![Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-25-320.jpg)
![Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-26-320.jpg)
![Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-27-320.jpg)
![Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-28-320.jpg)
![Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-29-320.jpg)
![Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
= 9 – 2[ –14 ]
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-30-320.jpg)
![Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
= 9 – 2[ –14 ]
= 9 + 28
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-31-320.jpg)
![Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
= 9 – 2[ –14 ]
= 9 + 28
= 37
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-32-320.jpg)
![Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
c. 9 – 2[7 – 3(6 + 1)]
= 9 – 2[7 – 3(7)]
= 9 – 2[7 – 21]
= 9 – 2[ –14 ]
= 9 + 28
= 37
(Don’t perform “4 + 3” or “9 – 2” in the above problems!!)
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-33-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Coefficients
Starting with 0, adding N copies
of x’s to 0 is written as Nx:](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-34-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Coefficients
Starting with 0, adding N copies
of x’s to 0 is written as Nx:
0 + x + x + x .. + x = Nx
N copies added](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-35-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Coefficients
Starting with 0, adding N copies
of x’s to 0 is written as Nx:
So 0 = 0x
0 + x + x + x .. + x = Nx
N copies added
0 + x = 1x
0 + x + x = 2x
0 + x + x + x = 3x
0 + x + x + x + x = 4x
.](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-36-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Coefficients
Starting with 0, adding N copies
of x’s to 0 is written as Nx:
So 0 = 0x
0 + x + x + x .. + x = Nx
N copies added
0 + x = 1x
0 + x + x = 2x
0 + x + x + x = 3x
The number N of added copies is called the coefficient.
0 + x + x + x + x = 4x
.](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-37-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Coefficients
Starting with 0, adding N copies
of x’s to 0 is written as Nx:
So 0 = 0x
0 + x + x + x .. + x = Nx
N copies added
0 + x = 1x
0 + x + x = 2x
0 + x + x + x = 3x
The number N of added copies is called the coefficient.
So the coefficient of 3x is 3.
0 + x + x + x + x = 4x
.](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-38-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Coefficients
Starting with 0, adding N copies
of x’s to 0 is written as Nx:
So 0 = 0x
0 + x + x + x .. + x = Nx
N copies added
0 + x = 1x
0 + x + x = 2x
0 + x + x + x = 3x
The number N of added copies is called the coefficient.
So the coefficient of 3x is 3.
Similarly ab + ab + ab + ab is 4ab, with coefficient 4,
0 + x + x + x + x = 4x
.](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-39-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Coefficients
Starting with 0, adding N copies
of x’s to 0 is written as Nx:
So 0 = 0x
0 + x + x + x .. + x = Nx
N copies added
0 + x = 1x
0 + x + x = 2x
0 + x + x + x = 3x
The number N of added copies is called the coefficient.
So the coefficient of 3x is 3.
Similarly ab + ab + ab + ab is 4ab, with coefficient 4,
and that 3(x + y) is (x + y) + (x + y) + (x + y).
0 + x + x + x + x = 4x
.](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-40-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Coefficients
Starting with 0, adding N copies
of x’s to 0 is written as Nx:
So 0 = 0x
0 + x + x + x .. + x = Nx
N copies added
0 + x = 1x
0 + x + x = 2x
0 + x + x + x = 3x
The number N of added copies is called the coefficient.
So the coefficient of 3x is 3.
Similarly ab + ab + ab + ab is 4ab, with coefficient 4,
and that 3(x + y) is (x + y) + (x + y) + (x + y). Note that 0x = 0.
0 + x + x + x + x = 4x
.](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-41-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
Starting with 1, multiplying N copies
of x’s to 1 is written as xN.](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-42-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
Starting with 1, multiplying N copies
of x’s to 1 is written as xN.
1* x * x * x…* x as xN
N copies of x’s](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-43-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
Starting with 1, multiplying N copies
of x’s to 1 is written as xN.
1* x * x * x…* x as xN
N copies of x’s
1 * x = x1
1 * x * x = x2
1 * x * x * x = x3
1 * x * x * x * x = x4
.
