1. **State the problem:** Simplify the fraction $\frac{8}{24}$ to its lowest terms. 2. **Formula and rules:** To simplify a fraction, find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by the GCF. 3. **Find factors:** - Factors of numerator (8): 1, 2, 4, 8 - Factors of denominator (24): 1, 2, 3, 4, 6, 8, 12, 24 4. **Find common factors:** 1, 2, 4, 8 5. **Find GCF:** The greatest common factor is $8$. 6. **Divide numerator and denominator by GCF:** $$\frac{8 \div 8}{24 \div 8} = \frac{1}{3}$$ 7. **Final answer:** The fraction $\frac{8}{24}$ simplified to lowest terms is $\frac{1}{3}$. | No. | Given | Factors of Numerator and Denominator | Common Factor/s | GCF | Fraction in Simplest Form/Lowest Term (with solution) | |-----|-------|--------------------------------------|-----------------|-----|-------------------------------------------------------| | 1 | 8/24 | 8: 1,2,4,8; 24: 1,2,3,4,6,8,12,24 | 1,2,4,8 | 8 | $\frac{8}{24} = \frac{1}{3}$ | | 2 | 4/28 | 4: 1,2,4; 28: 1,2,4,7,14,28 | 1,2,4 | 4 | $\frac{4}{28} = \frac{1}{7}$ | | 3 | 6/30 | 6: 1,2,3,6; 30: 1,2,3,5,6,10,15,30 | 1,2,3,6 | 6 | $\frac{6}{30} = \frac{1}{5}$ | | 4 | 30/20 | 30: 1,2,3,5,6,10,15,30; 20: 1,2,4,5,10,20 | 1,2,5,10 | 10 | $\frac{30}{20} = \frac{3}{2}$ | | 5 | 2 12/36 | 12: 1,2,3,4,6,12; 36: 1,2,3,4,6,9,12,18,36 | 1,2,3,4,6,12 | 12 | $\frac{12}{36} = \frac{1}{3}$ so $2 \frac{12}{36} = 2 \frac{1}{3}$ | This table summarizes the factors, common factors, GCF, and simplified fractions for all given problems.