Math worksheet practicing order of operations with various expressions.

To solve the given problems, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Let's solve each problem step by step:

---

a) \( 4(3 + 2) \)

1. Solve the expression inside the parentheses:
\[
3 + 2 = 5
\]
2. Multiply:
\[
4 \times 5 = 20
\]

Answer:
\[
\boxed{20}
\]

---

b) \( \frac{4(3 + 2)}{10} \)

1. Solve the expression inside the parentheses:
\[
3 + 2 = 5
\]
2. Multiply:
\[
4 \times 5 = 20
\]
3. Divide:
\[
\frac{20}{10} = 2
\]

Answer:
\[
\boxed{2}
\]

---

c) \( \frac{3 + 2(5) + 7}{4} \)

1. Perform multiplication first:
\[
2(5) = 10
\]
2. Add the numbers in the numerator:
\[
3 + 10 + 7 = 20
\]
3. Divide:
\[
\frac{20}{4} = 5
\]

Answer:
\[
\boxed{5}
\]

---

d) \( \frac{4(5 + 2 - 1 + 2)}{2 \times 2} \)

1. Solve the expression inside the parentheses:
\[
5 + 2 - 1 + 2 = 8
\]
2. Multiply:
\[
4 \times 8 = 32
\]
3. Solve the denominator:
\[
2 \times 2 = 4
\]
4. Divide:
\[
\frac{32}{4} = 8
\]

Answer:
\[
\boxed{8}
\]

---

e) \( \frac{21 + 3}{14 - 10} \)

1. Solve the numerator:
\[
21 + 3 = 24
\]
2. Solve the denominator:
\[
14 - 10 = 4
\]
3. Divide:
\[
\frac{24}{4} = 6
\]

Answer:
\[
\boxed{6}
\]

---

f) \( \frac{2(5 + 1)}{14 - 10} \)

1. Solve the expression inside the parentheses in the numerator:
\[
5 + 1 = 6
\]
2. Multiply:
\[
2 \times 6 = 12
\]
3. Solve the denominator:
\[
14 - 10 = 4
\]
4. Divide:
\[
\frac{12}{4} = 3
\]

Answer:
\[
\boxed{3}
\]

---

g) \( \frac{6 + 2(5 + 1)}{3} \)

1. Solve the expression inside the parentheses:
\[
5 + 1 = 6
\]
2. Multiply:
\[
2 \times 6 = 12
\]
3. Add:
\[
6 + 12 = 18
\]
4. Divide:
\[
\frac{18}{3} = 6
\]

Answer:
\[
\boxed{6}
\]

---

h) \( \frac{6 + (5^2 + 1)}{8} \)

1. Solve the exponent:
\[
5^2 = 25
\]
2. Add inside the parentheses:
\[
25 + 1 = 26
\]
3. Add:
\[
6 + 26 = 32
\]
4. Divide:
\[
\frac{32}{8} = 4
\]

Answer:
\[
\boxed{4}
\]

---

i) \( \frac{2(\sqrt{36})}{8} \)

1. Solve the square root:
\[
\sqrt{36} = 6
\]
2. Multiply:
\[
2 \times 6 = 12
\]
3. Divide:
\[
\frac{12}{8} = \frac{3}{2}
\]

Answer:
\[
\boxed{\frac{3}{2}}
\]

---

j) \( \frac{6 + 2(\sqrt{4})}{5} \)

1. Solve the square root:
\[
\sqrt{4} = 2
\]
2. Multiply:
\[
2 \times 2 = 4
\]
3. Add:
\[
6 + 4 = 10
\]
4. Divide:
\[
\frac{10}{5} = 2
\]

Answer:
\[
\boxed{2}
\]

---

k) \( \frac{6 - 3 + 3(\sqrt{16})}{\sqrt{9}} \)

1. Solve the square roots:
\[
\sqrt{16} = 4 \quad \text{and} \quad \sqrt{9} = 3
\]
2. Multiply:
\[
3 \times 4 = 12
\]
3. Perform addition and subtraction in the numerator:
\[
6 - 3 + 12 = 15
\]
4. Divide:
\[
\frac{15}{3} = 5
\]

Answer:
\[
\boxed{5}
\]

---

l) \( \frac{2(\sqrt{4^3})}{5 + 3} \)

1. Solve the exponent:
\[
4^3 = 64
\]
2. Solve the square root:
\[
\sqrt{64} = 8
\]
3. Multiply:
\[
2 \times 8 = 16
\]
4. Solve the denominator:
\[
5 + 3 = 8
\]
5. Divide:
\[
\frac{16}{8} = 2
\]

Answer:
\[
\boxed{2}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ccc}
a) & 20 & \\
b) & 2 & \\
c) & 5 & \\
d) & 8 & \\
e) & 6 & \\
f) & 3 & \\
g) & 6 & \\
h) & 4 & \\
i) & \frac{3}{2} & \\
j) & 2 & \\
k) & 5 & \\
l) & 2 &
\end{array}
}
\]