301 Moved Permanently - Free Printable

Let's solve each expression step by step. We will evaluate the subtraction and addition of rational numbers, which includes fractions, integers, and negative numbers.

---

Key Rules to Remember:

- Subtracting a negative number is like adding: $ a - (-b) = a + b $
- Adding or subtracting fractions requires a common denominator.
- When combining positive and negative numbers, follow sign rules.

We'll go through each problem:

---

1) $ \frac{3}{7} + \frac{2}{3} - \frac{5}{3} $

First, combine $ \frac{2}{3} - \frac{5}{3} = -\frac{3}{3} = -1 $

Now: $ \frac{3}{7} + (-1) = \frac{3}{7} - 1 = \frac{3}{7} - \frac{7}{7} = -\frac{4}{7} $

✔ Answer: $ -\frac{4}{7} $

---

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

Simplify: $ -\frac{4}{5} + 1 + \frac{3}{2} $

Convert to common denominator (LCM of 5, 1, 2 = 10):

$ -\frac{8}{10} + \frac{10}{10} + \frac{15}{10} = \frac{-8 + 10 + 15}{10} = \frac{17}{10} $

✔ Answer: $ \frac{17}{10} $

---

3) $ 0 + (-2) + \left(-\frac{3}{2}\right) $

$ -2 - \frac{3}{2} = -\frac{4}{2} - \frac{3}{2} = -\frac{7}{2} $

✔ Answer: $ -\frac{7}{2} $

---

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

$ -\frac{5}{4} + 1 + \frac{3}{5} $

Common denominator = 20:

$ -\frac{25}{20} + \frac{20}{20} + \frac{12}{20} = \frac{-25 + 20 + 12}{20} = \frac{7}{20} $

✔ Answer: $ \frac{7}{20} $

---

5) $ \left(-\frac{1}{2}\right) - (-2) + \frac{1}{8} $

$ -\frac{1}{2} + 2 + \frac{1}{8} $

Convert: $ -\frac{4}{8} + \frac{16}{8} + \frac{1}{8} = \frac{13}{8} $

✔ Answer: $ \frac{13}{8} $

---

6) $ \left(-\frac{3}{4}\right) + (-1) - \frac{3}{8} $

$ -\frac{3}{4} - 1 - \frac{3}{8} $

Convert to eighths: $ -\frac{6}{8} - \frac{8}{8} - \frac{3}{8} = -\frac{17}{8} $

✔ Answer: $ -\frac{17}{8} $

---

7) $ \left(-\frac{9}{7}\right) + \left(-\frac{7}{4}\right) + \left(-\frac{4}{3}\right) $

All negative: $ -\left( \frac{9}{7} + \frac{7}{4} + \frac{4}{3} \right) $

LCM of 7, 4, 3 = 84

$ \frac{9}{7} = \frac{108}{84},\ \frac{7}{4} = \frac{147}{84},\ \frac{4}{3} = \frac{112}{84} $

Sum: $ \frac{108 + 147 + 112}{84} = \frac{367}{84} $

So answer: $ -\frac{367}{84} $

✔ Answer: $ -\frac{367}{84} $

---

8) $ \frac{12}{7} + (-2) - \left(-\frac{3}{7}\right) $

$ \frac{12}{7} - 2 + \frac{3}{7} = \left(\frac{12}{7} + \frac{3}{7}\right) - 2 = \frac{15}{7} - 2 $

$ \frac{15}{7} - \frac{14}{7} = \frac{1}{7} $

✔ Answer: $ \frac{1}{7} $

---

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

$ \frac{4}{3} - 1 - \frac{7}{4} $

Convert to twelfths: LCM of 3, 4 = 12

$ \frac{16}{12} - \frac{12}{12} - \frac{21}{12} = \frac{16 - 12 - 21}{12} = \frac{-17}{12} $

✔ Answer: $ -\frac{17}{12} $

---

10) $ \frac{5}{3} - 2 - \frac{5}{3} $

$ \left(\frac{5}{3} - \frac{5}{3}\right) - 2 = 0 - 2 = -2 $

✔ Answer: $ -2 $

---

11) $ \left(-\frac{3}{2}\right) - \frac{3}{2} + \left(-\frac{5}{8}\right) $

$ -\frac{3}{2} - \frac{3}{2} = -3 $, then $ -3 - \frac{5}{8} = -\frac{24}{8} - \frac{5}{8} = -\frac{29}{8} $

✔ Answer: $ -\frac{29}{8} $

---

12) $ 0 - (-2) - \left(-\frac{4}{3}\right) $

$ 0 + 2 + \frac{4}{3} = 2 + \frac{4}{3} = \frac{6}{3} + \frac{4}{3} = \frac{10}{3} $

