When doing these problems, try to also do them using your calculator, (if possible) to get more practice using it.
- Write the following expressions without absolute value bars, simplifying also, if possible:
- |8| =
- | –7.2| =
- |10 – 16| =
- |10| – |16| =
- |1 – 5| – | –3 – 6| =
- Rewrite the following without absolute values, leaving the answer in EXACT form:
- |2 – π| =
- Find the opposites of the following:
- 5. The opposite is: _____________
- –8. The opposite is: ____________
The opposite is: ___________- – (– 6). The opposite is: ________
- – x. The opposite is: ___________
- Perform the following operations:
- 8 + (–2) =
- –8 + 2 =
- –8 + (–2) =
- Subtract –2 from –8:
- –8 –2 =
- 8 × 2
- –8(2) =
- (– 8)(– 2) =
- 8 ÷ 2 =
- 43 =
- Find the square of negative five =
- What is the distance between –5 and 7?
- What is the distance between x and y?
- Which of the following is considered <well… by this tutor, anyway> as the BEST way to input "two times three" in a calculator?
- What is the expanded form of 64?
- Write the Exponential Notation for 7 × 7 × 7:
- What is the base of –52?
- What is the exponent of 95?
- Which operation is performed first for: 1 × 2 + 3 – 42
- Which of the following are not typical grouping symbols used in math expressions?
- What is PEMDAS?
- True or False. Subtraction has a higher order of precedence than Division. ________
- Simplify. Show all steps. Write work on a separate sheet of paper.
- –3 × 2 + 8 =
- (2 + 3) × 5 =
- (6 – 2)(8 + 1) =
- 2(1 – 3 + 22) =
- 10 – [2 + (4 – 23)] =
- (23)2 =
- 12 + 2[– 4 + (2 – 3)2] =
- – |– 3| + (8 + 2)2 =
- 7 – 6 + {5 – 4[1 – (2 + 3)]}
=
| (A) (2) (3) | (B) 2 (3) | (C) (2) 3 | (D) 2 × |
| (E) (2) × (3) | (F) 2 × (3) | (G) (2) × 3 |
| (A) [ ] | (B) { } | (C) ( ) | (E)  |
(F) | | |
Answers
- Write the following expressions without absolute value bars, simplifying also, if possible:
- |8| = 8
- | –7.2| = 7.2
- |10 – 16| = 6
- |10| – |16| = 10 – 16 = – 6
- |1 – 5| – | –3 – 6| = – 5
- Rewrite the following without absolute values, leaving the answer in EXACT form:
- |2 – π| = π – 2
- π –
- = 3 –
- Find the opposites of the following:
- 5. The opposite is: – 5
- –8. The opposite is: 8
- The opposite is:
- – (– 6). The opposite is: – 6
- – x. The opposite is: x
- Perform the following operations:
- 8 + (–2) = 6
- –8 + 2 = – 6
- –8 + (–2) = – 10
- Subtract –2 from –8:
This is written as: – 8 – (–2) = – 8 + 2 =– 6 - – 8 –2 = 8 – 8 + (– 2) = – 10
- 8 × 2 = 16
- – 8(2) = – 16
- (– 8)(– 2) = 16
- 8 ÷ 2 = 4
- – 4
- 43 = 4 × 4 × 4 = 64 (or just use calculator to get this value).
- Find the square of negative five = (– 5)2 = 25
- 1
- 301
Note: The answer is NOT – 25, since we want: (– 5)2 = (– 5)(– 5) = 25. A typical error is to write what was asked for as:
– 5 2 = 5 × 5 = – 25
- What is the distance between –5 and 7?
- What is the distance between x and y?
- Which of the following is considered by as the BEST way to input "two times three" in a calculator?
- What is the expanded form of 64?
- Write the Exponential Notation for 7 × 7 × 7:
- What is the base of –52?
- What is the exponent of 95?
- Which operation is performed first for: 1 × 2 + 3 – 42
- Which of the following are not typical grouping symbols used in math expressions?
- What is PEMDAS?
- True or False. Subtraction has a higher order of precedence than Division.
- Simplify. Steps are shown below each problem.