So](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-44-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
Starting with 1, multiplying N copies
of x’s to 1 is written as xN.
1* x * x * x…* x as xN
N copies of x’s
1 * x = x1
1 * x * x = x2
1 * x * x * x = x3
1 * x * x * x * x = x4
.
So 1 = x0 (x ≠ 0)](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-45-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
Starting with 1, multiplying N copies
of x’s to 1 is written as xN.
1* x * x * x…* x as xN
N copies of x’s
1 * x = x1
1 * x * x = x2
1 * x * x * x = x3
The number of multiplied copies N of xN is called the exponent.
1 * x * x * x * x = x4
.
So 1 = x0 (x ≠ 0)](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-46-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
Starting with 1, multiplying N copies
of x’s to 1 is written as xN.
1* x * x * x…* x as xN
N copies of x’s
1 * x = x1
1 * x * x = x2
1 * x * x * x = x3
The number of multiplied copies N of xN is called the exponent.
So the exponent of x3 is 3.
1 * x * x * x * x = x4
.
So 1 = x0 (x ≠ 0)](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-47-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
Starting with 1, multiplying N copies
of x’s to 1 is written as xN.
1* x * x * x…* x as xN
N copies of x’s
1 * x = x1
1 * x * x = x2
1 * x * x * x = x3
The number of multiplied copies N of xN is called the exponent.
So the exponent of x3 is 3.
An exponent applies only to the quantity directly under it.
1 * x * x * x * x = x4
.
So 1 = x0 (x ≠ 0)](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-48-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
Starting with 1, multiplying N copies
of x’s to 1 is written as xN.
So 1 = x0 (x ≠ 0)
1* x * x * x…* x as xN
N copies of x’s
1 * x = x1
1 * x * x = x2
1 * x * x * x = x3
The number of multiplied copies N of xN is called the exponent.
So the exponent of x3 is 3.
An exponent applies only to the quantity directly under it.
So ab3 = a*b*b*b and that (ab)3 = ab*ab*ab.
1 * x * x * x * x = x4
.](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-49-320.jpg)
![Exercise: Don’t do the part that you shouldn’t do!
1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4)
3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)]
Order of Operations
Ans: a. 18 b. 18 c. 23 4. 15
Exponents
Starting with 1, multiplying N copies
of x’s to 1 is written as xN.
So 1 = x0 (x ≠ 0)
1* x * x * x…* x as xN
N copies of x’s
1 * x = x1
1 * x * x = x2
1 * x * x * x = x3
The number of multiplied copies N of xN is called the exponent.
So the exponent of x3 is 3.
An exponent applies only to the quantity directly under it.
So ab3 = a*b*b*b and that (ab)3 = ab*ab*ab. Note that x0 =1.
1 * x * x * x * x = x4
.](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-50-320.jpg)
![Make sure that you interpret the operations correctly.
Exercise A. Calculate the following expressions.
Order of Operations
7. 1 + 2(3) 8. 4 – 5(6) 9. 7 – 8(–9)
1. 3(–3) 2. (3) – 3 3. 3 – 3(3) 4. 3(–3) + 3
5. +3(–3)(+3) 6. 3 + (–3)(+3)
B.Make sure that you don’t do the ± too early.
10. 1 + 2(3 – 4) 11. 5 – 6(7 – 8) 12. (4 – 3)2 + 1
13. [1 – 2(3 – 4)] – 2 14. 6 + [5 + 6(7 – 8)](+5)
15. 1 + 2[1 – 2(3 + 4)] 16. 5 – 6[5 – 6(7 – 8)]
17. 1 – 2[1 – 2(3 – 4)] 18. 5 + 6[5 + 6(7 – 8)]
19. (1 + 2)[1 – 2(3 + 4)] 20. (5 – 6)[5 – 6(7 – 8)]
C.Make sure that you apply the powers to the correct bases.
