MODULE A - 6

1. MODULE A - 6 Rearranging Equations

2. OBJECTIVES • At the end of this module, the student will be able to… • State the three rules for rearranging formulas. • Given a mathematical problem requiring rearranging of the equation, derive the correct answer. • Distinguish between a direct and an indirect relationship.

3. The Rules of Rearranging – Rule #1 #1Balance the equation: EITHER Whole numbers on both sides or Fractions on both sides EXAMPLE:

4. The Rules of Rearranging – Rule #2 #2Get the item you are looking for alone on one side of the equal sign. : EXAMPLE: SOLVE FOR “A”

5. The Rules of Rearranging – Rule #3 #3 Get the item you are trying to find in the numerator (on top) EXAMPLE: SOLVE FOR “A”

6. General Rule Remember, you can do whatever you want to an equation, so long as you do the same thing to both sides of the equal sign! • Addition • Subtraction • Multiplication • Division • Inversion

7. Practice Find “A: A X C = B X D ______________________ C X B = D X A _______________________ A / B = C / D ________________________

8. Find “A” B / A = C / D _________________________ A X B = C / D ________________________ A / B = CX D _________________________ B / A = C X D _________________________

9. Rearrange. X A = ------- Y X = ------- and Y = -------

10. Clinical Example: Minute Ventilation = Tidal Volume x Frequency Solve for Vt: Solve for f:

11. Relationships between Variables • Relationships depend on: • How the formula is set up. • What is held constant. • When one of the numbers is held constant, the other two are related to each other • Directly (same direction) • Indirectly (opposite directions)

12. Indirect Relationship E = Vt x f If E is constant: When Vt increases, f must decrease When Vt decreases, f must increase This is an inverse relationship EXAMPLE: 5,000 mL/min = 500 mL/breath x 10 breaths/min If we want to keep minute ventilation constant, but want to increase the tidal volume to 1,000 mL/breath, what respiratory rate is needed? 5,000 mL/min =

13. Direct Relationship EXAMPLE: If Vt is 500mL/breath and the minute ventilation increases from 5000 mL/min to 10,000 mL/min, the rate must go from 10 breaths/minute to 20 breaths/minute to keep the tidal volume the same.

14. Summary The way a problem is set up will determine the relationship of the variables. • Give an example of a “Direct” relationship • Give an example of an “Indirect” relationship

15. ASSIGNMENTS • Sibberson’s Math Book – Chapter #1 • Read pages 1 and 4-5 • Third Sample Set page 5 • Self-Assessment