Simplify fractions worksheet for Grade 5 students, provided by K5 Learning.

To solve the problem of simplifying fractions, we need to reduce each fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD). Let's go through each fraction step by step.

Problem: Simplify the fractions

#### 1. \( \frac{6}{30} \)
- Step 1: Find the GCD of 6 and 30.
- Factors of 6: 1, 2, 3, 6
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- GCD = 6
- Step 2: Divide both the numerator and the denominator by 6.
\[
\frac{6 \div 6}{30 \div 6} = \frac{1}{5}
\]
- Answer: \( \frac{1}{5} \)

#### 2. \( \frac{5}{10} \)
- Step 1: Find the GCD of 5 and 10.
- Factors of 5: 1, 5
- Factors of 10: 1, 2, 5, 10
- GCD = 5
- Step 2: Divide both the numerator and the denominator by 5.
\[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\]
- Answer: \( \frac{1}{2} \)

#### 3. \( \frac{4}{40} \)
- Step 1: Find the GCD of 4 and 40.
- Factors of 4: 1, 2, 4
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- GCD = 4
- Step 2: Divide both the numerator and the denominator by 4.
\[
\frac{4 \div 4}{40 \div 4} = \frac{1}{10}
\]
- Answer: \( \frac{1}{10} \)

#### 4. \( \frac{24}{30} \)
- Step 1: Find the GCD of 24 and 30.
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- GCD = 6
- Step 2: Divide both the numerator and the denominator by 6.
\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\]
- Answer: \( \frac{4}{5} \)

#### 5. \( \frac{6}{8} \)
- Step 1: Find the GCD of 6 and 8.
- Factors of 6: 1, 2, 3, 6
- Factors of 8: 1, 2, 4, 8
- GCD = 2
- Step 2: Divide both the numerator and the denominator by 2.
\[
\frac{6 \div 2}{8 \div 2} = \frac{3}{4}
\]
- Answer: \( \frac{3}{4} \)

#### 6. \( \frac{8}{12} \)
- Step 1: Find the GCD of 8 and 12.
- Factors of 8: 1, 2, 4, 8
- Factors of 12: 1, 2, 3, 4, 6, 12
- GCD = 4
- Step 2: Divide both the numerator and the denominator by 4.
\[
\frac{8 \div 4}{12 \div 4} = \frac{2}{3}
\]
- Answer: \( \frac{2}{3} \)

#### 7. \( \frac{12}{24} \)
- Step 1: Find the GCD of 12 and 24.
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- GCD = 12
- Step 2: Divide both the numerator and the denominator by 12.
\[
\frac{12 \div 12}{24 \div 12} = \frac{1}{2}
\]
- Answer: \( \frac{1}{2} \)

#### 8. \( \frac{99}{108} \)
- Step 1: Find the GCD of 99 and 108.
- Factors of 99: 1, 3, 9, 11, 33, 99
- Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- GCD = 9
- Step 2: Divide both the numerator and the denominator by 9.
\[
\frac{99 \div 9}{108 \div 9} = \frac{11}{12}
\]
- Answer: \( \frac{11}{12} \)

#### 9. \( \frac{4}{8} \)
- Step 1: Find the GCD of 4 and 8.
- Factors of 4: 1, 2, 4
- Factors of 8: 1, 2, 4, 8
- GCD = 4
- Step 2: Divide both the numerator and the denominator by 4.
\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\]
- Answer: \( \frac{1}{2} \)

#### 10. \( \frac{18}{90} \)
- Step 1: Find the GCD of 18 and 90.
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- GCD = 18
- Step 2: Divide both the numerator and the denominator by 18.
\[
\frac{18 \div 18}{90 \div 18} = \frac{1}{5}
\]
- Answer: \( \frac{1}{5} \)

#### 11. \( \frac{50}{80} \)
- Step 1: Find the GCD of 50 and 80.
- Factors of 50: 1, 2, 5, 10, 25, 50
- Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
- GCD = 10
- Step 2: Divide both the numerator and the denominator by 10.
\[
\frac{50 \div 10}{80 \div 10} = \frac{5}{8}
\]
- Answer: \( \frac{5}{8} \)

#### 12. \( \frac{63}{72} \)
- Step 1: Find the GCD of 63 and 72.
- Factors of 63: 1, 3, 7, 9, 21, 63
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- GCD = 9
- Step 2: Divide both the numerator and the denominator by 9.
\[
\frac{63 \div 9}{72 \div 9} = \frac{7}{8}
\]
- Answer: \( \frac{7}{8} \)

#### 13. \( \frac{9}{72} \)
- Step 1: Find the GCD of 9 and 72.
- Factors of 9: 1, 3, 9
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- GCD = 9
- Step 2: Divide both the numerator and the denominator by 9.
\[
\frac{9 \div 9}{72 \div 9} = \frac{1}{8}
\]
- Answer: \( \frac{1}{8} \)

#### 14. \( \frac{48}{86} \)
- Step 1: Find the GCD of 48 and 86.
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 86: 1, 2, 43, 86
- GCD = 2
- Step 2: Divide both the numerator and the denominator by 2.
\[
\frac{48 \div 2}{86 \div 2} = \frac{24}{43}
\]
- Answer: \( \frac{24}{43} \)

#### 15. \( \frac{2}{6} \)
- Step 1: Find the GCD of 2 and 6.
- Factors of 2: 1, 2
- Factors of 6: 1, 2, 3, 6
- GCD = 2
- Step 2: Divide both the numerator and the denominator by 2.
\[
\frac{2 \div 2}{6 \div 2} = \frac{1}{3}
\]
- Answer: \( \frac{1}{3} \)

#### 16. \( \frac{49}{70} \)
- Step 1: Find the GCD of 49 and 70.
- Factors of 49: 1, 7, 49
- Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
- GCD = 7
- Step 2: Divide both the numerator and the denominator by 7.
\[
\frac{49 \div 7}{70 \div 7} = \frac{7}{10}
\]
- Answer: \( \frac{7}{10} \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. \frac{1}{5} & 2. \frac{1}{2} \\
3. \frac{1}{10} & 4. \frac{4}{5} \\
5. \frac{3}{4} & 6. \frac{2}{3} \\
7. \frac{1}{2} & 8. \frac{11}{12} \\
9. \frac{1}{2} & 10. \frac{1}{5} \\
11. \frac{5}{8} & 12. \frac{7}{8} \\
13. \frac{1}{8} & 14. \frac{24}{43} \\
15. \frac{1}{3} & 16. \frac{7}{10}
\end{array}
}
\]