23. (–2)2 and –22 24 (–2)3 and –23 25. (–2)4 and –24
26. (–2)5 and –25 27. 2*32 28. (2*3)2
21. 1 – 2(–3)(–4) 22. (–5)(–6) – (–7)(–8)](https://image.slidesharecdn.com/1-s4orderofoperations-110622200533-phpapp01/85/1-s4-order-of-operations-94-320.jpg)
1 s4 order of operations
- 2. If we have two $5-bills and two $10-bills, Order of Operations
- 3. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. Order of Operations
- 4. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, Order of Operations
- 5. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. Order of Operations
- 6. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, Order of Operations
- 7. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, we have 3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $. Order of Operations
- 8. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, we have 3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $. In this case, we group the 3 + 4 in the “( )” to indicate that we are to add them first, Order of Operations
- 9. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, we have 3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $. In this case, we group the 3 + 4 in the “( )” to indicate that we are to add them first, then multiply the sum to 10. Order of Operations
- 10. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, we have 3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $. In this case, we group the 3 + 4 in the “( )” to indicate that we are to add them first, then multiply the sum to 10. Order of Operations This motivates us to set the rules for the order of operations.
- 11. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, we have 3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $. In this case, we group the 3 + 4 in the “( )” to indicate that we are to add them first, then multiply the sum to 10. Order of Operations Order of Operations (excluding raising power) This motivates us to set the rules for the order of operations.
- 12. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, we have 3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $. In this case, we group the 3 + 4 in the “( )” to indicate that we are to add them first, then multiply the sum to 10. Order of Operations Order of Operations (excluding raising power) Given an arithmetic expression, we perform the operations in the following order . This motivates us to set the rules for the order of operations.
- 13. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, we have 3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $. In this case, we group the 3 + 4 in the “( )” to indicate that we are to add them first, then multiply the sum to 10. Order of Operations Order of Operations (excluding raising power) Given an arithmetic expression, we perform the operations in the following order . 1st . Do the operations within grouping symbols, starting with the innermost grouping symbol. This motivates us to set the rules for the order of operations.
- 14. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, we have 3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $. In this case, we group the 3 + 4 in the “( )” to indicate that we are to add them first, then multiply the sum to 10. Order of Operations Order of Operations (excluding raising power) Given an arithmetic expression, we perform the operations in the following order . 1st . Do the operations within grouping symbols, starting with the innermost grouping symbol. 2nd. Do multiplications and divisions (from left to right). This motivates us to set the rules for the order of operations.
- 15. If we have two $5-bills and two $10-bills, we have the total of 2(5) + 2(10) = 30 dollars. To get the correct answer 30, we multiply the 2 and the 5 and multiply the 2 and the10 first, then we add the products 10 and 20. If I have three $10-bills and you have four $10-bills, we have 3 + 4 = 7 $10-bills, and we have a total of (3 + 4)10 = 70 $. In this case, we group the 3 + 4 in the “( )” to indicate that we are to add them first, then multiply the sum to 10. Order of Operations Order of Operations (excluding raising power) Given an arithmetic expression, we perform the operations in the following order . 1st . Do the operations within grouping symbols, starting with the innermost grouping symbol. 2nd. Do multiplications and divisions (from left to right). 3rd. Do additions and subtractions (from left to right). This motivates us to set the rules for the order of operations.
