Math worksheet for practicing order of operations with fractions and integers.

Let's solve each problem step by step, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

---

1. $ 2 - \left(\frac{3}{5} - \left(-\frac{2}{5}\right)\right) $

First, simplify inside the parentheses:

$$
\frac{3}{5} - (-\frac{2}{5}) = \frac{3}{5} + \frac{2}{5} = \frac{5}{5} = 1
$$

Now subtract:
$$
2 - 1 = 1
$$

✔ Answer: 1

---

2. $ \frac{3}{8} - \left(-\frac{6}{5} + (-\frac{3}{4})\right) $

Simplify inside the parentheses:

$$
-\frac{6}{5} + (-\frac{3}{4}) = -\frac{6}{5} - \frac{3}{4}
$$

Find common denominator (LCM of 5 and 4 is 20):

$$
-\frac{6}{5} = -\frac{24}{20}, \quad -\frac{3}{4} = -\frac{15}{20}
\Rightarrow -\frac{24}{20} - \frac{15}{20} = -\frac{39}{20}
$$

Now:
$$
\frac{3}{8} - (-\frac{39}{20}) = \frac{3}{8} + \frac{39}{20}
$$

Common denominator (LCM of 8 and 20 is 40):

$$
\frac{3}{8} = \frac{15}{40}, \quad \frac{39}{20} = \frac{78}{40}
\Rightarrow \frac{15}{40} + \frac{78}{40} = \frac{93}{40}
$$

✔ Answer: $ \frac{93}{40} $ or $ 2\frac{13}{40} $

---

3. $ \frac{2}{5}^{(-3)} \div (-\frac{1}{4}) $

This expression is ambiguous in notation. But it likely means:

$$
\left(\frac{2}{5}\right)^{-3} \div \left(-\frac{1}{4}\right)
$$

First, compute $ \left(\frac{2}{5}\right)^{-3} $:

$$
= \left(\frac{5}{2}\right)^3 = \frac{125}{8}
$$

Now divide by $ -\frac{1}{4} $:

$$
\frac{125}{8} \div \left(-\frac{1}{4}\right) = \frac{125}{8} \times (-4) = -\frac{500}{8} = -\frac{125}{2}
$$

✔ Answer: $ -\frac{125}{2} $ or $ -62.5 $

---

4. $ \frac{1}{2}^{-3} \cdot (-6) $

Again, this means $ \left(\frac{1}{2}\right)^{-3} \cdot (-6) $

$$
\left(\frac{1}{2}\right)^{-3} = (2)^3 = 8
$$

Now multiply:
$$
8 \cdot (-6) = -48
$$

✔ Answer: -48

---

5. $ \frac{11}{5} - \left(\frac{12}{5} - \frac{7}{4}\right) $

First, simplify inside parentheses:

$$
\frac{12}{5} - \frac{7}{4}
$$

LCM of 5 and 4 is 20:

$$
\frac{12}{5} = \frac{48}{20}, \quad \frac{7}{4} = \frac{35}{20}
\Rightarrow \frac{48}{20} - \frac{35}{20} = \frac{13}{20}
$$

Now:
$$
\frac{11}{5} - \frac{13}{20}
$$

Convert $ \frac{11}{5} = \frac{44}{20} $

$$
\frac{44}{20} - \frac{13}{20} = \frac{31}{20}
$$

✔ Answer: $ \frac{31}{20} $ or $ 1\frac{11}{20} $

---

6. $ -\frac{3}{2} + \frac{1}{4} + \frac{1}{6} $

Find a common denominator. LCM of 2, 4, 6 is 12.

$$
-\frac{3}{2} = -\frac{18}{12}, \quad \frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12}
$$

Add:
$$
-\frac{18}{12} + \frac{3}{12} + \frac{2}{12} = -\frac{13}{12}
$$

✔ Answer: $ -\frac{13}{12} $ or $ -1\frac{1}{12} $

---

7. $ (-\frac{3}{4}) \div (\frac{3}{4} \div \frac{1}{4}) $

First, simplify inside the parentheses:

$$
\frac{3}{4} \div \frac{1}{4} = \frac{3}{4} \times \frac{4}{1} = 3
$$

Now:
$$
-\frac{3}{4} \div 3 = -\frac{3}{4} \times \frac{1}{3} = -\frac{3}{12} = -\frac{1}{4}
$$

✔ Answer: $ -\frac{1}{4} $

---

8. $ \frac{8}{3} \div (-2) - 1 $

First, divide:
$$
\frac{8}{3} \div (-2) = \frac{8}{3} \times \left(-\frac{1}{2}\right) = -\frac{8}{6} = -\frac{4}{3}
$$

Now subtract 1:
$$
-\frac{4}{3} - 1 = -\frac{4}{3} - \frac{3}{3} = -\frac{7}{3}
$$

✔ Answer: $ -\frac{7}{3} $ or $ -2\frac{1}{3} $

---

9. $ (-1)^{(-8)^2} $

First, evaluate exponent: $ (-8)^2 = 64 $

So we have:
$$
(-1)^{64}
$$

Any negative number raised to an even power is positive:
$$
(-1)^{64} = 1
$$

✔ Answer: 1

---

10. $ 7 + \left(-\frac{1}{3}\right) + \frac{4}{3} $

Combine the fractions:

$$
-\frac{1}{3} + \frac{4}{3} = \frac{3}{3} = 1
$$

Then:
$$
7 + 1 = 8
$$

✔ Answer: 8

---

✔ Final Answers:

1. $ 1 $
2. $ \frac{93}{40} $
3. $ -\frac{125}{2} $
4. $ -48 $
5. $ \frac{31}{20} $
6. $ -\frac{13}{12} $
7. $ -\frac{1}{4} $
8. $ -\frac{7}{3} $
9. $ 1 $
10. $ 8 $

Let me know if you'd like these as mixed numbers or decimals!