ORDER OF OPERATIONS 1. Multiplication & Division 2. Addition & Subtraction + - ÷

ORDER OF OPERATIONSORDER OF OPERATIONS

1. Multiplication & Division

2. Addition & Subtraction

+ - • ÷

1. Multiplication & Division

• Solve in the order they appear from left to right.

2. Addition & Subtraction

• Solve in the order they appear from left to right.

In the problem below:5 + 6 • 3 - 4

Which operation is solved first?

In the problem below:5 + 6 • 3 - 4


•Multiply first… and rewrite the rest of the problem.

5 + 6 • 3 - 45 + 18 - 4

Next?

•Multiply first… and rewrite the rest of the problem.

5 + 6 • 3 - 45 + 18 - 4

Next?

•Add…and rewrite the rest of the problem.

5 + 6 • 3 - 45 + 18 - 423 - 4

•Add…and rewrite the rest of the problem.

5 + 6 • 3 - 45 + 18 - 423 - 4

•Last…subtract.5 + 6 • 3 - 45 + 18 - 423 - 419

•Last…subtract.5 + 6 • 3 - 45 + 18 - 423 - 419

Let’s try another one!24 ÷ 2 • 4


Let’s try another one!24 ÷ 2 • 4


•Divide first. It appears first. Rewrite the rest of the problem.

24 ÷ 2 • 412 • 4

•Divide first. It appears first. Rewrite the rest of the problem.

24 ÷ 2 • 412 • 4

•Multiply and rewrite the rest of the problem.

24 ÷ 2 • 412 • 4

48


24 ÷ 2 • 412 • 4

48


24 ÷ 2 • 4

12 • 4

48

Notice….The problem will be in a triangular

shape.


24 ÷ 2 • 4

12 • 4

48

Notice….The problem will be in a triangular

shape.

Solve this one.

18 + 4 ÷ 2 - 8

Solve this one.

18 + 4 ÷ 2 - 8

Divide first….even though it is in the middle of the problem.

Divide first….even though it is in the middle of the problem.

18 + 4 ÷ 2 - 8 18 + 2 - 8

Next add…rewrite the rest of the problem.

18 + 4 ÷ 2 - 8 18 + 2 - 8 20 - 8

18 + 4 ÷ 2 - 818 + 2 - 8 20 - 8

12

Try this with me…..

35 + 5 • 7 - 14

Try this with me…..

35 + 5 • 7 - 14

35 + 5 • 7 - 14 35 + 35 - 1435 + 5 • 7 - 14

35 + 35 - 14

35 + 5 • 7 - 14 35 + 35 - 14 70 - 14

35 + 5 • 7 - 14 35 + 35 - 14 70 - 14

35 + 5 • 7 - 14 35 + 35 - 14 70 - 14 56

35 + 5 • 7 - 14 35 + 35 - 14 70 - 14 56

Get an answer to this one!

15 ÷ 3 + 20 • 5

5 + 20 • 5

5 + 100

105

Simplify these on topic paper!

1. 45 - 5 + 13

2. 20 ÷ 4 • 7

3. 10 - 24 ÷ 4 • 2

4. 4 • 3 + 25 ÷ 5

5. 6 + 8 ÷ 2 • 5

Solutions

1. 45 - 5 + 13

2. 20 ÷ 4 • 7

3. 10 - 24 ÷ 4 • 2

4. 4 • 3 + 25 ÷ 5

5. 6 + 8 ÷ 2 • 5

1. 45 - 5 + 13 40 + 13

53

1. 45 - 5 + 13 40 + 13

53

2. 20 ÷ 4 • 7 5 • 7

35

2. 20 ÷ 4 • 7 5 • 7

35

3. 10 - 24 ÷ 4 • 2 10 - 6 • 2

10 - 12- 2

3. 10 - 24 ÷ 4 • 2 10 - 6 • 2

10 - 12- 2

4. 4 • 3 + 25 ÷ 5 12 + 25 ÷ 5

12 + 5 17

4. 4 • 3 + 25 ÷ 5 12 + 25 ÷ 5

12 + 5 17

5. 6 + 8 ÷ 2 • 5 6 + 4 • 5 6 + 20

26

5. 6 + 8 ÷ 2 • 5 6 + 4 • 5 6 + 20

26

Grouping Symbols( parentheses )

[ brackets ]

{ braces }

( ) parentheses

•Solve first…using order of operations rules inside.

( ) parentheses

•Solve first…using order of operations rules inside.

[ ]brackets

• Solve second…using order of operations rules inside.

{ }braces

•Solve third…using order of operations rules inside.

• Grouping symbols are nested inside each other and are worked from the inside to the outside.

{ [ ( ) ] }

• Grouping symbols are nested inside each other and are worked from the inside to the outside.

{ [ ( ) ] }

• A number or grouping symbols next to grouping symbols indicates multiplication.

7(6 - 4)

• This means 7 times the (6 - 4) answer or

7•2

• A number or grouping symbols next to grouping symbols indicates multiplication.

7(6 - 4)

• This means 7 times the (6 - 4) answer or

7•2

• When several grouping symbols are in the same problem simplify ( ), then [ ], then { }.

(1) [2] {3}

• Follow order of operations rules in the grouping symbols.

