**Math 6A, Lesson 5, Fall 2017, 10/15/2017**

**1. Negative Numbers**: we often across quantities that have opposite directions or meanings. For example, traveling due east and west, the rise and fall in price, profit and loss, and being above or below sea level. When we assign a certain meaning of quantity to be **positive**, a value of the quantity that has the opposite meaning may be considered as **negative** and is represented with a **“-”** sign.

Positive numbers: 1, 2, 3, 0.8, ⅜, …

Negative numbers: -1, -2, -3, -⅔, -0.0025, …

Meanings of positive and negative numbers: teaching on whiteboard in the class.

**2. The (horizontal) number line:**

**How to draw a number line:**

- Draw a line, and mark the zero point on it;
- Choose a unit length, e.g., 1 cm, to mark the points 1, 2, 3, … at equal unit intervals on the right of 0, and the points -1, -2, -3, … on the left of 0;
- Draw an arrow at each end.

**Inequality signs:**

- > greater than
- < less than
- >= greater or equal
- <= less than or equal

**On a horizontal number line:**

- All the positive numbers are to the right of 0
- All the negative numbers are to the left of 0
- Numbers are arranged in ascending (increasing) order from left to right
- Every number is smaller than any number on its right and greater than any number on its left

**3. Absolute Value:** the absolute value of a number is the distance that number is from 0 on the number line. Both 3 and -3 are the same distance from 0. The absolute value of a number is never negative.

|3| = 3, or |x| = x if x >= 0

|-3| = 3, or |x| = -x if x < 0

**4. Home Work:**

- Handout: one page
- Workbook: page 7: 1, 2, 3, 5