PEMDAS Problems - Free Printable

Here are the step-by-step solutions for the math problems on the sheet. We will follow the order of operations (PEMDAS): solve Parentheses first, then Exponents, then Multiplication/Division, and finally Addition/Subtraction.

Part 1: Basic Problems

1) $(2^3 + 1) \times 2$
* First, solve inside the parentheses. Calculate the exponent: $2^3 = 8$.
* Add inside the parentheses: $8 + 1 = 9$.
* Multiply by 2: $9 \times 2 = 18$.
* Answer: $9 \times 2 = 18$

2) $3 + (5 + 4^2)$
* Inside parentheses, do the exponent first: $4^2 = 16$.
* Add inside the parentheses: $5 + 16 = 21$.
* Add the outer number: $3 + 21 = 24$.
* Answer: $3 + 21 = 24$

3) $(15 - 3^2) \div 2$
* Inside parentheses, do the exponent first: $3^2 = 9$.
* Subtract inside the parentheses: $15 - 9 = 6$.
* Divide by 2: $6 \div 2 = 3$.
* Answer: $6 \div 2 = 3$

4) $50 - (7^2 - 10)$
* Inside parentheses, do the exponent first: $7^2 = 49$.
* Subtract inside the parentheses: $49 - 10 = 39$.
* Subtract from 50: $50 - 39 = 11$.
* Answer: $50 - 39 = 11$

5) $20 \times (3^2 - 7)$
* Inside parentheses, do the exponent first: $3^2 = 9$.
* Subtract inside the parentheses: $9 - 7 = 2$.
* Multiply by 20: $20 \times 2 = 40$.
* Answer: $20 \times 2 = 40$

6) $(3^2 - 2^3) \times 3$
* Inside parentheses, calculate exponents: $3^2 = 9$ and $2^3 = 8$.
* Subtract inside the parentheses: $9 - 8 = 1$.
* Multiply by 3: $1 \times 3 = 3$.
* Answer: $1 \times 3 = 3$

7) $6 + (3 \times 1^3)$
* Inside parentheses, calculate the exponent: $1^3 = 1$.
* Multiply inside the parentheses: $3 \times 1 = 3$.
* Add the outer number: $6 + 3 = 9$.
* Answer: $6 + 3 = 9$

8) $24 \div (4^2 - 2^3)$
* Inside parentheses, calculate exponents: $4^2 = 16$ and $2^3 = 8$.
* Subtract inside the parentheses: $16 - 8 = 8$.
* Divide 24 by the result: $24 \div 8 = 3$.
* Answer: $24 \div 8 = 3$

9) $(2 - 3^2) \times 2$
* Inside parentheses, calculate the exponent: $3^2 = 9$.
* Subtract inside the parentheses: $2 - 9 = -7$.
* Multiply by 2: $-7 \times 2 = -14$.
* Answer: $-7 \times 2 = -14$

10) $3^2 \times (4^2 - 10)$
* Calculate the outer exponent: $3^2 = 9$.
* Inside parentheses, calculate the exponent: $4^2 = 16$.
* Subtract inside the parentheses: $16 - 10 = 6$.
* Multiply: $9 \times 6 = 54$.
* Answer: $9 \times 6 = 54$

11) $7^2 - (6^2 + 2^3)$
* Calculate outer exponent: $7^2 = 49$.
* Inside parentheses, calculate exponents: $6^2 = 36$ and $2^3 = 8$.
* Add inside parentheses: $36 + 8 = 44$.
* Subtract: $49 - 44 = 5$.
* Answer: $49 - 44 = 5$

12) $10^2 \div (5^2 - 5)$
* Calculate outer exponent: $10^2 = 100$.
* Inside parentheses, calculate exponent: $5^2 = 25$.
* Subtract inside parentheses: $25 - 5 = 20$.
* Divide: $100 \div 20 = 5$.
* Answer: $100 \div 20 = 5$

13) $3^3 - (2^2 + 4^2)$
* Calculate outer exponent: $3^3 = 27$.
* Inside parentheses, calculate exponents: $2^2 = 4$ and $4^2 = 16$.
* Add inside parentheses: $4 + 16 = 20$.
* Subtract: $27 - 20 = 7$.
* Answer: $27 - 20 = 7$

14) $9^2 - (2^3 \times 10)$
* Calculate outer exponent: $9^2 = 81$.
* Inside parentheses, calculate exponent: $2^3 = 8$.
* Multiply inside parentheses: $8 \times 10 = 80$.
* Subtract: $81 - 80 = 1$.
* Answer: $81 - 80 = 1$