- 16. Example A. a. 4(–8) + 3(5) Order of Operations
- 17. Example A. a. 4(–8) + 3(5) Order of Operations
- 18. Example A. a. 4(–8) + 3(5) = –32 + 15 Order of Operations
- 19. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 Order of Operations
- 20. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 Order of Operations b. 4 + 3(5 + 2)
- 21. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 Order of Operations b. 4 + 3(5 + 2)
- 22. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7)
- 23. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21
- 24. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 25. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 c. 9 – 2[7 – 3(6 + 1)] Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 26. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 c. 9 – 2[7 – 3(6 + 1)] Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 27. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 c. 9 – 2[7 – 3(6 + 1)] = 9 – 2[7 – 3(7)] Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 28. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 c. 9 – 2[7 – 3(6 + 1)] = 9 – 2[7 – 3(7)] Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 29. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 c. 9 – 2[7 – 3(6 + 1)] = 9 – 2[7 – 3(7)] = 9 – 2[7 – 21] Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 30. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 c. 9 – 2[7 – 3(6 + 1)] = 9 – 2[7 – 3(7)] = 9 – 2[7 – 21] = 9 – 2[ –14 ] Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 31. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 c. 9 – 2[7 – 3(6 + 1)] = 9 – 2[7 – 3(7)] = 9 – 2[7 – 21] = 9 – 2[ –14 ] = 9 + 28 Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 32. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 c. 9 – 2[7 – 3(6 + 1)] = 9 – 2[7 – 3(7)] = 9 – 2[7 – 21] = 9 – 2[ –14 ] = 9 + 28 = 37 Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 33. Example A. a. 4(–8) + 3(5) = –32 + 15 = –17 c. 9 – 2[7 – 3(6 + 1)] = 9 – 2[7 – 3(7)] = 9 – 2[7 – 21] = 9 – 2[ –14 ] = 9 + 28 = 37 (Don’t perform “4 + 3” or “9 – 2” in the above problems!!) Order of Operations b. 4 + 3(5 + 2) = 4 + 3(7) = 4 + 21 = 25
- 34. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Coefficients Starting with 0, adding N copies of x’s to 0 is written as Nx:
- 35. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Coefficients Starting with 0, adding N copies of x’s to 0 is written as Nx: 0 + x + x + x .. + x = Nx N copies added
- 36. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Coefficients Starting with 0, adding N copies of x’s to 0 is written as Nx: So 0 = 0x 0 + x + x + x .. + x = Nx N copies added 0 + x = 1x 0 + x + x = 2x 0 + x + x + x = 3x 0 + x + x + x + x = 4x .
- 37. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Coefficients Starting with 0, adding N copies of x’s to 0 is written as Nx: So 0 = 0x 0 + x + x + x .. + x = Nx N copies added 0 + x = 1x 0 + x + x = 2x 0 + x + x + x = 3x The number N of added copies is called the coefficient. 0 + x + x + x + x = 4x .
- 38. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Coefficients Starting with 0, adding N copies of x’s to 0 is written as Nx: So 0 = 0x 0 + x + x + x .. + x = Nx N copies added 0 + x = 1x 0 + x + x = 2x 0 + x + x + x = 3x The number N of added copies is called the coefficient. So the coefficient of 3x is 3. 0 + x + x + x + x = 4x .
- 39. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Coefficients Starting with 0, adding N copies of x’s to 0 is written as Nx: So 0 = 0x 0 + x + x + x .. + x = Nx N copies added 0 + x = 1x 0 + x + x = 2x 0 + x + x + x = 3x The number N of added copies is called the coefficient. So the coefficient of 3x is 3. Similarly ab + ab + ab + ab is 4ab, with coefficient 4, 0 + x + x + x + x = 4x .
- 40. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Coefficients Starting with 0, adding N copies of x’s to 0 is written as Nx: So 0 = 0x 0 + x + x + x .. + x = Nx N copies added 0 + x = 1x 0 + x + x = 2x 0 + x + x + x = 3x The number N of added copies is called the coefficient. So the coefficient of 3x is 3. Similarly ab + ab + ab + ab is 4ab, with coefficient 4, and that 3(x + y) is (x + y) + (x + y) + (x + y). 0 + x + x + x + x = 4x .
- 41. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Coefficients Starting with 0, adding N copies of x’s to 0 is written as Nx: So 0 = 0x 0 + x + x + x .. + x = Nx N copies added 0 + x = 1x 0 + x + x = 2x 0 + x + x + x = 3x The number N of added copies is called the coefficient. So the coefficient of 3x is 3. Similarly ab + ab + ab + ab is 4ab, with coefficient 4, and that 3(x + y) is (x + y) + (x + y) + (x + y). Note that 0x = 0. 0 + x + x + x + x = 4x .
- 42. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Exponents Starting with 1, multiplying N copies of x’s to 1 is written as xN.
