50+ Operations With Rational Numbers worksheets for 7th Class on ... - Free Printable

Problem: Solve the given expressions involving rational numbers using the order of operations (PEMDAS/BODMAS).

#### Expressions to Solve:
1. \( -1 - 3 \frac{1}{5} \times -\frac{3}{2} \)
2. \( 2 \frac{4}{5} + 3 \frac{3}{4} \div -2 \frac{1}{2} \)
3. \( \frac{7}{4} \left( 2 \frac{1}{2} + \frac{1}{5} \right) \)
4. \( -6 + 3 \frac{5}{6} - \frac{3}{2} \)
5. \( \frac{1}{2} \div -\frac{2}{3} - \frac{7}{5} \)
6. \( \left( \frac{1}{2} - 2 \frac{1}{6} \right) \div -\frac{7}{4} \)
7. \( -6 \frac{1}{3} + \frac{3}{4} + 1 \frac{5}{6} \)
8. \( \frac{3}{2} \div \frac{5}{6} \times \frac{2}{3} \)
9. \( \left( \frac{2}{3} - 2 \frac{3}{4} \right) \div -\frac{7}{4} \)
10. \( \frac{5}{6} \div 1 \frac{1}{6} - 1 \frac{5}{6} \)
11. \( \left( \frac{5}{3} \div -\frac{4}{3} \right)^2 \)
12. \( \frac{3}{4} \div \left( -\frac{3}{4} - 2 \frac{5}{6} \right) \)

---

Solution:

#### 1. \( -1 - 3 \frac{1}{5} \times -\frac{3}{2} \)

- Convert mixed numbers to improper fractions:
\[
3 \frac{1}{5} = \frac{16}{5}
\]
- Apply the order of operations (multiplication before subtraction):
\[
-1 - \left( \frac{16}{5} \times -\frac{3}{2} \right)
\]
- Perform the multiplication:
\[
\frac{16}{5} \times -\frac{3}{2} = \frac{16 \times -3}{5 \times 2} = \frac{-48}{10} = -\frac{24}{5}
\]
- Substitute back:
\[
-1 - \left( -\frac{24}{5} \right) = -1 + \frac{24}{5}
\]
- Convert \(-1\) to a fraction with a denominator of 5:
\[
-1 = -\frac{5}{5}
\]
- Add the fractions:
\[
-\frac{5}{5} + \frac{24}{5} = \frac{-5 + 24}{5} = \frac{19}{5}
\]

Answer:
\[
\boxed{\frac{19}{5}}
\]

---

#### 2. \( 2 \frac{4}{5} + 3 \frac{3}{4} \div -2 \frac{1}{2} \)

- Convert mixed numbers to improper fractions:
\[
2 \frac{4}{5} = \frac{14}{5}, \quad 3 \frac{3}{4} = \frac{15}{4}, \quad -2 \frac{1}{2} = -\frac{5}{2}
\]
- Apply the order of operations (division before addition):
\[
\frac{14}{5} + \left( \frac{15}{4} \div -\frac{5}{2} \right)
\]
- Perform the division:
\[
\frac{15}{4} \div -\frac{5}{2} = \frac{15}{4} \times -\frac{2}{5} = \frac{15 \times -2}{4 \times 5} = \frac{-30}{20} = -\frac{3}{2}
\]
- Substitute back:
\[
\frac{14}{5} + \left( -\frac{3}{2} \right)
\]
- Find a common denominator (10) and add:
\[
\frac{14}{5} = \frac{28}{10}, \quad -\frac{3}{2} = -\frac{15}{10}
\]
\[
\frac{28}{10} + \left( -\frac{15}{10} \right) = \frac{28 - 15}{10} = \frac{13}{10}
\]

Answer:
\[
\boxed{\frac{13}{10}}
\]

---

#### 3. \( \frac{7}{4} \left( 2 \frac{1}{2} + \frac{1}{5} \right) \)

- Convert mixed numbers to improper fractions:
\[
2 \frac{1}{2} = \frac{5}{2}
\]
- Simplify inside the parentheses:
\[
2 \frac{1}{2} + \frac{1}{5} = \frac{5}{2} + \frac{1}{5}
\]
- Find a common denominator (10) and add:
\[
\frac{5}{2} = \frac{25}{10}, \quad \frac{1}{5} = \frac{2}{10}
\]
\[
\frac{25}{10} + \frac{2}{10} = \frac{27}{10}
\]
- Multiply by \(\frac{7}{4}\):
\[
\frac{7}{4} \times \frac{27}{10} = \frac{7 \times 27}{4 \times 10} = \frac{189}{40}
\]

