Order of operations online activity for GRADE 6 - Free Printable

Problem: Solve the given expressions using the GEMDAS rule (Grouping, Exponents, Multiplication and Division, Addition and Subtraction).

#### GEMDAS Rule Recap:
1. Grouping: Solve expressions inside parentheses, brackets, or braces.
2. Exponents: Evaluate exponents.
3. Multiplication and Division: Perform multiplication and division from left to right.
4. Addition and Subtraction: Perform addition and subtraction from left to right.

---

Solutions:

#### 1. \( 90 \div (3 \times 3) - 3^2 \)

1. Grouping: Solve inside the parentheses first.
\[
3 \times 3 = 9
\]
So the expression becomes:
\[
90 \div 9 - 3^2
\]

2. Exponents: Evaluate \( 3^2 \).
\[
3^2 = 9
\]
So the expression becomes:
\[
90 \div 9 - 9
\]

3. Division: Perform the division.
\[
90 \div 9 = 10
\]
So the expression becomes:
\[
10 - 9
\]

4. Subtraction: Perform the subtraction.
\[
10 - 9 = 1
\]

Answer: \(\boxed{1}\)

---

#### 2. \( 8 \times 4 \div 2 + (15 \div 5) - 4^2 \)

1. Grouping: Solve inside the parentheses first.
\[
15 \div 5 = 3
\]
So the expression becomes:
\[
8 \times 4 \div 2 + 3 - 4^2
\]

2. Exponents: Evaluate \( 4^2 \).
\[
4^2 = 16
\]
So the expression becomes:
\[
8 \times 4 \div 2 + 3 - 16
\]

3. Multiplication and Division: Perform multiplication and division from left to right.
\[
8 \times 4 = 32
\]
So the expression becomes:
\[
32 \div 2 + 3 - 16
\]
Next, perform the division:
\[
32 \div 2 = 16
\]
So the expression becomes:
\[
16 + 3 - 16
\]

4. Addition and Subtraction: Perform addition and subtraction from left to right.
\[
16 + 3 = 19
\]
So the expression becomes:
\[
19 - 16 = 3
\]

Answer: \(\boxed{3}\)

---

#### 3. \( \{ (15 - 3 \times 3) - (18 \div 9) \} + 10^2 \)

1. Grouping: Solve inside the innermost parentheses first.
- For \( 3 \times 3 \):
\[
3 \times 3 = 9
\]
So the expression becomes:
\[
\{ (15 - 9) - (18 \div 9) \} + 10^2
\]
- For \( 18 \div 9 \):
\[
18 \div 9 = 2
\]
So the expression becomes:
\[
\{ (15 - 9) - 2 \} + 10^2
\]
- For \( 15 - 9 \):
\[
15 - 9 = 6
\]
So the expression becomes:
\[
\{ 6 - 2 \} + 10^2
\]
- For \( 6 - 2 \):
\[
6 - 2 = 4
\]
So the expression becomes:
\[
4 + 10^2
\]

2. Exponents: Evaluate \( 10^2 \).
\[
10^2 = 100
\]
So the expression becomes:
\[
4 + 100
\]

3. Addition: Perform the addition.
\[
4 + 100 = 104
\]

Answer: \(\boxed{104}\)

---

#### 4. \( 100 - 45 \div 3 \times 3^2 + 56 \)

1. Exponents: Evaluate \( 3^2 \).
\[
3^2 = 9
\]
So the expression becomes:
\[
100 - 45 \div 3 \times 9 + 56
\]

2. Division and Multiplication: Perform division and multiplication from left to right.
- First, divide \( 45 \div 3 \):
\[
45 \div 3 = 15
\]
So the expression becomes:
\[
100 - 15 \times 9 + 56
\]
- Next, multiply \( 15 \times 9 \):
\[
15 \times 9 = 135
\]
So the expression becomes:
\[
100 - 135 + 56
\]

3. Subtraction and Addition: Perform subtraction and addition from left to right.
- First, subtract \( 100 - 135 \):
\[
100 - 135 = -35
\]
So the expression becomes:
\[
-35 + 56
\]
- Next, add \( -35 + 56 \):
\[
-35 + 56 = 21
\]

Answer: \(\boxed{21}\)

---

#### 5. \( 6^2 \div 3 \times 4 - 28 + (7 + 3) \)

1. Grouping: Solve inside the parentheses first.
\[
7 + 3 = 10
\]
So the expression becomes:
\[
6^2 \div 3 \times 4 - 28 + 10
\]

