1. Formulas with Fractions 1MPES2 Ecole Supérieure de Commerce de Neuchâtel Pierre Marchal 21.03.2016 http://creativecommons.org/licences/by/3.0/ Attribute to: Tyler Wallace (University of Memphis)

2. Objectives of the course By the end of the course, you should be able to: – Distribute first – Clear the fraction – Solve formulas with fractions

3. Formulas with fractions Clear fractions by May have to first Multiplying by the Least Common Denominator distribute

4. EXAMPLES OF APPLICATION

5. for x To do that we will focus on the negative 7 which is multiplied by x and the positive 5 which is added to the x. We know that we do order of operation in reverse, so we must start with the adding and subtracting. So let us focus on 5, to get rid of the 5, as it is a positive 5, we need to subtract 5. Just as always, if we subtract 5 on the left, we subtract 5 on the right. Now, the 5s subtract out to zero, and all that remains on the left side is negative 7 x equals 21. Remember that because there is nothing between the negative 7 and the x, that implies the operation is the multiplication. So to get the x alone, we must do the opposite of the multiplying, which is dividing out negative 7. Doing the same thing to the other side, we notice that the negative 7s divide out. We are left with x equals 21 divided by negative 7 which is negative 3. Notice, the negative 3 is the number that we can plug in for x to make this equation true. Negative 7 times negative 3 is positive 21, and 5 more is 26. Let us try another example. LCD = x  x  5 + 4ax = b - 5 4ax = ÷4a x = b - 5 4a Solution b - 5

6. Verification Substitue x by solution Distribute then x PPMC = (b-5) Simplify then distribute CLT ✔

7. The opposite of a negative 2 is a positive 2. And if we add 2 on the right side, we also must ad 2 on the left side. Notice the 2s subtract out to zero and all that remains on the right side is the 4 x. On the left side 14 + 2 is 16. Now to get the x alone, right now we have 4 x, the opposite of multiplying is dividing. To get rid of the 4 and to get x alone we divide by 4, on both sides. The 4s divide out, and we are left with x = 16 fourth or 4. Again, notice the 4 is the number that makes this equation works. Replace the x by 4, we have 4 times 4 equals 16, minus 2 equals 14. First we add and subtract, then we multiply or dive to get the x alone. for b LCD = 2  2  - hc ÷ h = b 2A – hc h Solution 2A = hb+ hc = hb 2A – hc = 2 

8. Verification Substitute x by solution Distribute then x LCD = 2 Simplify then distribute CLT ✔

9. By the end of this course You are able to : – Distribute first – Clear the fraction – Solve formulas with fractions

10. Any question ?

11. THANK YOU FOR YOUR ATTENTION Be ready for the exam, so don’t forget to practice !