Answer:
\[
\boxed{\frac{189}{40}}
\]

---

#### 4. \( -6 + 3 \frac{5}{6} - \frac{3}{2} \)

- Convert mixed numbers to improper fractions:
\[
3 \frac{5}{6} = \frac{23}{6}
\]
- Rewrite the expression:
\[
-6 + \frac{23}{6} - \frac{3}{2}
\]
- Convert all terms to fractions with a common denominator (6):
\[
-6 = -\frac{36}{6}, \quad \frac{3}{2} = \frac{9}{6}
\]
- Combine the fractions:
\[
-\frac{36}{6} + \frac{23}{6} - \frac{9}{6} = \frac{-36 + 23 - 9}{6} = \frac{-22}{6} = -\frac{11}{3}
\]

Answer:
\[
\boxed{-\frac{11}{3}}
\]

---

#### 5. \( \frac{1}{2} \div -\frac{2}{3} - \frac{7}{5} \)

- Perform the division:
\[
\frac{1}{2} \div -\frac{2}{3} = \frac{1}{2} \times -\frac{3}{2} = \frac{1 \times -3}{2 \times 2} = -\frac{3}{4}
\]
- Subtract \(\frac{7}{5}\):
\[
-\frac{3}{4} - \frac{7}{5}
\]
- Find a common denominator (20) and subtract:
\[
-\frac{3}{4} = -\frac{15}{20}, \quad \frac{7}{5} = \frac{28}{20}
\]
\[
-\frac{15}{20} - \frac{28}{20} = \frac{-15 - 28}{20} = \frac{-43}{20}
\]

Answer:
\[
\boxed{-\frac{43}{20}}
\]

---

#### 6. \( \left( \frac{1}{2} - 2 \frac{1}{6} \right) \div -\frac{7}{4} \)

- Convert mixed numbers to improper fractions:
\[
2 \frac{1}{6} = \frac{13}{6}
\]
- Simplify inside the parentheses:
\[
\frac{1}{2} - \frac{13}{6}
\]
- Find a common denominator (6) and subtract:
\[
\frac{1}{2} = \frac{3}{6}
\]
\[
\frac{3}{6} - \frac{13}{6} = \frac{3 - 13}{6} = -\frac{10}{6} = -\frac{5}{3}
\]
- Divide by \(-\frac{7}{4}\):
\[
-\frac{5}{3} \div -\frac{7}{4} = -\frac{5}{3} \times -\frac{4}{7} = \frac{5 \times 4}{3 \times 7} = \frac{20}{21}
\]

Answer:
\[
\boxed{\frac{20}{21}}
\]

---

#### 7. \( -6 \frac{1}{3} + \frac{3}{4} + 1 \frac{5}{6} \)

- Convert mixed numbers to improper fractions:
\[
-6 \frac{1}{3} = -\frac{19}{3}, \quad 1 \frac{5}{6} = \frac{11}{6}
\]
- Rewrite the expression:
\[
-\frac{19}{3} + \frac{3}{4} + \frac{11}{6}
\]
- Find a common denominator (12) and combine:
\[
-\frac{19}{3} = -\frac{76}{12}, \quad \frac{3}{4} = \frac{9}{12}, \quad \frac{11}{6} = \frac{22}{12}
\]
\[
-\frac{76}{12} + \frac{9}{12} + \frac{22}{12} = \frac{-76 + 9 + 22}{12} = \frac{-45}{12} = -\frac{15}{4}
\]

Answer:
\[
\boxed{-\frac{15}{4}}
\]

---

#### 8. \( \frac{3}{2} \div \frac{5}{6} \times \frac{2}{3} \)

- Perform the division first:
\[
\frac{3}{2} \div \frac{5}{6} = \frac{3}{2} \times \frac{6}{5} = \frac{3 \times 6}{2 \times 5} = \frac{18}{10} = \frac{9}{5}
\]
- Multiply by \(\frac{2}{3}\):
\[
\frac{9}{5} \times \frac{2}{3} = \frac{9 \times 2}{5 \times 3} = \frac{18}{15} = \frac{6}{5}
\]

Answer:
\[
\boxed{\frac{6}{5}}
\]

