24 order of operations

Order of Operations

Back to Algebra–Ready Review Content.

If we have two $5-bill and two $10-bills,

Order of Operations

If we have two $5-bill and two $10-bills, we have the total of

2(5) + 2(10) = 30 dollars.

Order of Operations

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

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

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

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

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

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

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.

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.

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.

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.

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.

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.

Example A.

a. 4(–8) + 3(5)

Order of Operations

Example A.

a. 4(–8) + 3(5)

Order of Operations

Example A.

a. 4(–8) + 3(5)

= –32 + 15

Order of Operations

Example A.

a. 4(–8) + 3(5)

= –32 + 15

= –17

Order of Operations

Example A.

a. 4(–8) + 3(5)

= –32 + 15

= –17

Order of Operations

b. 4 + 3(5 + 2)

Example A.

a. 4(–8) + 3(5)

= –32 + 15

= –17

Order of Operations

b. 4 + 3(5 + 2)

Example A.

a. 4(–8) + 3(5)

= –32 + 15

= –17

Order of Operations

b. 4 + 3(5 + 2)

= 4 + 3(7)

Example A.

a. 4(–8) + 3(5)

= –32 + 15

= –17

Order of Operations

b. 4 + 3(5 + 2)

= 4 + 3(7)

= 4 + 21

Example A.

a. 4(–8) + 3(5)

= –32 + 15

= –17

Order of Operations

b. 4 + 3(5 + 2)

= 4 + 3(7)

= 4 + 21

= 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

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

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

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

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

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

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

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

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

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

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

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.

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

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.

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,

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

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.

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,

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

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.

Order of Operations

Example B. (Exponential Notation)

a. Expand (–3)2 and simplify the answer.

Order of Operations

Example B. (Exponential Notation)

a. Expand (–3)2 and simplify the answer.

The base is (–3).

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

Order of Operationse. Expand (–3y)3 and simplify the answer.

Order of Operationse. Expand (–3y)3 and simplify the answer.

(–3y)3

= (–3y)(–3y)(–3y)

Order of Operationse. Expand (–3y)3 and simplify the answer.

(–3y)3

= (–3y)(–3y)(–3y) (the product of three negatives number is negative)

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)

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 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.

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.

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.

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.

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.

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.

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.

Example C. Order of Operations

a. 52 – 32

Order of Operations

Example C. Order of Operations

a. 52 – 32

= 25 – 9

Order of Operations

Example C. Order of Operations

a. 52 – 32

= 25 – 9

= 16

Order of Operations

Example C. Order of Operations

a. 52 – 32

= 25 – 9

= 16

b. – (5 – 3)2

Order of Operations

Example C. Order of Operations

a. 52 – 32

= 25 – 9

= 16

b. – (5 – 3)2

= – (2)2

Order of Operations

Example C. Order of Operations

a. 52 – 32

= 25 – 9

= 16

b. – (5 – 3)2

= – (2)2

= – 4

Order of Operations

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

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

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

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

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

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

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

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

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

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)

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.