Order of Operations with Decimals Worksheets - Free Printable

Problem: Solve the following equations using the order of operations (PEMDAS/BODMAS).

The equations are as follows:

1. \( (6.1 + 7.0) - 8.3 \)
2. \( (5.5 + 1.4) - (3.2) \)
3. \( (6.5 + 7.1) - 8 \)
4. \( (4.5 + 5.5) - 2.5 \)
5. \( (7 - 6) + (7.5 - 6.5) \)
6. \( (9.6 + 3.3) - (8.5) \)
7. \( (6.4 + (9.2 - 6.1)) \times 5 \)
8. \( (4.5 + 4) - (5 - 1.5) \)
9. \( 9.5 - (7 + 3.6) \times 4 \)
10. \( 8 = (X + Z) - Z \)

---

Solution:

#### Step 1: Recall the Order of Operations
The order of operations is:
1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

---

#### Equation 1: \( (6.1 + 7.0) - 8.3 \)

1. Solve inside the parentheses:
\[
6.1 + 7.0 = 13.1
\]
2. Subtract:
\[
13.1 - 8.3 = 4.8
\]

Answer: \( 4.8 \)

---

#### Equation 2: \( (5.5 + 1.4) - (3.2) \)

1. Solve inside the parentheses:
\[
5.5 + 1.4 = 6.9
\]
2. Subtract:
\[
6.9 - 3.2 = 3.7
\]

Answer: \( 3.7 \)

---

#### Equation 3: \( (6.5 + 7.1) - 8 \)

1. Solve inside the parentheses:
\[
6.5 + 7.1 = 13.6
\]
2. Subtract:
\[
13.6 - 8 = 5.6
\]

Answer: \( 5.6 \)

---

#### Equation 4: \( (4.5 + 5.5) - 2.5 \)

1. Solve inside the parentheses:
\[
4.5 + 5.5 = 10.0
\]
2. Subtract:
\[
10.0 - 2.5 = 7.5
\]

Answer: \( 7.5 \)

---

#### Equation 5: \( (7 - 6) + (7.5 - 6.5) \)

1. Solve inside the first set of parentheses:
\[
7 - 6 = 1
\]
2. Solve inside the second set of parentheses:
\[
7.5 - 6.5 = 1.0
\]
3. Add:
\[
1 + 1.0 = 2.0
\]

Answer: \( 2.0 \)

---

#### Equation 6: \( (9.6 + 3.3) - (8.5) \)

1. Solve inside the first set of parentheses:
\[
9.6 + 3.3 = 12.9
\]
2. Subtract:
\[
12.9 - 8.5 = 4.4
\]

Answer: \( 4.4 \)

---

#### Equation 7: \( (6.4 + (9.2 - 6.1)) \times 5 \)

1. Solve inside the innermost parentheses:
\[
9.2 - 6.1 = 3.1
\]
2. Solve inside the outer parentheses:
\[
6.4 + 3.1 = 9.5
\]
3. Multiply:
\[
9.5 \times 5 = 47.5
\]

Answer: \( 47.5 \)

---

#### Equation 8: \( (4.5 + 4) - (5 - 1.5) \)

1. Solve inside the first set of parentheses:
\[
4.5 + 4 = 8.5
\]
2. Solve inside the second set of parentheses:
\[
5 - 1.5 = 3.5
\]
3. Subtract:
\[
8.5 - 3.5 = 5.0
\]

Answer: \( 5.0 \)

---

#### Equation 9: \( 9.5 - (7 + 3.6) \times 4 \)

1. Solve inside the parentheses:
\[
7 + 3.6 = 10.6
\]
2. Multiply:
\[
10.6 \times 4 = 42.4
\]
3. Subtract:
\[
9.5 - 42.4 = -32.9
\]

Answer: \( -32.9 \)

---

#### Equation 10: \( 8 = (X + Z) - Z \)

1. Simplify the right-hand side:
\[
(X + Z) - Z = X
\]
2. The equation becomes:
\[
8 = X
\]

Answer: \( X = 8 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 4.8 \\
2. & \ 3.7 \\
3. & \ 5.6 \\
4. & \ 7.5 \\
5. & \ 2.0 \\
6. & \ 4.4 \\
7. & \ 47.5 \\
8. & \ 5.0 \\
9. & \ -32.9 \\
10. & \ 8
\end{aligned}
}
\]