2. Exponents: Evaluate \( 6^2 \).
\[
6^2 = 36
\]
So the expression becomes:
\[
36 \div 3 \times 4 - 28 + 10
\]

3. Division and Multiplication: Perform division and multiplication from left to right.
- First, divide \( 36 \div 3 \):
\[
36 \div 3 = 12
\]
So the expression becomes:
\[
12 \times 4 - 28 + 10
\]
- Next, multiply \( 12 \times 4 \):
\[
12 \times 4 = 48
\]
So the expression becomes:
\[
48 - 28 + 10
\]

4. Subtraction and Addition: Perform subtraction and addition from left to right.
- First, subtract \( 48 - 28 \):
\[
48 - 28 = 20
\]
So the expression becomes:
\[
20 + 10
\]
- Next, add \( 20 + 10 \):
\[
20 + 10 = 30
\]

Answer: \(\boxed{30}\)

---

#### 6. \( 60 \div (5 \times 2) + 4^3 \)

1. Grouping: Solve inside the parentheses first.
\[
5 \times 2 = 10
\]
So the expression becomes:
\[
60 \div 10 + 4^3
\]

2. Exponents: Evaluate \( 4^3 \).
\[
4^3 = 64
\]
So the expression becomes:
\[
60 \div 10 + 64
\]

3. Division: Perform the division.
\[
60 \div 10 = 6
\]
So the expression becomes:
\[
6 + 64
\]

4. Addition: Perform the addition.
\[
6 + 64 = 70
\]

Answer: \(\boxed{70}\)

---

#### 7. \( 120 \div 12 \times 5 \div 2 - 4 \)

1. Division and Multiplication: Perform division and multiplication from left to right.
- First, divide \( 120 \div 12 \):
\[
120 \div 12 = 10
\]
So the expression becomes:
\[
10 \times 5 \div 2 - 4
\]
- Next, multiply \( 10 \times 5 \):
\[
10 \times 5 = 50
\]
So the expression becomes:
\[
50 \div 2 - 4
\]
- Next, divide \( 50 \div 2 \):
\[
50 \div 2 = 25
\]
So the expression becomes:
\[
25 - 4
\]

2. Subtraction: Perform the subtraction.
\[
25 - 4 = 21
\]

Answer: \(\boxed{21}\)

---

#### 8. \( 95 - 24 \div (8 \times 3) + 2^4 \)

1. Grouping: Solve inside the parentheses first.
\[
8 \times 3 = 24
\]
So the expression becomes:
\[
95 - 24 \div 24 + 2^4
\]

2. Exponents: Evaluate \( 2^4 \).
\[
2^4 = 16
\]
So the expression becomes:
\[
95 - 24 \div 24 + 16
\]

3. Division: Perform the division.
\[
24 \div 24 = 1
\]
So the expression becomes:
\[
95 - 1 + 16
\]

4. Subtraction and Addition: Perform subtraction and addition from left to right.
- First, subtract \( 95 - 1 \):
\[
95 - 1 = 94
\]
So the expression becomes:
\[
94 + 16
\]
- Next, add \( 94 + 16 \):
\[
94 + 16 = 110
\]

Answer: \(\boxed{110}\)

---

#### 9. \( 9 \times 12 \div 3 + 5 - 15 \)

1. Multiplication and Division: Perform multiplication and division from left to right.
- First, multiply \( 9 \times 12 \):
\[
9 \times 12 = 108
\]
So the expression becomes:
\[
108 \div 3 + 5 - 15
\]
- Next, divide \( 108 \div 3 \):
\[
108 \div 3 = 36
\]
So the expression becomes:
\[
36 + 5 - 15
\]

2. Addition and Subtraction: Perform addition and subtraction from left to right.
- First, add \( 36 + 5 \):
\[
36 + 5 = 41
\]
So the expression becomes:
\[
41 - 15
\]
- Next, subtract \( 41 - 15 \):
\[
41 - 15 = 26
\]

Answer: \(\boxed{26}\)

---

#### 10. \( (36 \div 9 + 14) \div 9 + 12 - 10 \)

1. Grouping: Solve inside the parentheses first.
- First, divide \( 36 \div 9 \):
\[
36 \div 9 = 4
\]
So the expression becomes:
\[
(4 + 14) \div 9 + 12 - 10
\]
- Next, add \( 4 + 14 \):
\[
4 + 14 = 18
\]
So the expression becomes:
\[
18 \div 9 + 12 - 10
\]

2. Division: Perform the division.
\[
18 \div 9 = 2
\]
So the expression becomes:
\[
2 + 12 - 10
\]

3. Addition and Subtraction: Perform addition and subtraction from left to right.
- First, add \( 2 + 12 \):
\[
2 + 12 = 14
\]
So the expression becomes:
\[
14 - 10
\]
- Next, subtract \( 14 - 10 \):
\[
14 - 10 = 4
\]

Answer: \(\boxed{4}\)

---

Final Answers:

\[
\boxed{1, 3, 104, 21, 30, 70, 21, 110, 26, 4}
\]