- 43. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Exponents Starting with 1, multiplying N copies of x’s to 1 is written as xN. 1* x * x * x…* x as xN N copies of x’s
- 44. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Exponents Starting with 1, multiplying N copies of x’s to 1 is written as xN. 1* x * x * x…* x as xN N copies of x’s 1 * x = x1 1 * x * x = x2 1 * x * x * x = x3 1 * x * x * x * x = x4 . So
- 45. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Exponents Starting with 1, multiplying N copies of x’s to 1 is written as xN. 1* x * x * x…* x as xN N copies of x’s 1 * x = x1 1 * x * x = x2 1 * x * x * x = x3 1 * x * x * x * x = x4 . So 1 = x0 (x ≠ 0)
- 46. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Exponents Starting with 1, multiplying N copies of x’s to 1 is written as xN. 1* x * x * x…* x as xN N copies of x’s 1 * x = x1 1 * x * x = x2 1 * x * x * x = x3 The number of multiplied copies N of xN is called the exponent. 1 * x * x * x * x = x4 . So 1 = x0 (x ≠ 0)
- 47. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Exponents Starting with 1, multiplying N copies of x’s to 1 is written as xN. 1* x * x * x…* x as xN N copies of x’s 1 * x = x1 1 * x * x = x2 1 * x * x * x = x3 The number of multiplied copies N of xN is called the exponent. So the exponent of x3 is 3. 1 * x * x * x * x = x4 . So 1 = x0 (x ≠ 0)
- 48. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Exponents Starting with 1, multiplying N copies of x’s to 1 is written as xN. 1* x * x * x…* x as xN N copies of x’s 1 * x = x1 1 * x * x = x2 1 * x * x * x = x3 The number of multiplied copies N of xN is called the exponent. So the exponent of x3 is 3. An exponent applies only to the quantity directly under it. 1 * x * x * x * x = x4 . So 1 = x0 (x ≠ 0)
- 49. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Exponents Starting with 1, multiplying N copies of x’s to 1 is written as xN. So 1 = x0 (x ≠ 0) 1* x * x * x…* x as xN N copies of x’s 1 * x = x1 1 * x * x = x2 1 * x * x * x = x3 The number of multiplied copies N of xN is called the exponent. So the exponent of x3 is 3. An exponent applies only to the quantity directly under it. So ab3 = a*b*b*b and that (ab)3 = ab*ab*ab. 1 * x * x * x * x = x4 .
- 50. Exercise: Don’t do the part that you shouldn’t do! 1. 6 + 3(3 + 1) 2. 10 – 4(2 – 4) 3. 5 + 2[3 + 2(1 + 2)] 4. 5 – 2[3 + 2(5 – 9)] Order of Operations Ans: a. 18 b. 18 c. 23 4. 15 Exponents Starting with 1, multiplying N copies of x’s to 1 is written as xN. So 1 = x0 (x ≠ 0) 1* x * x * x…* x as xN N copies of x’s 1 * x = x1 1 * x * x = x2 1 * x * x * x = x3 The number of multiplied copies N of xN is called the exponent. So the exponent of x3 is 3. An exponent applies only to the quantity directly under it. So ab3 = a*b*b*b and that (ab)3 = ab*ab*ab. Note that x0 =1. 1 * x * x * x * x = x4 .
- 51. Order of Operations Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer.
- 52. Order of Operations Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3).
