1. Lesson 66: Signs of Fractions, 30-60-90 Degree Triangles

2. Every fraction has three signs
Every fraction has three signs. If one of the signs is not written, it is understood to be a plus sign. One of the signs is in front of the fraction, and the other two are above and below, as shown here

3. In this case it is unnecessary to record the plus signs, for the fraction can be written with just one sign as -3/4.

4. Any two of the three signs of a fraction may be changed without changing the value of the fraction.+3 +4
+ -3
+ +3 -4 -3

5. Each of these four notations designates the same number, which is – ¾
Each of these four notations designates the same number, which is – ¾. We find that the ability to change signs is often helpful when we add fractions.

6. Example: Add 1 7a x – 3 -x + 3

7. Answer: 1 + 7a x – 3 x – a x – 3

8. Example: Add 4x + 5 + 2x – 3 x – 3 3 – x

9. Answer: 4x + 5 + -2x + 3 x – 3 x – 3 2x + 8 x – 3

10. Right triangles whose acute angles are 30° and 60° are encountered often in physics and engineering. These triangles are often called degree triangles. These triangles are all similar to the following triangle.

12. Sometimes we forget the lengths of the sides of this triangle and forget which length goes where. If we can remember to begin with an equilateral triangle whose sides are 2 units long, we can develop this triangle quickly.

13. Example: Use similar triangles to find x and y.
60°

14. Answer: X = 5√3 2 Y = 5/2

15. HW: Lesson 66 #1-30