MODULE IN MATHEMATICS 6 Quarter 2 / Week 4/ Day 3

MODULE IN MATHEMATICS 6 Quarter 2 / Week 4/ Day 3

OBJECTIVE: Interprets and explains the Grouping, Exponent, Multiplication, Division, Addition, Subtraction (GEMDAS) rule.

Rules in solving more than one arithmetic operation:

• Simplify the operation in grouping symbols. Start from the innermost grouping symbol.

• Evaluate exponential expressions.

• Multiply and divide in the order they appear from left or right.

• Add and subtract in the order they appear from left or right.

• GEMDAS rule means Groupings symbols, Exponents, Multiplication, Division, Addition and Subtraction.

Hazel and Eden are both working on the Value of the expression: 14 + 7 x 6 – 8 ÷ 2. However, they have different answers. Hazel answered 59, while Eden answered 52. Of the two pupils, who answered correctly? 

In a series of operations without grouping symbols, multiplication and division are performed first from left to right, followed by addition and subtraction, whichever comes first from left to right.

Answer: 52

The multiplication symbol x may be omitted in a multiplication expression involving grouping symbols.

1. 3 x (8 + 42 ) may be written as 3(8 + 42 )

2. 23 x (122 – 5 2 ) may be written as 23(122 – 5 2 )

3. (2 + 3 + 8 ÷ 2) x (16 – 4 x 3) = (2 + 3 + 8 ÷ 2) (16 – 4 x 3)

 Simplify: 2 + (7 x 3) – 5

• = 2 + 7 x 3 – 5 Multiply 7 and 3 First.

• = 2 + 21 – 5 Add and subtract from left to right.

• = 18

• ANSWER 18

 Simplify: 3 x 4 ÷ (7 – 5) – 12 ÷ 4

•  = 3 x 4 ÷ (7 – 5) – 12 ÷ 4 Simplify first the expression inside the parenthesis.

• = 3 x 4 ÷ 2 – 12 ÷ 4 Then, perform the multiplication and division from left to right. 

• = 12 ÷ 2 – 12 ÷ 4 

• = 6 – 3 Subtract.

• = 3

 Simplify: 7 + [2(12 – 5) + 32] – 18 ÷ 3

• = 7 + [2(12 – 5) + 32] – 18 ÷ 3 Simplify first the expression inside the parenthesis.

• = 7 + [2(7) + 32] – 18 ÷ 3 Next, multiply 2 and 7 inside the bracket.

• = 7 + [14 + 32] – 18 ÷ 3 Add the number inside the bracket.

• = 7 + 46 – 18 ÷ 3 Perform the division. Divide 18 by 3.

• = 7 + 46 – 6 Then, add and subtract the numbers from left to right.

• = 47

• ANSWER: 47

Fill in the Blanks

solve the expression.

40 ÷ 8 + (25 – 12)

Fill in the Blanks

solve the expression.

12 x 65 + (34 -11)

Fill in the Blanks

solve the expression. 

 $14\ +\ 7\ \times\ 6\ \left(4^2\ \div\ 2\right)$  

Fill in the Blanks

solve the expression.

4 x 4 ÷ (7 – 5) – 12 ÷ 4

Fill in the Blanks

 $42\ -\ 4\ \cdot\ 3^2\ +\ \left(5-2\right)^3$  

solve the expression.