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Rearranging Equations

HSA-CED.A.4
Answer Keys Here

Aligned To Common Core Standard:

High School - HSA-CED.A.4

How to Rearrange Formulas and Equations? Manipulating or rearranging an equation might scare the students away, but it is not as difficult as it may seem. The skill to rearrange formulae and equations can significantly help students solve problems with much ease and convenience. If you manipulate an equation and make your required variable the subject before adding the numeric values, solving for the variable becomes simpler. You can solve a variable for a number of different values. Rules to follow when Rearranging Formulae and Equations There are certain rules you have to follow when you are rearranging equations. Rule 1: A Balanced Change - You can easily add, subtract, divide, or multiply by a value, as long as you do that on both sides of the equation. A balanced change is a crucial step and it keeps the target equation unchanged. If you make a change to one side of the equation it will change its meaning. Rule 2: Cancelling a Quantity - There are cases when you have to cancel out a quantity from an equation. It is possible if you perform the opposite operation on both sides of the equation. Rearranging and Equation - Step 1: Assess the problem and identify the variable you need to isolate. Step 2: Place the like terms together, variables with variables and constants with constants. Step 3: Isolate the target variable by applying the rules of equation manipulation. Step 4: Plug in the numbers and solve. These worksheets help students learn the ins and outs of using formulas.

Printable Worksheets And Lessons


  • Simple Rearrangements Step-by-step Lesson- Rearranging products are quite simple. This lesson will walk you through it.
  • Guided Lesson - These are much more challenging for students. They start with a middle level operation in place.
  • Guided Lesson Explanation - I display opposite operations that cancel each other out.
  • Practice Worksheet - Students have trouble with the second half of the sheet, so you might want to work one through with them before you set them loose on it.
  • Matching Worksheet - I left the variable in there while using different operations. The variable labels may help them get it quicker. This matching worksheet is great for spotting patterns and since all the variables slightly differ, it makes it easier to spot.
  • Multiplication Principle Five Pack - As simple as it gets for you. Anyone who is behind, should be able to get some use out of these. All the moves in here revolve around either multiplication or division operations.




Homework Sheets

These get progressively harder as you follow along.

  • Homework 1 - An example problem for this sheet: Rearrange the following formula to solve for p. f = qpw
  • Homework 2 - Write out the steps as you complete them. Multiply both sides by f. Subtract both sides by 1x.
  • Homework 3 - These are more complex problems because they involve several different operations.



Practice Worksheets

I tried my best to accommodate all levels here with this.

  • Practice 1 - Rearrange the following formulas to solve for p. You will have a wide range of operations to deal with here.
  • Practice 2 - The goal of all of these is to rearrange the formulas and get p by itself. We take all the necessary steps to do so.
  • Practice 3 - Multiplication and division are opposite operations.



Math Skill Quizzes

I get rave reviews about the third quiz. I'm not sure why.

  • Quiz 1 - To get variables by themselves just counter the operations that are holding it together.
  • Quiz 2 - It is important to remember that what ever operation you perform on one side of the equal symbol must be performed on the other side as well.
  • Quiz 3 - Rearranging what ever you need to help you make sense of these equations.