**Exam on ratio, rate, average rate, speed, uniform/constant speed and average speed, and Conversion of units.**

## Math 6A, Lesson 11, Spring 2021, 5/2/2021

## Math 6A, Lesson 10, Spring 2021, 4/11/2021

**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 9, Spring 2021, 4/4/2021

**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 8, Spring 2021, 4/3/2021

**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