- –3 × 2 + 8 = 2
- (2 + 3) × 5 = 25
- (6 – 2)(8 + 1) = 36
- 2(1 – 3 + 22) = 4
- 10 – [2 + (4 – 23)] = 12
- (23)2 = 64
- 12 + 2[– 4 + (2 – 3)2] = 6
- – |– 3| + (8 + 2)2 = 97
- 7 – 6 + {5 – 4[1 – (2 + 3)]} = – 20
- = 4
- = – 5
Answer: 3 × 2 + 8 6 + 8 = 2
Answer: (2 + 3) × 5 = (5) × 5 = 25
Answer: (6 – 2) (8 + 1) <Do what is in both sets of parentheses first> = (4)(9) = 36
Answer: 2(1 – 3 + 2 = 2(1 – 3 + 22) = 2(1 – 3 + 22) = 2(1 – 3 + 4) = 2(1 – 3 + 4) = 2(– 2 + 4) = 2(– 2 + 4) = 2(2) = 4
Answer: 10 – [2 + (4 – 23)] = 10 – [2 + (4 – 23)] = 10 – [2 + (4 – 8)] = 10 – [2 + (4 – 8)] = 2(– 2 + 4) = 10 – [2 + (– 4)] = 10 – [2 + (–4)] = 10 – [– 2] = 10 + 2 = 12
Answer: (23)2 = (83) = 64
Answer: 12 + 2[– 4 + (2 – 3)2] = 12 + 2[– 4 + (– 1)2] = 12 + 2[– 4 + (– 1)2] = 10 – [2 + (4 – 8)] = 12 + 2[– 4 + 1] = 12 + 2[– 4 + 1] = 12 + 2[– 3] = 12 + ( – 6) <parantheses placed for clarity> = 6
Answer: – |– 3| + (8 + 2)2<do what’s in the grouping symbol first> = – (3) + (10)2 <parantheses placed around the 3 for clarity> = – (3) + (10)2 = 10 – [2 + (4 – 8)] = 12 + 2[– 4 + 1] = – (3) + 100 = – (3) + 100 = 97
Answer: 7 – 6 + {5 – 4[1 – (2 + 3)]} = 7 – 6 + {5 – 4[1 – (2 + 3)]} = 7 – 6 + {5 – 4[1 – 5]} = 7 – 6 + {5 – 4[1 – 5]} = 7 – 6 + {5 – 4[– 4]} = 7 – 6 + {5 – (– 16)} = 7 – 6 + {5 + 16} = 7 – 6 + {21} = 7 – 6 + {21}<If only a plus sign is in "front" of a grouping = 7 – 6 + 21 symbol, the grouping symbol may be removed. = 7 – 21 So the braces are removed> = – 20
Answer: <I will do steps in both the numerator & denominator> = 27 – 1 + 6
4 × 3 – 4= 27 – 1 + 6
4 × 3 – 4= 26 + 6
12 – 4= 32
8= 4
Answer: = = 
= 
= 
= 
= 
= – 11 – 3 [– 2] = – 11 – (– 6) = – 11 + 6 = – 5
Using the distance formula, we get: |7 – (– 5)| = |7 + 5| = |12| = 12
By The Way… We could have also written: |x – y|
| (A) (2) (3) | (B) 2 (3) | (C) (2) 3 | (D) 2 × 3 |
| (E) (2) × (3) | (F) 2 × (3) | (G) (2) × 3 |
By The Way… All of the above are acceptable. I want you to use the one that would involve the fewest keystrokes; however, if you need to add more keystrokes so that the expression seems clearer to you, then go ahead and add more.
Answer: 6 × 6 × 6 × 6
Answer: 73
Answer: The base is 5. The base is NOT –5. By "order of precedence," the square is just with the 5, and does not include the negative sign. If we wanted the base to be –5, then the expression should have been written: (– 5)2.
Answer: The exponent is 5.
Answer: The Exponent or Square the Four. Exponents are done before the other operations.
| (A) [ ] | (B) { } | (C) ( ) | (D) |
(E) | | |
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
Answer: FALSE. Subtraction (along with addition) has the lowest order of precedence presented in this lesson.