Fraction subtraction worksheet for simplifying to lowest terms.

To solve the given problems, we need to simplify each expression step by step. The key steps involve:

1. Finding a common denominator for all fractions in the expression.
2. Rewriting each fraction with the common denominator.
3. Performing the subtraction.
4. Simplifying the resulting fraction to its lowest terms.

Let's go through each problem one by one.

---

Problem 1:

$$
\frac{23}{24} - \frac{1}{4} - \frac{2}{12}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 24, 4, and 12. The LCD of these numbers is 24.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{23}{24}$ remains $\frac{23}{24}$.
- $\frac{1}{4} = \frac{1 \times 6}{4 \times 6} = \frac{6}{24}$.
- $\frac{2}{12} = \frac{2 \times 2}{12 \times 2} = \frac{4}{24}$.

#### Step 3: Perform the subtraction.
$$
\frac{23}{24} - \frac{6}{24} - \frac{4}{24} = \frac{23 - 6 - 4}{24} = \frac{13}{24}
$$

#### Step 4: Simplify the result.
$\frac{13}{24}$ is already in its lowest terms.

Answer:
$$
\boxed{\frac{13}{24}}
$$

---

Problem 2:

$$
\frac{53}{54} - \frac{4}{6} - \frac{1}{27}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 54, 6, and 27. The LCD of these numbers is 54.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{53}{54}$ remains $\frac{53}{54}$.
- $\frac{4}{6} = \frac{4 \times 9}{6 \times 9} = \frac{36}{54}$.
- $\frac{1}{27} = \frac{1 \times 2}{27 \times 2} = \frac{2}{54}$.

#### Step 3: Perform the subtraction.
$$
\frac{53}{54} - \frac{36}{54} - \frac{2}{54} = \frac{53 - 36 - 2}{54} = \frac{15}{54}
$$

#### Step 4: Simplify the result.
$\frac{15}{54}$ can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 3:
$$
\frac{15 \div 3}{54 \div 3} = \frac{5}{18}
$$

Answer:
$$
\boxed{\frac{5}{18}}
$$

---

Problem 3:

$$
\frac{30}{32} - \frac{2}{4} - \frac{1}{16}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 32, 4, and 16. The LCD of these numbers is 32.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{30}{32}$ remains $\frac{30}{32}$.
- $\frac{2}{4} = \frac{2 \times 8}{4 \times 8} = \frac{16}{32}$.
- $\frac{1}{16} = \frac{1 \times 2}{16 \times 2} = \frac{2}{32}$.

#### Step 3: Perform the subtraction.
$$
\frac{30}{32} - \frac{16}{32} - \frac{2}{32} = \frac{30 - 16 - 2}{32} = \frac{12}{32}
$$

#### Step 4: Simplify the result.
$\frac{12}{32}$ can be simplified by dividing both numerator and denominator by their GCD, which is 4:
$$
\frac{12 \div 4}{32 \div 4} = \frac{3}{8}
$$

Answer:
$$
\boxed{\frac{3}{8}}
$$

---

Problem 4:

$$
\frac{23}{24} - \frac{1}{3} - \frac{2}{12}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 24, 3, and 12. The LCD of these numbers is 24.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{23}{24}$ remains $\frac{23}{24}$.
- $\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}$.
- $\frac{2}{12} = \frac{2 \times 2}{12 \times 2} = \frac{4}{24}$.

#### Step 3: Perform the subtraction.
$$
\frac{23}{24} - \frac{8}{24} - \frac{4}{24} = \frac{23 - 8 - 4}{24} = \frac{11}{24}
$$

#### Step 4: Simplify the result.
$\frac{11}{24}$ is already in its lowest terms.

Answer:
$$
\boxed{\frac{11}{24}}
$$

---

Problem 5:

$$
\frac{16}{18} - \frac{4}{6} - \frac{1}{9}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 18, 6, and 9. The LCD of these numbers is 18.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{16}{18}$ remains $\frac{16}{18}$.
- $\frac{4}{6} = \frac{4 \times 3}{6 \times 3} = \frac{12}{18}$.
- $\frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18}$.

#### Step 3: Perform the subtraction.
$$
\frac{16}{18} - \frac{12}{18} - \frac{2}{18} = \frac{16 - 12 - 2}{18} = \frac{2}{18}
$$

#### Step 4: Simplify the result.
$\frac{2}{18}$ can be simplified by dividing both numerator and denominator by their GCD, which is 2:
$$
\frac{2 \div 2}{18 \div 2} = \frac{1}{9}
$$

Answer:
$$
\boxed{\frac{1}{9}}
$$

---

Problem 6:

$$
\frac{43}{45} - \frac{3}{5} - \frac{1}{15}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 45, 5, and 15. The LCD of these numbers is 45.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{43}{45}$ remains $\frac{43}{45}$.
- $\frac{3}{5} = \frac{3 \times 9}{5 \times 9} = \frac{27}{45}$.
- $\frac{1}{15} = \frac{1 \times 3}{15 \times 3} = \frac{3}{45}$.