- 53. Order of Operations Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3)
- 54. Order of Operations Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 55. Order of Operations b. Expand – 32 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 56. Order of Operations b. Expand – 32 The base of the 2nd power is 3. Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 57. Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 58. Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) = – 9 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 59. c. Expand (3*2)2 and simplify the answer. Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) = – 9 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 60. c. Expand (3*2)2 and simplify the answer. The base for the 2nd power is (3*2). Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) = – 9 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 61. c. Expand (3*2)2 and simplify the answer. The base for the 2nd power is (3*2). Hence(3*2)2 is (3*2)(3*2) Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) = – 9 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 62. c. Expand (3*2)2 and simplify the answer. The base for the 2nd power is (3*2). Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36 Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) = – 9 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 63. c. Expand (3*2)2 and simplify the answer. The base for the 2nd power is (3*2). Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36 d. Expand 3*22 and simplify the answer. Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) = – 9 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 64. c. Expand (3*2)2 and simplify the answer. The base for the 2nd power is (3*2). Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36 d. Expand 3*22 and simplify the answer. The base for the 2nd power is 2. Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) = – 9 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 65. c. Expand (3*2)2 and simplify the answer. The base for the 2nd power is (3*2). Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36 d. Expand 3*22 and simplify the answer. The base for the 2nd power is 2. Hence 3*22 means 3*2*2 Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) = – 9 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 66. c. Expand (3*2)2 and simplify the answer. The base for the 2nd power is (3*2). Hence(3*2)2 is (3*2)(3*2) = (6)(6) = 36 d. Expand 3*22 and simplify the answer. The base for the 2nd power is 2. Hence 3*22 means 3*2*2 = 12 Order of Operations b. Expand – 32 The base of the 2nd power is 3. Hence – 32 means – (3*3) = – 9 Example B. (Exponential Notation) a. Expand (–3)2 and simplify the answer. The base is (–3). Hence (–3)2 is (–3)(–3) = 9
- 67. Order of Operations e. Expand (–3y)3 and simplify the answer.
- 68. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y)
- 69. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative)
- 70. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative) = –(3)(3)(3)(y)(y)(y)
- 71. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative) = –(3)(3)(3)(y)(y)(y) = –27y3
- 72. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative) = –(3)(3)(3)(y)(y)(y) = –27y3 From part b above, we see that the power is to be carried out before multiplication.
- 73. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative) = –(3)(3)(3)(y)(y)(y) = –27y3 From part b above, we see that the power is to be carried out before multiplication. Below is the complete rules of order of operations.
- 74. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative) = –(3)(3)(3)(y)(y)(y) = –27y3 Order of Operations (PEMDAS) From part b above, we see that the power is to be carried out before multiplication. Below is the complete rules of order of operations.
- 75. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative) = –(3)(3)(3)(y)(y)(y) = –27y3 Order of Operations (PEMDAS) 1st. (Parenthesis) Do the operations within grouping symbols, starting with the innermost one. From part b above, we see that the power is to be carried out before multiplication. Below is the complete rules of order of operations.
- 76. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative) = –(3)(3)(3)(y)(y)(y) = –27y3 Order of Operations (PEMDAS) 1st. (Parenthesis) Do the operations within grouping symbols, starting with the innermost one. 2nd. (Exponents) Do the exponentiation From part b above, we see that the power is to be carried out before multiplication. Below is the complete rules of order of operations.
- 77. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative) = –(3)(3)(3)(y)(y)(y) = –27y3 Order of Operations (PEMDAS) 1st. (Parenthesis) Do the operations within grouping symbols, starting with the innermost one. 2nd. (Exponents) Do the exponentiation 3rd. (Multiplication and Division) Do multiplications and divisions in order from left to right. From part b above, we see that the power is to be carried out before multiplication. Below is the complete rules of order of operations.
- 78. Order of Operations e. Expand (–3y)3 and simplify the answer. (–3y)3 = (–3y)(–3y)(–3y) (the product of three negatives number is negative) = –(3)(3)(3)(y)(y)(y) = –27y3 Order of Operations (PEMDAS) 1st. (Parenthesis) Do the operations within grouping symbols, starting with the innermost one. 2nd. (Exponents) Do the exponentiation 3rd. (Multiplication and Division) Do multiplications and divisions in order from left to right. 4th. (Addition and Subtraction) Do additions and subtractions in order from left to right. From part b above, we see that the power is to be carried out before multiplication. Below is the complete rules of order of operations.