✔ Answer: $ \frac{10}{3} $

---

13) $ \left(-\frac{3}{2}\right) - \frac{13}{7} + (-2) $

$ -\frac{3}{2} - \frac{13}{7} - 2 $

Convert to common denominator (LCM of 2, 7 = 14)

$ -\frac{21}{14} - \frac{26}{14} - \frac{28}{14} = \frac{-21 - 26 - 28}{14} = \frac{-75}{14} $

✔ Answer: $ -\frac{75}{14} $

---

14) $ (-2) + \left(-\frac{3}{2}\right) - \frac{1}{2} $

$ -2 - \frac{3}{2} - \frac{1}{2} = -2 - \frac{4}{2} = -2 - 2 = -4 $

✔ Answer: $ -4 $

---

15) $ \left(-\frac{8}{7}\right) - \left(-\frac{3}{2}\right) + (-1) $

$ -\frac{8}{7} + \frac{3}{2} - 1 $

LCM of 7 and 2 = 14

$ -\frac{16}{14} + \frac{21}{14} - \frac{14}{14} = \frac{-16 + 21 - 14}{14} = \frac{-9}{14} $

✔ Answer: $ -\frac{9}{14} $

---

16) $ \left(-\frac{3}{2}\right) - 1 - \left(-\frac{7}{6}\right) $

$ -\frac{3}{2} - 1 + \frac{7}{6} $

Convert to sixths:

$ -\frac{9}{6} - \frac{6}{6} + \frac{7}{6} = \frac{-9 - 6 + 7}{6} = \frac{-8}{6} = -\frac{4}{3} $

✔ Answer: $ -\frac{4}{3} $

---

17) $ \frac{10}{7} + 6 + \left(-\frac{1}{2}\right) $

$ \frac{10}{7} + 6 - \frac{1}{2} $

Convert to 14ths:

$ \frac{20}{14} + \frac{84}{14} - \frac{7}{14} = \frac{20 + 84 - 7}{14} = \frac{97}{14} $

✔ Answer: $ \frac{97}{14} $

---

18) $ 3 + \frac{1}{2} - \left(-\frac{3}{5}\right) $

$ 3 + \frac{1}{2} + \frac{3}{5} $

LCM of 2 and 5 = 10

$ 3 + \frac{5}{10} + \frac{6}{10} = 3 + \frac{11}{10} = \frac{30}{10} + \frac{11}{10} = \frac{41}{10} $

✔ Answer: $ \frac{41}{10} $

---

19) $ 7 - \left(-\frac{3}{4}\right) + 1 $

$ 7 + \frac{3}{4} + 1 = 8 + \frac{3}{4} = \frac{32}{4} + \frac{3}{4} = \frac{35}{4} $

✔ Answer: $ \frac{35}{4} $

---

20) $ \frac{5}{3} + \frac{3}{4} - 2 $

LCM of 3 and 4 = 12

$ \frac{20}{12} + \frac{9}{12} - \frac{24}{12} = \frac{5}{12} $

✔ Answer: $ \frac{5}{12} $

---

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

LCM of 2, 3, 5 = 30

$ \frac{45}{30} + \frac{40}{30} - \frac{36}{30} = \frac{49}{30} $

✔ Answer: $ \frac{49}{30} $

---

22) $ (-1) + 0 + \left(-\frac{10}{7}\right) $

$ -1 - \frac{10}{7} = -\frac{7}{7} - \frac{10}{7} = -\frac{17}{7} $

✔ Answer: $ -\frac{17}{7} $

---

## ✔ Final Answers:

| Problem | Answer |
|--------|----------------|
| 1 | $ -\frac{4}{7} $ |
| 2 | $ \frac{17}{10} $ |
| 3 | $ -\frac{7}{2} $ |
| 4 | $ \frac{7}{20} $ |
| 5 | $ \frac{13}{8} $ |
| 6 | $ -\frac{17}{8} $ |
| 7 | $ -\frac{367}{84} $ |
| 8 | $ \frac{1}{7} $ |
| 9 | $ -\frac{17}{12} $ |
| 10 | $ -2 $ |
| 11 | $ -\frac{29}{8} $ |
| 12 | $ \frac{10}{3} $ |
| 13 | $ -\frac{75}{14} $ |
| 14 | $ -4 $ |
| 15 | $ -\frac{9}{14} $ |
| 16 | $ -\frac{4}{3} $ |
| 17 | $ \frac{97}{14} $ |
| 18 | $ \frac{41}{10} $ |
| 19 | $ \frac{35}{4} $ |
| 20 | $ \frac{5}{12} $ |
| 21 | $ \frac{49}{30} $ |
| 22 | $ -\frac{17}{7} $ |

---

Let me know if you'd like these answers formatted as a printable worksheet or need explanations for any specific ones!