---

#### 9. \( \left( \frac{2}{3} - 2 \frac{3}{4} \right) \div -\frac{7}{4} \)

- Convert mixed numbers to improper fractions:
\[
2 \frac{3}{4} = \frac{11}{4}
\]
- Simplify inside the parentheses:
\[
\frac{2}{3} - \frac{11}{4}
\]
- Find a common denominator (12) and subtract:
\[
\frac{2}{3} = \frac{8}{12}, \quad \frac{11}{4} = \frac{33}{12}
\]
\[
\frac{8}{12} - \frac{33}{12} = \frac{8 - 33}{12} = -\frac{25}{12}
\]
- Divide by \(-\frac{7}{4}\):
\[
-\frac{25}{12} \div -\frac{7}{4} = -\frac{25}{12} \times -\frac{4}{7} = \frac{25 \times 4}{12 \times 7} = \frac{100}{84} = \frac{25}{21}
\]

Answer:
\[
\boxed{\frac{25}{21}}
\]

---

#### 10. \( \frac{5}{6} \div 1 \frac{1}{6} - 1 \frac{5}{6} \)

- Convert mixed numbers to improper fractions:
\[
1 \frac{1}{6} = \frac{7}{6}, \quad 1 \frac{5}{6} = \frac{11}{6}
\]
- Perform the division:
\[
\frac{5}{6} \div \frac{7}{6} = \frac{5}{6} \times \frac{6}{7} = \frac{5 \times 6}{6 \times 7} = \frac{5}{7}
\]
- Subtract \(\frac{11}{6}\):
\[
\frac{5}{7} - \frac{11}{6}
\]
- Find a common denominator (42) and subtract:
\[
\frac{5}{7} = \frac{30}{42}, \quad \frac{11}{6} = \frac{77}{42}
\]
\[
\frac{30}{42} - \frac{77}{42} = \frac{30 - 77}{42} = \frac{-47}{42}
\]

Answer:
\[
\boxed{-\frac{47}{42}}
\]

---

#### 11. \( \left( \frac{5}{3} \div -\frac{4}{3} \right)^2 \)

- Perform the division inside the parentheses:
\[
\frac{5}{3} \div -\frac{4}{3} = \frac{5}{3} \times -\frac{3}{4} = \frac{5 \times -3}{3 \times 4} = -\frac{5}{4}
\]
- Square the result:
\[
\left( -\frac{5}{4} \right)^2 = \left( -\frac{5}{4} \right) \times \left( -\frac{5}{4} \right) = \frac{25}{16}
\]

Answer:
\[
\boxed{\frac{25}{16}}
\]

---

#### 12. \( \frac{3}{4} \div \left( -\frac{3}{4} - 2 \frac{5}{6} \right) \)

- Convert mixed numbers to improper fractions:
\[
2 \frac{5}{6} = \frac{17}{6}
\]
- Simplify inside the parentheses:
\[
-\frac{3}{4} - \frac{17}{6}
\]
- Find a common denominator (12) and subtract:
\[
-\frac{3}{4} = -\frac{9}{12}, \quad \frac{17}{6} = \frac{34}{12}
\]
\[
-\frac{9}{12} - \frac{34}{12} = \frac{-9 - 34}{12} = -\frac{43}{12}
\]
- Divide \(\frac{3}{4}\) by \(-\frac{43}{12}\):
\[
\frac{3}{4} \div -\frac{43}{12} = \frac{3}{4} \times -\frac{12}{43} = \frac{3 \times -12}{4 \times 43} = -\frac{36}{172} = -\frac{9}{43}
\]

Answer:
\[
\boxed{-\frac{9}{43}}
\]

---

Final Answers:

1. \(\boxed{\frac{19}{5}}\)
2. \(\boxed{\frac{13}{10}}\)
3. \(\boxed{\frac{189}{40}}\)
4. \(\boxed{-\frac{11}{3}}\)
5. \(\boxed{-\frac{43}{20}}\)
6. \(\boxed{\frac{20}{21}}\)
7. \(\boxed{-\frac{15}{4}}\)
8. \(\boxed{\frac{6}{5}}\)
9. \(\boxed{\frac{25}{21}}\)
10. \(\boxed{-\frac{47}{42}}\)
11. \(\boxed{\frac{25}{16}}\)
12. \(\boxed{-\frac{9}{43}}\)