- 79. Example C. Order of Operations a. 52 – 32 Order of Operations
- 80. Example C. Order of Operations a. 52 – 32 = 25 – 9 Order of Operations
- 81. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 Order of Operations
- 82. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 Order of Operations
- 83. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 Order of Operations
- 84. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 Order of Operations
- 85. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 c. –2*32 + (2*3)2 Order of Operations
- 86. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 c. –2*32 + (2*3)2 = –2*9 + (6)2 Order of Operations
- 87. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 c. –2*32 + (2*3)2 = –2*9 + (6)2 = –18 + 36 Order of Operations
- 88. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 c. –2*32 + (2*3)2 = –2*9 + (6)2 = –18 + 36 = 18 Order of Operations
- 89. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 c. –2*32 + (2*3)2 = –2*9 + (6)2 = –18 + 36 = 18 d. –32 – 5(3 – 6)2 Order of Operations
- 90. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 c. –2*32 + (2*3)2 = –2*9 + (6)2 = –18 + 36 = 18 d. –32 – 5(3 – 6)2 = –9 – 5(–3)2 Order of Operations
- 91. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 c. –2*32 + (2*3)2 = –2*9 + (6)2 = –18 + 36 = 18 d. –32 – 5(3 – 6)2 = –9 – 5(–3)2 = –9 – 5(9) Order of Operations
- 92. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 c. –2*32 + (2*3)2 = –2*9 + (6)2 = –18 + 36 = 18 d. –32 – 5(3 – 6)2 = –9 – 5(–3)2 = –9 – 5(9) = –9 – 45 Order of Operations
- 93. Example C. Order of Operations a. 52 – 32 = 25 – 9 = 16 b. – (5 – 3)2 = – (2)2 = – 4 c. –2*32 + (2*3)2 = –2*9 + (6)2 = –18 + 36 = 18 d. –32 – 5(3 – 6)2 = –9 – 5(–3)2 = –9 – 5(9) = –9 – 45 = –54 Order of Operations
- 94. Make sure that you interpret the operations correctly. Exercise A. Calculate the following expressions. Order of Operations 7. 1 + 2(3) 8. 4 – 5(6) 9. 7 – 8(–9) 1. 3(–3) 2. (3) – 3 3. 3 – 3(3) 4. 3(–3) + 3 5. +3(–3)(+3) 6. 3 + (–3)(+3) B.Make sure that you don’t do the ± too early. 10. 1 + 2(3 – 4) 11. 5 – 6(7 – 8) 12. (4 – 3)2 + 1 13. [1 – 2(3 – 4)] – 2 14. 6 + [5 + 6(7 – 8)](+5) 15. 1 + 2[1 – 2(3 + 4)] 16. 5 – 6[5 – 6(7 – 8)] 17. 1 – 2[1 – 2(3 – 4)] 18. 5 + 6[5 + 6(7 – 8)] 19. (1 + 2)[1 – 2(3 + 4)] 20. (5 – 6)[5 – 6(7 – 8)] C.Make sure that you apply the powers to the correct bases. 23. (–2)2 and –22 24 (–2)3 and –23 25. (–2)4 and –24 26. (–2)5 and –25 27. 2*32 28. (2*3)2 21. 1 – 2(–3)(–4) 22. (–5)(–6) – (–7)(–8)
- 95. Order of Operations D.Make sure that you apply the powers to the correct bases. 29. (2)2 – 3(2) + 1 30. 3(–2)2 + 4(–2) – 1 31. –2(3)2 + 3(3) – 5 32. –3(–1)2 + 4(–1) – 4 33. 3(–2)3 – 4(–2)2 – 1 34. (2)3 – 3(2)2 + 4(2) – 1 35. 2(–1)3 – 3(–1)2 + 4(–1) – 1 36. –3(–2)3 – 4(–2)2 – 4(–2) – 3 37. (6 + 3)2 38. 62 + 32 39. (–4 + 2)3 40. (–4)3 + (2)3 E. Calculate. 41. 72 – 42 42. (7 + 4)(7 – 4 ) 43. (– 5)2 – 32 44. (–5 + 3)(–5 – 3 ) 45. 53 – 33 46. (5 – 3) (52 + 5*3 + 32) 47. 43 + 23 48. (4 + 2)(42 – 4*2 + 22) 7 – (–5) 5 – 353. 8 – 2 –6 – (–2) 54. 49. (3)2 – 4(2)(3) 50. (3)2 – 4(1)(– 4) 51. (–3)2 – 4(–2)(3) 52. (–2)2 – 4(–1)(– 4) (–4) – (–8) (–5) – 3 55. (–7) – (–2) (–3) – (–6) 56.