The GEMDAS Rule

The GEMDAS Rule

Quarter 2 – Module 5:

​OBJECTIVES

​1. interprets and explains the Grouping, Exponent, Multiplication, Division, Addition, Subtraction (GEMDAS) rule. (M6NS-IIf-148)

​

​2. performs two or more different operations on whole numbers with or without exponents and grouping symbols. (M6NS-IIf-149)

​

What I Know​

Choose the letter of the correct answer.​ Each question will have a 2-minute time frame.

Multiple Choice

What is 940 more than the product of 89 and 76?

• 6 704

• 7 704

• 8 704

• 9 704

Multiple Choice

Divide the product of 684 and 15 by 6.

• 1 710

• 1 720

• 1 730

• 1 740

Multiple Choice

Increase the product of 36 and 549 by 343.

• 20 207

• 20 117

• 20 107

• 20 701

Multiple Choice

Decrease the product of 856 and 23 by 1 627

• 18 061

• 18 106

• 18 601

• 18 610

Multiple Choice

Find the number that is 8 less than the product of 9 times the sum of 6 and 2.

• 74

• 64

• 54

• 44

Multiple Choice

Which should be solved first in the expression below?

32 x 6 ÷ 2 + 8 – 4

• 8 – 4

• 4 + 8

• 32 x 6

• 6 ÷ 2

Multiple Choice

What operation symbol should be written on the line to make the equation correct?

48÷6 ____ 4 x 3 + 9 = 15

• -

• +

• x

• ÷

Multiple Choice

Which of the following sentences is true when n = 4?

I. (9 + 15) ÷ 2 + n x 6 = 32

II. (9 + 15) ÷ 3 + n x 6 = 32

III. (9 + 16) ÷ 3 + n + 6 = 32

• I only

• I and II only

• II only

• I and III only

Multiple Choice

Which of the following sentences is true?

I. 7 + 4 x 9 – 3 = 66

II. (7 + 4) x 9 - 3 = 66

III. (7 + 4) x (9 - 3) = 66

• I only

• II only

• II and III only

• III only

Multiple Choice

Simplify the expression [(25-4 x 4) – (36 ÷ 9)] + 8²

• 99

• 89

• 79

• 69

Draw

How many correct answers did you get? Write it down below.

​Lesson 1:

​Interprets and explains the Grouping, Exponent, Multiplication, Division, Addition, and Subtraction (GEMDAS) Rule.

​What’s In

​Perform the indicated operations in each number. Each item will have a 1 minute time frame.

Fill in the Blanks

54 ÷ 6 x 8

Fill in the Blanks

35 x 6 -18

Fill in the Blanks

42 x 3 ÷ 2 + 9

Fill in the Blanks

89 – 6 x 4

Fill in the Blanks

8 x (32 ÷ 4)+15

Fill in the Blanks

(15 + 35) ÷ 5 x 4

Fill in the Blanks

(3 x 10) + (18÷6)

Fill in the Blanks

8 – (3 x 15) ÷ 9 + 2

​What is It

​GEMDAS is the acronym for the Groupings Exponent Multiplication Division Addition Subtraction. The GEMDAS rule is often followed when solving numerical expressions involving several operations, grouping symbols, and exponents.

​The following rules can help in solving accurately a given expression.

​1. Remove the grouping symbols (G) like ( ), [ ], { }, by simplifying first the enclosed expressions, beginning in the innermost pair.

2. Simplify the expressions with exponents (E).

3. Perform all multiplication (M) and division (D) as they occur from left to right.

4. Perform all addition (A) and subtraction (S) as they occur from left to right.

​24 + 10 ÷ 2 x 8

​Divide first. 10 ÷ 2 = 5

​24 + 5 x 8

​Multiply before adding. 5 x 8 = 40

​24 + 40

​Add. 24 + 40 = 64

Final Answer: 64

32 – 9 x (14 – 12) ÷ 3

Do the operation inside the parentheses first. (14 - 12) = 2

32 – 9 x 2 ÷ 3

Multiply 9 x 2 = 18

32 – 18 ÷ 3

Divide 18 ÷ 3 = 6

32 – 6

Subtract 32 - 6 = 24

Final Answer: 24

​55 – 24 ÷12 + 6 x 2³

​Simplify the expression with exponent. 2³ = 2 x 2 x 2 = 8

​55 – 24 ÷12 + 6 x 8

Divide.​ 24 ÷12 = 2

​55 – 2 + 6 x 8

Multiply. 6 x 8 = 48

​55 – 2 + 48

Subtract. 55 – 2 = 53

​53 + 48

Add. 53 + 48 = 101

Final Answer: 101

​What’s More

​Let us sharpen your skill by doing the exercises below. Perform the indicated operation to find the value of n. Each item will have 5 minute time frame.

Fill in the Blanks

(16 + 9) – 10 = n

Fill in the Blanks

8 (7 + 5) = n

Fill in the Blanks

45 ÷ 5 + 12 = n

Fill in the Blanks

3² + 6÷ 3 - 4= n

Fill in the Blanks

4 x [(7 +14) ÷ 3] -17 = n

Fill in the Blanks

(43 – 14) + (12 + 3²) = n

Fill in the Blanks

(28 ÷ 7) + (15 × 4) = n

Fill in the Blanks

72 ÷ 3² x ( 8 +4) = n

Fill in the Blanks

(43 - 6) x 34 + 8 = n

Fill in the Blanks

(36+45) ÷ (9x3) =n

​What I Have Learned

​Place parentheses in the following equations so that each will be a true statement.

