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:
  • two page
• Page 33:
  • 1, 2, 3, 4

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

Continue on Chapter 5.4 Forming Linear Equations to Solve Problems

1. Quiz

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:

• Handout
  • Two pages
• Workbook:
  • Page 31: 21, 22, 23, 24, 25
  • Page 32: 26, 27, 28, 29

Chapter 5.3 Simple Fractional Equations

Chapter 5.4 Forming Linear Equations to Solve Problems

1. Fractional equation: when the variable of an equation is in the denominations of a term, the equation is called fractional equation

6 /(x – 2) = 3

1/(x + 3) = 2/x

Note: it is important to check the solutions, that they can’t be those values that make a denominator of the original equation zero.

2. Constructing/Forming Linear Equations to Solve Problems

Two pages handout of teaching material. 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. Review basic concept of “open parenthesis”

• 2(3x+y) – 5(0.2x-0.6y) =
• -2(3x+y) + 5(0.2x-0.6y) =
• -2(3x-y) + 5(-0.2x-0.6y) =
• 2(3x-y) – 5(0.2x+0.6y) =

4.Homework:

• Handout
  • Two pages
• Workbook:
  • Page 30: 15, 16, 17, 18, 19, 20

Chapter 5.2. Equations involving Parentheses

1. We apply the distributive law of multiplication over addition to help us solve equations involving parentheses.

Recall a(x + b) = ax + ab

Solve equation 9(x + 1) = 2(3x + 8)

2. When working with equations, always apply the same action to both sides of the equation.

Solve equation 5(2x – 9)/3 -8 = 2x

Solve equation (3x + 2)/5 = (4x – 7)/6

3. Rewriting equations

Giving the formula A = ½ * (a + b)h, find the value of a when b = 13, h = 9, and A = 90.

4. Homework:

• Handout
  • Two pages
• Workbook:
  • Page 27: 4
  • Page 28: 5
  • Page 29: 11, 12, 13, 14