#### Step 3: Perform the subtraction.
$$
\frac{43}{45} - \frac{27}{45} - \frac{3}{45} = \frac{43 - 27 - 3}{45} = \frac{13}{45}
$$

#### Step 4: Simplify the result.
$\frac{13}{45}$ is already in its lowest terms.

Answer:
$$
\boxed{\frac{13}{45}}
$$

---

Problem 7:

$$
\frac{49}{50} - \frac{5}{10} - \frac{2}{25}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 50, 10, and 25. The LCD of these numbers is 50.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{49}{50}$ remains $\frac{49}{50}$.
- $\frac{5}{10} = \frac{5 \times 5}{10 \times 5} = \frac{25}{50}$.
- $\frac{2}{25} = \frac{2 \times 2}{25 \times 2} = \frac{4}{50}$.

#### Step 3: Perform the subtraction.
$$
\frac{49}{50} - \frac{25}{50} - \frac{4}{50} = \frac{49 - 25 - 4}{50} = \frac{20}{50}
$$

#### Step 4: Simplify the result.
$\frac{20}{50}$ can be simplified by dividing both numerator and denominator by their GCD, which is 10:
$$
\frac{20 \div 10}{50 \div 10} = \frac{2}{5}
$$

Answer:
$$
\boxed{\frac{2}{5}}
$$

---

Problem 8:

$$
\frac{30}{32} - \frac{2}{4} - \frac{2}{16}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 32, 4, and 16. The LCD of these numbers is 32.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{30}{32}$ remains $\frac{30}{32}$.
- $\frac{2}{4} = \frac{2 \times 8}{4 \times 8} = \frac{16}{32}$.
- $\frac{2}{16} = \frac{2 \times 2}{16 \times 2} = \frac{4}{32}$.

#### Step 3: Perform the subtraction.
$$
\frac{30}{32} - \frac{16}{32} - \frac{4}{32} = \frac{30 - 16 - 4}{32} = \frac{10}{32}
$$

#### Step 4: Simplify the result.
$\frac{10}{32}$ can be simplified by dividing both numerator and denominator by their GCD, which is 2:
$$
\frac{10 \div 2}{32 \div 2} = \frac{5}{16}
$$

Answer:
$$
\boxed{\frac{5}{16}}
$$

---

Problem 9:

$$
\frac{55}{56} - \frac{11}{14} - \frac{1}{28}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 56, 14, and 28. The LCD of these numbers is 56.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{55}{56}$ remains $\frac{55}{56}$.
- $\frac{11}{14} = \frac{11 \times 4}{14 \times 4} = \frac{44}{56}$.
- $\frac{1}{28} = \frac{1 \times 2}{28 \times 2} = \frac{2}{56}$.

#### Step 3: Perform the subtraction.
$$
\frac{55}{56} - \frac{44}{56} - \frac{2}{56} = \frac{55 - 44 - 2}{56} = \frac{9}{56}
$$

#### Step 4: Simplify the result.
$\frac{9}{56}$ is already in its lowest terms.

Answer:
$$
\boxed{\frac{9}{56}}
$$

---

Problem 10:

$$
\frac{58}{60} - \frac{4}{20} - \frac{2}{30}
$$

#### Step 1: Find the least common denominator (LCD).
The denominators are 60, 20, and 30. The LCD of these numbers is 60.

#### Step 2: Rewrite each fraction with the LCD.
- $\frac{58}{60}$ remains $\frac{58}{60}$.
- $\frac{4}{20} = \frac{4 \times 3}{20 \times 3} = \frac{12}{60}$.
- $\frac{2}{30} = \frac{2 \times 2}{30 \times 2} = \frac{4}{60}$.

#### Step 3: Perform the subtraction.
$$
\frac{58}{60} - \frac{12}{60} - \frac{4}{60} = \frac{58 - 12 - 4}{60} = \frac{42}{60}
$$

#### Step 4: Simplify the result.
$\frac{42}{60}$ can be simplified by dividing both numerator and denominator by their GCD, which is 6:
$$
\frac{42 \div 6}{60 \div 6} = \frac{7}{10}
$$

Answer:
$$
\boxed{\frac{7}{10}}
$$

---

Final Answers:

1. $\boxed{\frac{13}{24}}$
2. $\boxed{\frac{5}{18}}$
3. $\boxed{\frac{3}{8}}$
4. $\boxed{\frac{11}{24}}$
5. $\boxed{\frac{1}{9}}$
6. $\boxed{\frac{13}{45}}$
7. $\boxed{\frac{2}{5}}$
8. $\boxed{\frac{5}{16}}$
9. $\boxed{\frac{9}{56}}$
10. $\boxed{\frac{7}{10}}$