Draw

Place parentheses in the following equations so that each will be a true statement.

​Lesson 2:

Performs two or More Different Operations on Whole Numbers with or without Exponents and

Grouping symbols.​

​What is It

​An expression with more than one operation, such as 28 – 4 x 5 + 6, cannot have two different values. Rules are needed to make sure everyone gets the same result when an expression is simplified.

​Mathematicians have established order of Operations

​1. Do all operations inside grouping symbols

2. Simplify all numbers with exponents.

3. Multiply and divide from left to right.

4. Add and subtract from left to right.

​A. Simplifying Expressions with No Parenthesis

​A. Simplifying Expressions with No Parenthesis

B. Simplifying Expressions with Grouping Symbols

B. Simplifying Expressions with Grouping Symbols

B. Simplifying Expressions with Grouping Symbols

C. Simplifying Expressions with Exponents

B. Simplifying Expressions with Grouping Symbols

​What’s More

​Simplify each expression and solve for the value of n. Each item will have 5 minute time frame.

Fill in the Blanks

(1 + 3 + 5) (7+ 37+3) = n

Fill in the Blanks

3 (4 + 2 + 3) ÷3 = n

Fill in the Blanks

8 [5 + 3 (2³ + 4)] = n

Fill in the Blanks

25 - 6² ÷ (2³ + 2²) = n

Fill in the Blanks

42 [7²- (5² + 3²) + 3] = n

Fill in the Blanks

[(9 + 6) ÷3] + (8²- 23) = n

Fill in the Blanks

[(25 – 5 x 3) – (12 ÷ 6) + 9² = n

Fill in the Blanks

8 + 5 [(2 + 2)³ - 24] = n

Fill in the Blanks

[(6 + 4) ÷ 2 + (2⁴ - 8)] = n

Fill in the Blanks

(5 + 9)² ÷ 4 = n

Draw

How many correct answers did you get? Write your scores below.

​What I Have Learned

​REMEMBER: In performing the Order of Operations:

1. Do all operations inside grouping symbols

2. Simplify all numbers with exponents.

3. Multiply and divide from left to right.

4. Add and subtract from left to right.

​What I Have Learned

A. Simplifying Expressions with No Parenthesis

​

To simplify expressions with no parenthesis, first multiply or divide in order from left to right. Then, add or subtract in order from left to right.

​What I Have Learned

B. Simplifying Expressions with Grouping Symbols

​

To simplify expressions with parentheses or brackets, do first what is in the innermost grouping symbol. Then follow the Order of Operations.

​What I Have Learned

C. Simplifying Expressions with Exponents

​

In simplifying expressions always simplify the powers first. If there are grouping symbols, do the operations within the parentheses followed by the operations within the brackets. Then follow the order of operations.

​Assessment

​Choose the letter of your answer. Each item will have 1 minute time frame.

Multiple Choice

Which numerical expression has the value of 60?

• (12 + 4) 3

• 12 + (4 + 3)

• 4 x (12 + 3)

• 12 – 4 + 3

Poll

Simplify the numerical expression: 54 ÷ (3 + 6) x 7

• 22

• 32

• 42

Poll

What is the product of 6² and 4³?

• 2 304

• 3 204

• 3 402

Poll

What is the product of 9 and 8 subtracted from the sum of 57 and 86?

• 117

• 107

• 71

• 17

Multiple Choice

The sum of the ages of Maxine and Irish is 32 years. If Maxine is 8 years older than Irish, How old is Maxine?

• 20

• 12

• 18

• 22

Multiple Choice

In the equation [(45 - 3) ÷ 7] + (9²- 3) = n, what is the value of n?

• 48

• 84

• 184

• 548

Multiple Choice

Find the value of n in the equation: (68 + 4) ÷ 8 + (4 x 2)² = n

• 84

• 73

• 54

• 45

Multiple Choice

Twenty chicos weigh 3 kilograms. If Aling Susan paid ₱ 195.00 for the 3 kilograms, how much is the cost of one chico?

• ₱ 8.95

• ₱ 9.25

• ₱ 9.75

• ₱ 9.15

Multiple Choice

Arnold bought a pair of shoes for ₱1946.00 and 6 shirts for ₱587.00 each.

If he gave the cashier ₱6000.00, how much change did he receive?

• ₱652.00

• ₱593.00

• ₱532.00

• ₱395.00

Multiple Choice

A cargo truck travelled 703 kilometres the other day, 629 kilometres yesterday and 125 kilometres today. The total distance that the truck had to travel is 1604 kilometres. How far did it still have to go after three days of travel?

• 157

• 147

• 117

• 174

Draw

How many correct answers did you get? Write it below.

Open Ended

Did you find the lesson easy? If no, then what part of the lesson is difficult for you?

Open Ended

Is the time limit per questions given enough for you? If not, then how many minutes can you spend in solving each activity?

​That ends our discussion for this week. I will see you on the next module.

Open Ended

What are other examples that you need clarification?