Math 6A, Lesson 9, Spring 2020, 4/26/2020

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1. Average Rate

Rate involves two quantities and it is usually expressed as one quantity per unit of another quantity.

• \$/oz, mile/gal, words/min, \$/sq.ft, \$/hour

2. Speed, uniform/constant speed and average speed

• Speed = (distance traveled) / (time taken)
• Average Speed =  (Total distance traveled) / (total time taken)

3. Conversion of units

• km/hr → m/s → miles/hr
• \$/inch → \$/ft
• \$/ticket → euro/ticket

4. Home Work:

• Handout:
• Three pages
• Workbook:
• Page 34: 5, 6, 7, 8, 9, 10
• Page 35: 11, 12, 13, 14, 15, 16, 17
• Page 36: 18, 19, 20, 21, 22

Math 6A, Lesson 8, Spring 2020, 4/19/2020

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1. Ratio

• Meaning of ratio – Given any two similar quantities, a and b, the ratio of a to b (denoted by a:b) is defined as a:b = a/b, where b != 0
• The quantities have to have same/similar unit.
• Simplification of ratios: a:b = (ma): (mb) =  (a/m): (b/m), where m !=0

2. Ratios of three quantities: the ratio involving three quantities cannot be written as a fraction. However, it can be simplified by multiplying or dividing each term by the same constant.  For example, a:b = 5:6, b:c = 8:11, find a:b:c. Recall LCM, we convert each ratio to an equivalent ratio where the new value of b is the LCM of the original values of b:

• a:b = 5:6 = 5*4 : 6*4 = 20:24
• b:c = 8:11 = 8*3 :11*3 = 24:33
• hence , a:b:c = 20:24:33

3. Word problems involving ratios

4. Home Work:

• Handout:
• three pages
• Page 33:
• 1, 2, 3, 4

Math 6A, Lesson 7, Spring 2020, 4/5/2020

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Continue on Chapter 5.4 Forming Linear Equations to Solve Problems

1. Midterm Exam: all about equations

2. Constructing/Forming Linear Equations to Solve Problems

The steps involved in problem solving with linear equations are:

• Step 1. Read the question carefully and identify the unknown quantity
• Step 2. Use a letter to represent the unknown quantity (e.g. x)
• Step 3. Express other quantities in terms of x
• Step 4. Construct/Form an equation based on the given information
• Step 5. Solve the equation
• Step 6. Write down the answer statement

3. Homework:

• Redo the problems you got wrong in last two homework assignments