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Part 2: Complex Calculations (Use a calculator)

13) $(12^2 - 10^2) \times 4^2$
* Inside parentheses: $12^2 = 144$ and $10^2 = 100$.
* Subtract inside parentheses: $144 - 100 = 44$.
* Outer exponent: $4^2 = 16$.
* Multiply: $44 \times 16 = 704$.
* Answer: $44 \times 16 = 704$

14) $9^2 \times (5^3 - 10^2)$
* Outer exponent: $9^2 = 81$.
* Inside parentheses: $5^3 = 125$ and $10^2 = 100$.
* Subtract inside parentheses: $125 - 100 = 25$.
* Multiply: $81 \times 25 = 2025$.
* Answer: $81 \times 25 = 2025$

15) $10^3 - (9^2 \times 2^3)$
* Outer exponent: $10^3 = 1000$.
* Inside parentheses: $9^2 = 81$ and $2^3 = 8$.
* Multiply inside parentheses: $81 \times 8 = 648$.
* Subtract: $1000 - 648 = 352$.
* Answer: $1000 - 648 = 352$

16) $(8^2 - 4^2) \div 2^3$
* Inside parentheses: $8^2 = 64$ and $4^2 = 16$.
* Subtract inside parentheses: $64 - 16 = 48$.
* Outer exponent: $2^3 = 8$.
* Divide: $48 \div 8 = 6$.
* Answer: $48 \div 8 = 6$

17) $(9^3 + 1) \div (8^2 + 3^2)$
* Left parentheses: $9^3 = 729$, so $729 + 1 = 730$.
* Right parentheses: $8^2 = 64$ and $3^2 = 9$, so $64 + 9 = 73$.
* Divide: $730 \div 73 = 10$.
* Answer: $730 \div 73 = 10$

17) $3^2 \times (4^3 - 5^2)$ *(Note: This is the second problem labeled 17)*
* Outer exponent: $3^2 = 9$.
* Inside parentheses: $4^3 = 64$ and $5^2 = 25$.
* Subtract inside parentheses: $64 - 25 = 39$.
* Multiply: $9 \times 39 = 351$.
* Answer: $9 \times 39 = 351$

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Part 3: Order from Smallest to Largest

Let's solve each expression to find their values.

Expression A: $6^3 - (5^2 \times 2^3)$
1. Calculate exponents: $6^3 = 216$, $5^2 = 25$, $2^3 = 8$.
2. Multiply inside parentheses: $25 \times 8 = 200$.
3. Subtract: $216 - 200 = \mathbf{16}$.

Expression B: $(10^3 \div 5^2) - (5^2 \times 2)$
1. Calculate exponents: $10^3 = 1000$, $5^2 = 25$.
2. First part (division): $1000 \div 25 = 40$.
3. Second part (multiplication): $25 \times 2 = 50$.
4. Subtract: $40 - 50 = \mathbf{-10}$.

Expression C: $(15^2 - 10^2) \div 5$
1. Calculate exponents inside parentheses: $15^2 = 225$, $10^2 = 100$.
2. Subtract inside parentheses: $225 - 100 = 125$.
3. Divide: $125 \div 5 = \mathbf{25}$.

Comparison:
* Expression B is -10 (Smallest)
* Expression A is 16
* Expression C is 25 (Largest)

Final Answer:
1) $9 \times 2 = 18$
2) $3 + 21 = 24$
3) $6 \div 2 = 3$
4) $50 - 39 = 11$
5) $20 \times 2 = 40$
6) $1 \times 3 = 3$
7) $6 + 3 = 9$
8) $24 \div 8 = 3$
9) $-7 \times 2 = -14$
10) $9 \times 6 = 54$
11) $49 - 44 = 5$
12) $100 \div 20 = 5$
13) $27 - 20 = 7$
14) $81 - 80 = 1$

Complex Calculations:
13) $44 \times 16 = 704$
14) $81 \times 25 = 2025$
15) $1000 - 648 = 352$
16) $48 \div 8 = 6$
17) $730 \div 73 = 10$
17) $9 \times 39 = 351$

Ordering Task:
Smallest: $(10^3 \div 5^2) - (5^2 \times 2)$ [Value: -10]
Middle: $6^3 - (5^2 \times 2^3)$ [Value: 16]
Largest: $(15^2 - 10^2) \div 5$ [Value: 25]