Lesson notes
Problem set 0.1
Problem set 1
Problem set 2
Problem set 3
Problem set 4
Problem set 5
Problem set 6
Problem set 7
Problem set 8
Problem set 9
Problem set 10
Problem set 11
Problem set 12
Problem set 13
Problem set 14

Lesson notes

• Purpose of using parentheses is to group parts of an expressions into whole units.
• In each step of algebra work, ask yourself if parentheses need to be added to group parts of an expression into whole units.
  • For example, if we want to evaluate when , we note that should be getting squared and whatever we put in place of as a whole must be squared. So, would evaluate to , not .
  • As a second example, if and , and we want to express in terms of , we write , not . Again, this is because in evaluating , whatever comes in place of , in this case , as a whole must be squared.
  • As another example, is equal to , not . This is because in , the second fraction is being subtracted, and when we subtract the numerator of the second fraction from the first, we need to subtract the whole of the second fraction’s numerator.
  • Sometimes, grouping of a part of an expression into a whole comes for free because of PEMDAS. For example, if and , and we want to express in terms of , we just say . Here, there is no reason to use parentheses around when replacing in because PEMDAS ensures is evaluated first and then 3 is added in evaluating .

Problem set 0.1

For each of the following, get rid of parentheses appropriately and simplify.

1. 
2. 

Problem set 1

For each of the following, get rid of parentheses appropriately and simplify.

1. 
2. 
3. 
4. 
5. 

Problem set 2

For each of the following, get rid of parentheses appropriately and simplify.

1. 
2. 
3. 
4. 
5. 

Problem set 3

For each of the following, get rid of parentheses appropriately and simplify.

1. 
2. 
3. 
4. 
5. 

Problem set 4

For each of the following, get rid of parentheses appropriately and simplify.

1. 
2. 
3. 
4. 
5. 

Problem set 5

For each of the following, get rid of parentheses appropriately and simplify.

1. 
2. 
3. 
4. 
5. 

Problem set 6

Which of the following are true? Justify with reasons.

1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 

Problem set 7

Which of the following are true? Justify with reasons.

1. 
2. 
3. 
4. 
5. 
6. 
7. 

Problem set 8

Which of the following are true? Justify with reasons.

1. 
2. 
3. 
4. 
5. 
6. 
7. 

Problem set 9

Which of the following are true? Justify with reasons.

1. 
2. 
3. 

Problem set 10

For each of the following problems, assume what is given and express in terms of .

1. and
2. and
3. and
4. and
5. and

Problem set 11

Simplify each of the following as possible.

1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 

Problem set 12

For each of the following problems, assume what is given and express in terms of .

1. and
2. and
3. and
4. and
5. and
6. and

Problem set 13

Simplify each of the following.

1. 
2. 
3. 
4. 
5. 
6. 

Problem set 14

Which of the following are true? Justify with reasons.

1. 
2. 
3. 
4. 
5. 
6.