24 order of operations
TRANSCRIPT
![Page 1: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/1.jpg)
Order of Operations
Back to Algebra–Ready Review Content.
![Page 2: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/2.jpg)
If we have two $5-bill and two $10-bills,
Order of Operations
![Page 3: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/3.jpg)
If we have two $5-bill and two $10-bills, we have the total of
2(5) + 2(10) = 30 dollars.
Order of Operations
![Page 4: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/4.jpg)
If we have two $5-bill 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
![Page 5: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/5.jpg)
If we have two $5-bill 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
![Page 6: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/6.jpg)
If we have two $5-bill 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
![Page 7: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/7.jpg)
If we have two $5-bill 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
![Page 8: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/8.jpg)
If we have two $5-bill 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
![Page 9: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/9.jpg)
If we have two $5-bill 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
![Page 10: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/10.jpg)
If we have two $5-bill 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.
![Page 11: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/11.jpg)
If we have two $5-bill 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.
![Page 12: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/12.jpg)
If we have two $5-bill 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.
![Page 13: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/13.jpg)
If we have two $5-bill 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.
![Page 14: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/14.jpg)
If we have two $5-bill 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.
![Page 15: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/15.jpg)
If we have two $5-bill 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.
![Page 16: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/16.jpg)
Example A.
a. 4(–8) + 3(5)
Order of Operations
![Page 17: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/17.jpg)
Example A.
a. 4(–8) + 3(5)
Order of Operations
![Page 18: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/18.jpg)
Example A.
a. 4(–8) + 3(5)
= –32 + 15
Order of Operations
![Page 19: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/19.jpg)
Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
![Page 20: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/20.jpg)
Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)
![Page 21: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/21.jpg)
Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)
![Page 22: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/22.jpg)
Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
![Page 23: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/23.jpg)
Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
![Page 24: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/24.jpg)
Example A.
a. 4(–8) + 3(5)
= –32 + 15
= –17
Order of Operations
b. 4 + 3(5 + 2)
= 4 + 3(7)
= 4 + 21
= 25
![Page 25: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/25.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
![Page 26: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/26.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
![Page 27: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/27.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
![Page 28: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/28.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
![Page 29: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/29.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
![Page 30: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/30.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
![Page 31: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/31.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
![Page 32: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/32.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
![Page 33: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/33.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
![Page 34: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/34.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
![Page 35: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/35.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
![Page 36: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/36.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
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself.
![Page 37: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/37.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
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
![Page 38: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/38.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
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
![Page 39: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/39.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
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
![Page 40: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/40.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
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3
![Page 41: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/41.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
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3 = 2*b*b*b.
![Page 42: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/42.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
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3 = 2*b*b*b.
If we want multiply 2b to itself three times, i.e. 2b to the third
power,
![Page 43: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/43.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
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3 = 2*b*b*b.
If we want multiply 2b to itself three times, i.e. 2b to the third
power, we write it as (2b)3
![Page 44: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/44.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
We write x*x*x…*x as xN where N is the number of copies of
x’s multiplied to itself. N is called the exponent, or the power
of x, and x is called the base.
The base is the quantity immediately beneath the exponent,
hence 2b3 means 2*b3 = 2*b*b*b.
If we want multiply 2b to itself three times, i.e. 2b to the third
power, we write it as (2b)3 which is (2b)*(2b)*(2b) =8b3.
![Page 45: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/45.jpg)
Order of Operations
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
![Page 46: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/46.jpg)
Order of Operations
Example B. (Exponential Notation)
a. Expand (–3)2 and simplify the answer.
The base is (–3).
![Page 47: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/47.jpg)
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)
![Page 48: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/48.jpg)
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
![Page 49: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/49.jpg)
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
![Page 50: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/50.jpg)
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
![Page 51: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/51.jpg)
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
![Page 52: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/52.jpg)
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
![Page 53: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/53.jpg)
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
![Page 54: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/54.jpg)
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
![Page 55: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/55.jpg)
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
![Page 56: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/56.jpg)
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
![Page 57: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/57.jpg)
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
![Page 58: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/58.jpg)
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
![Page 59: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/59.jpg)
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
![Page 60: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/60.jpg)
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
![Page 61: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/61.jpg)
Order of Operationse. Expand (–3y)3 and simplify the answer.
![Page 62: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/62.jpg)
Order of Operationse. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y)
![Page 63: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/63.jpg)
Order of Operationse. Expand (–3y)3 and simplify the answer.
(–3y)3
= (–3y)(–3y)(–3y) (the product of three negatives number is negative)
![Page 64: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/64.jpg)
Order of Operationse. 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)
![Page 65: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/65.jpg)
Order of Operationse. 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
![Page 66: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/66.jpg)
Order of Operationse. 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.
![Page 67: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/67.jpg)
Order of Operationse. 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.
![Page 68: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/68.jpg)
Order of Operationse. 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.
![Page 69: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/69.jpg)
Order of Operationse. 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.
![Page 70: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/70.jpg)
Order of Operationse. 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.
![Page 71: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/71.jpg)
Order of Operationse. 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.
![Page 72: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/72.jpg)
Order of Operationse. 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.
![Page 73: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/73.jpg)
Example C. Order of Operations
a. 52 – 32
Order of Operations
![Page 74: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/74.jpg)
Example C. Order of Operations
a. 52 – 32
= 25 – 9
Order of Operations
![Page 75: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/75.jpg)
Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
Order of Operations
![Page 76: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/76.jpg)
Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
Order of Operations
![Page 77: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/77.jpg)
Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
Order of Operations
![Page 78: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/78.jpg)
Example C. Order of Operations
a. 52 – 32
= 25 – 9
= 16
b. – (5 – 3)2
= – (2)2
= – 4
Order of Operations
![Page 79: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/79.jpg)
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
![Page 80: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/80.jpg)
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
![Page 81: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/81.jpg)
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
![Page 82: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/82.jpg)
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
![Page 83: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/83.jpg)
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
![Page 84: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/84.jpg)
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
![Page 85: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/85.jpg)
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
![Page 86: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/86.jpg)
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
![Page 87: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/87.jpg)
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
![Page 88: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/88.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)
![Page 89: 24 order of operations](https://reader034.vdocument.in/reader034/viewer/2022052413/55ab94651a28abce158b4820/html5/thumbnails/89.jpg)
Order of OperationsD.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 – 3
53.8 – 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.