Complex Fractions Worksheet featuring six problems to simplify, including mixed numbers and fractions.

Let’s solve each complex fraction one by one.

---

1 a.

We have:

> (1 2/9) / (-11/2)

Step 1: Convert mixed number to improper fraction.

1 2/9 = (9×1 + 2)/9 = 11/9

So now we have:

> (11/9) ÷ (-11/2)

Step 2: Dividing by a fraction is multiplying by its reciprocal.

= (11/9) × (-2/11)

Step 3: Cancel common factors.

The 11 in numerator and denominator cancels out.

= (1/9) × (-2/1) = -2/9

✔ Final for 1a: -2/9

---

1 b.

> (4 3/7) / (-22/3)

Step 1: Convert mixed number.

4 3/7 = (7×4 + 3)/7 = 31/7

Now:

> (31/7) ÷ (-22/3)

Step 2: Multiply by reciprocal.

= (31/7) × (-3/22)

Step 3: Multiply numerators and denominators.

Numerator: 31 × (-3) = -93
Denominator: 7 × 22 = 154

So: -93/154

Check if it can be simplified.

Factors of 93: 3 × 31
Factors of 154: 2 × 7 × 11 → no common factors with 93.

✔ Final for 1b: -93/154

---

2 a.

> (18/7) / (2 1/2)

Step 1: Convert mixed number.

2 1/2 = (2×2 + 1)/2 = 5/2

Now:

> (18/7) ÷ (5/2)

Step 2: Multiply by reciprocal.

= (18/7) × (2/5) = (18×2)/(7×5) = 36/35

Can’t simplify further.

✔ Final for 2a: 36/35

---

2 b.

> (-4 2/3) / (-22/9)

Step 1: Convert mixed number.

-4 2/3 = -(4×3 + 2)/3 = -14/3

Now:

> (-14/3) ÷ (-22/9)

Step 2: Multiply by reciprocal.

= (-14/3) × (-9/22)

Step 3: Multiply.

Negatives cancel → positive.

(14 × 9) / (3 × 22)

Simplify before multiplying:

9 and 3 → 9÷3=3, 3÷3=1 → so becomes (14 × 3) / (1 × 22) = 42/22

Simplify 42/22: divide numerator and denominator by 2 → 21/11

✔ Final for 2b: 21/11

---

3 a.

> (-8 4/8) / (13/10)

Step 1: Simplify mixed number first.

4/8 = 1/2 → so -8 4/8 = -8 1/2

Convert to improper: - (8×2 + 1)/2 = -17/2

Now:

> (-17/2) ÷ (13/10)

Step 2: Multiply by reciprocal.

= (-17/2) × (10/13)

Step 3: Multiply.

= (-17 × 10) / (2 × 13) = -170 / 26

Simplify: divide numerator and denominator by 2 → -85/13

✔ Final for 3a: -85/13

---

3 b.

> (-2/3) / (4 1/3)

Step 1: Convert mixed number.

4 1/3 = (4×3 + 1)/3 = 13/3

Now:

> (-2/3) ÷ (13/3)

Step 2: Multiply by reciprocal.

= (-2/3) × (3/13)

Step 3: Cancel 3s.

= (-2/1) × (1/13) = -2/13

✔ Final for 3b: -2/13

---

Final Answers:

1 a. -2/9
1 b. -93/154
2 a. 36/35
2 b. 21/11
3 a. -85/13
3 b. -2/13

──────────────────────────────────────

Final Answer:
1 a. -2/9
1 b. -93/154
2 a. 36/35
2 b. 21/11
3 a. -85/13
3 b. -2/13