4{7 +6[5(3+9)-(8-2)]}4{7+6[5(3+9)-(8-2)]}

4{7+6[5•12-6]}

• ( ) are now removed.

• When several grouping symbols are in the same problem simplify ( ), then [ ], then { }.

(1) [2] {3}

• Follow order of operations rules in the grouping symbols.

4{7 +6[5(3+9)-(8-2)]}4{7+6[5(3+9)-(8-2)]}

4{7+6[5•12-6]}

• ( ) are now removed.

• Next simplify inside the brackets remembering to use order of operations.

4{7+6[5(3+9)-(8-2)]} 4{7+6[5•12-6]}4{7+6[60-6]}4{7+6•54}

• Next simplify inside the brackets remembering to use order of operations.

4{7+6[5(3+9)-(8-2)]} 4{7+6[5•12-6]}4{7+6[60-6]}4{7+6•54}

•Simplify inside the braces remembering to use order of operations.

4{7+6[5(3+9)-(8-2)]} 4{7+6[5•12-6]}4{7+6[60-6]}4{7+6•54}4{7+324}4•3311324

•Simplify inside the braces remembering to use order of operations.

4{7+6[5(3+9)-(8-2)]} 4{7+6[5•12-6]}4{7+6[60-6]}4{7+6•54}4{7+324}4•3311324

• Last multiply to finish the problem.

4{7+6[5(3+9)-(8-2)]} 4{7+6[5•12-6]}4{7+6[60-6]}4{7+6•54}4{7+324}4•3311324

• Last multiply to finish the problem.

4{7+6[5(3+9)-(8-2)]} 4{7+6[5•12-6]}4{7+6[60-6]}4{7+6•54}4{7+324}4•3311324

• Simplify these on topic paper. SHOW ALL WORK!!!

1.8+7(5-1)2.3(10-2)÷43.15-2[36-4(5+3)]4.[3(6+5)-2(8-4)+2]55.20-1{3+3[2(4-3)+(7-5)]}

• Simplify these on topic paper. SHOW ALL WORK!!!

1.8+7(5-1)2.3(10-2)÷43.15-2[36-4(5+3)]4.[3(6+5)-2(8-4)+2]55.20-1{3+3[2(4-3)+(7-5)]}

Solution:8+7(5-1)8+7•48+2836

Solution:8+7(5-1)8+7•48+2836

Solution:3(10-2)÷43•8÷424÷46

Solution:3(10-2)÷43•8÷424÷46

Solution:15-2[36-4(5+3)]15-2[36-4•8]15-2[36-32]

15-2•415-87

Solution:15-2[36-4(5+3)]15-2[36-4•8]15-2[36-32]

15-2•415-87

Solution:[3(6+5)-2(8-4)+2]5

[3•11-2•4+2]5[33-8+2]5[25+2]527•5135

Solution:[3(6+5)-2(8-4)+2]5

[3•11-2•4+2]5[33-8+2]5[25+2]527•5135

Solution:20-1{3+3[2(4-3)+(7-5)]}

20-1{3+3[2•1+2]}20-1{3+3[2+2]}20-1{3+3•4}20-1{3+12}20-1•1520-15

5

Solution:20-1{3+3[2(4-3)+(7-5)]}

20-1{3+3[2•1+2]}20-1{3+3[2+2]}20-1{3+3•4}20-1{3+12}20-1•1520-15

5

Simplifying ExponentsSimplifying Exponents

42

4 is the base2 is the exponent. It tells

you how many times to take the base times itself.

42 = 4 • 4 = 16

42

4 is the base2 is the exponent. It tells

you how many times to take the base times itself.

42 = 4 • 4 = 16

When exponents are in order of operations problems they are usually simplified first.

For example, in the problem32+5-4

32 is simplified first.

When exponents are in order of operations problems they are usually simplified first.

For example, in the problem32+5-4

32 is simplified first.

32+5-4

Simplify using order of operation rules.

3•3+5-49+5-414-410

32+5-4

Simplify using order of operation rules.

3•3+5-49+5-414-410

• If exponents are outside of grouping symbols, you must simplify the grouping symbols first. Then follow order of operations.

2+5(6-4)3

2+5(2)3

2+5•82+4042

• If exponents are outside of grouping symbols, you must simplify the grouping symbols first. Then follow order of operations.

2+5(6-4)3

2+5(2)3

2+5•82+4042

• If exponents are outside of grouping symbols, you must simplify the grouping symbols first. Then follow order of operations. The exponent will be simplified second. DO NOT MULTIPLY BY THE 5 BEFORE YOU SIMPLIFY THE EXPONENT.

2+5(6-4)3

2+5(2)3

2+5•82+4042

• If exponents are outside of grouping symbols, you must simplify the grouping symbols first. Then follow order of operations. The exponent will be simplified second. DO NOT MULTIPLY BY THE 5 BEFORE YOU SIMPLIFY THE EXPONENT.

2+5(6-4)3

2+5(2)3

2+5•82+4042

ORDER OF OPERATIONS 1. Multiplication & Division 2. Addition & Subtraction + - ÷

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Transcript of ORDER OF OPERATIONS 1. Multiplication & Division 2. Addition & Subtraction + - ÷