5. Reduce the following fraction to its lowest terms. \( \begin{array}{lll}\text { (a) } \frac{24}{32} & \text { (b) } \frac{32}{80} & \text { (c) } \frac{25}{45} \\ \text { (d) } \frac{30}{48} & \text { (e) } \frac{160}{250} & \text { (f) } \frac{55}{66} \\ \text { (g) } \frac{36}{56} & \text { (h) } \frac{72}{144} & \text { (i) } \frac{84}{98} \\ \text { (j) } \frac{84}{98} & \text { (k) } \frac{225}{300} & \end{array} \)

To reduce each fraction to its lowest terms, we will find the greatest common divisor (GCD) of the numerator and denominator and then divide both by that GCD. (a) \( \frac{24}{32} \) GCD(24, 32) = 8 Reduced: \( \frac{24 \div 8}{32 \div 8} = \frac{3}{4} \) (b) \( \frac{32}{80} \) GCD(32, 80) = 16 Reduced: \( \frac{32 \div 16}{80 \div 16} = \frac{2}{5} \) (c) \( \frac{25}{45} \) GCD(25, 45) = 5 Reduced: \( \frac{25 \div 5}{45 \div 5} = \frac{5}{9} \) (d) \( \frac{30}{48} \) GCD(30, 48) = 6 Reduced: \( \frac{30 \div 6}{48 \div 6} = \frac{5}{8} \) (e) \( \frac{160}{250} \) GCD(160, 250) = 10 Reduced: \( \frac{160 \div 10}{250 \div 10} = \frac{16}{25} \) (f) \( \frac{55}{66} \) GCD(55, 66) = 11 Reduced: \( \frac{55 \div 11}{66 \div 11} = \frac{5}{6} \) (g) \( \frac{36}{56} \) GCD(36, 56) = 4 Reduced: \( \frac{36 \div 4}{56 \div 4} = \frac{9}{14} \) (h) \( \frac{72}{144} \) GCD(72, 144) = 72 Reduced: \( \frac{72 \div 72}{144 \div 72} = \frac{1}{2} \) (i) \( \frac{84}{98} \) GCD(84, 98) = 14 Reduced: \( \frac{84 \div 14}{98 \div 14} = \frac{6}{7} \) (j) \( \frac{84}{98} \) (same as (i)) Reduced: \( \frac{6}{7} \) (k) \( \frac{225}{300} \) GCD(225, 300) = 75 Reduced: \( \frac{225 \div 75}{300 \div 75} = \frac{3}{4} \) Here are the reduced fractions: (a) \( \frac{3}{4} \) (b) \( \frac{2}{5} \) (c) \( \frac{5}{9} \) (d) \( \frac{5}{8} \) (e) \( \frac{16}{25} \) (f) \( \frac{5}{6} \) (g) \( \frac{9}{14} \) (h) \( \frac{1}{2} \) (i) \( \frac{6}{7} \) (j) \( \frac{6}{7} \) (k) \( \frac{3}{4} \)