x 7 = 84.
- Then divide by 2 to get 42.
Answer: 42
Practice this interactively with instant feedback and an AI tutor.
Practice Formulas and Rearranging Equations Take the free placement check