## Math 6A, Lesson 7, Fall 2018, 10/29/2018

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1. Quiz on negative number and addition of integers

2. Subtraction of integers:.subtraction is the reverse process of addition. Using a number line:

• Subtraction of a positive number is taken as a movement to the LEFT of the number line
• Subtraction of a negative number is taken as a movement to the RIGHT of the number line

(-3)  – 4

2 –  3

(-1) –  (-3)

2 –  (-5)

0 – (-4)

3. Rule for subtraction: to subtract integers, we change the sign of the integer being subtracted and add them together according to the rule for addition of integers.

For any integers a, and,b,

a – b = a + (-b)

4. Absolute value of the difference:

For any integers a, and,b,

|a – b| = |b – a|

5. Home Work:

• Handout: two pages
• Workbook:
• page 8: 7
• page 9: 17
• page 10: 20

## Math 6A, Lesson 6, Fall 2018, 10/21/2018

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1. Opposite Numbers (additive inverse): is a number that when added to a given number yields 0. The opposite number for any number x is -x. Note that x may be positive or negative.

(-5) + 5 = 0

x + (-x) = 0

On the number line, the numbers 5 and -5 are located at the same distance from zero. We say that the numbers 5 and -5 are opposites. We can also say that -5 is opposite to 5, and 5 is opposite to -5 on the number line.

• Addition of a positive number is taken as a movement to the RIGHT of the number line
• Addition of a negative number is taken as a movement to the LEFT of the number line

(-3) + 4

2 + 3

(-1) + (-3)

2 + (-5)

0 + (-4)

• If the signs of the integers being added are the same, the sum has the same sign as the integers and we add the absolute values of the integers

For any a > 0, and b > 0,

a + b = a + b;        3 + 5 = 8

(-a) + (-b) = -(a+b);         (-3) + (-5) = – (3 + 5) = -8

• If the signs of the integers being added are different,, the sum takes the sign of the integer with the greater absolute value and we find the difference of the absolute values of the integers.

For any a > 0, and b > 0,

a + (-b) = +(a – b) if a >=b;        9 + (-6) = +(9 – 6) = +3 = 3

a + (-b) = – (b -a) if b > a;         15 + (-20) = -(20 -15) = -5

-a + b = -(a – b) if a >= b;         -18 + 12 = -(18 -12) = -6

-a + b = +(b -a) if b > a;          -23 + 27 = +(27 – 23) = +4 = 4

4. Home Work:

• Handout: one page
• Workbook: page 7: 4

## Math 6A, Lesson 5, Fall 2018, 10/14/2018

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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: two pages
• Workbook: page 7: 1, 2, 3, 5