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Welcome to our Math lesson on Rearranging Formulas, this is the second lesson of our suite of math lessons covering the topic of Types of Formulas. Rearranging Formulas, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Rearranging Formulas
In the last example, we rearranged the formula to isolate the weight W the iron bar could hold. We have done the same thing in other examples as well, when the quantity to the left part in the original formula was known, and we were interested to know any from the quantities in the right part of the formula. We can isolate the variable required by completing the inverse operations (as explained in the last paragraph of the previous tutorial). Recall that:
- the inverse operation of addition is subtraction,
- the inverse operation of multiplication is division
- the inverse operation of raise in power is finding the root
Moreover, sending a number or variable from left to right or vice-versa makes it change the sign to its opposite (plus becomes minus and minus becomes plus). Let's consider an example to clarify this point further.
Example 8
Make x the subject of the following formulas.
- y = 3 - 2x/5z
- y = 3x - z2/5
- 3y - x2 = 14 + a
Solution 8
In all examples we isolate x by considering all the other variables as constants. Thus, we have
y = 3 - 2x/5z
Multiplying both sides by 5z to remove fraction yields 5z ∙ y = 5z ∙ 3 - 2x/5z
5yz = 3 - 2x
2x = 3 - 5yz
x = 3 - 5yz/2
y = 3x - z2/5
Multiplying both sides by 5 to remove fraction yields 5y = 5(3x - z2/5)
5y = 5 ∙ 3x - 5 ∙ z2/5
5y = 15x - z2
5y + z2 = 15x
x = 5y/15 + z2/15
x = y/3 + z2/15
3y - x2 = 14 + a
3y - a + 14 = x2
x = √3y - a + 14
More Types of Formulas. Rearranging Formulas Lessons and Learning Resources
Formulas Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 8.2 | Types of Formulas. Rearranging Formulas | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 8.2.1 | Types of Formulas | | |
| 8.2.2 | Rearranging Formulas | | |
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- Continuing learning formulas - read our next math tutorial: Writing Formulas and Substituting in a Formula
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