4.3 Equivalent fractions, reducing fractions to lowest terms, and

$\frac{6}{\text{18}}=\frac{\stackrel{1}{\cancel{2}}\cdot \stackrel{1}{\cancel{3}}}{\underset{1}{\cancel{2}}\cdot \underset{1}{\cancel{3}}\cdot 3}=\frac{1}{3}$ 1 and 3 are relatively prime.

$\frac{\text{16}}{\text{20}}=\frac{\stackrel{1}{\cancel{2}}\cdot \stackrel{1}{\cancel{2}}\cdot 2\cdot 2}{\underset{1}{\cancel{2}}\cdot \underset{1}{\cancel{2}}\cdot 5}=\frac{4}{5}$ 4 and 5 are relatively prime.

$\frac{\text{56}}{\text{104}}=\frac{\stackrel{1}{\cancel{2}}\cdot \stackrel{1}{\cancel{2}}\cdot \stackrel{1}{\cancel{2}}\cdot 7}{\underset{1}{\cancel{2}}\cdot \underset{1}{\cancel{2}}\cdot \underset{1}{\cancel{2}}\cdot \text{13}}=\frac{7}{\text{13}}$ 7 and 13 are relatively prime (and also truly prime)

$\begin{array}{c}\frac{\text{315}}{\text{336}}=\frac{\stackrel{1}{\cancel{3}}\cdot 3\cdot 5\cdot \stackrel{1}{\cancel{7}}}{2\cdot 2\cdot 2\cdot 2\cdot \underset{1}{\cancel{3}}\cdot \underset{1}{\cancel{7}}\cdot }=\frac{\text{15}}{\text{16}}\\ \end{array}$ 15 and 16 are relatively prime.

$\frac{8}{\text{15}}=\frac{2\cdot 2\cdot 2}{3\cdot 5}$ No common prime factors, so 8 and 15 are relatively prime.

The fraction $\frac{8}{\text{15}}$ is reduced to lowest terms.

$\frac{\text{25}}{\text{30}}$ . 5 divides into both 25 and 30.

$\frac{\stackrel{5}{\cancel{25}}}{\underset{6}{\cancel{30}}}=\frac{5}{6}$ 5 and 6 are relatively prime.

$\frac{\text{18}}{\text{24}}$ . Both numbers are even so we can divide by 2.

$\frac{\stackrel{9}{\cancel{18}}}{\underset{\text{12}}{\cancel{24}}}$ Now, both 9 and 12 are divisible by 3.

$\frac{\stackrel{\stackrel{3}{\cancel{9}}}{\cancel{18}}}{\underset{\underset{4}{\cancel{\text{12}}}}{\cancel{24}}}=\frac{3}{4}$ 3 and 4 are relatively prime.

$\frac{\stackrel{\stackrel{7}{\cancel{21}}}{\cancel{210}}}{\underset{\underset{5}{\cancel{15}}}{\cancel{150}}}=\frac{7}{5}$ . 7 and 5 are relatively prime.

$\frac{\text{36}}{\text{96}}=\frac{\text{18}}{\text{48}}=\frac{9}{\text{24}}=\frac{3}{8}$ . 3 and 8 are relatively prime.