1. **Convert mixed numbers to improper fractions and improper fractions to mixed numbers:** - For mixed numbers $a \frac{b}{c}$, the improper fraction is $\frac{a \times c + b}{c}$. - For improper fractions $\frac{m}{n}$, the mixed number is $q \frac{r}{n}$ where $q = \lfloor \frac{m}{n} \rfloor$ and $r = m \bmod n$. **a) Convert $6 \frac{1}{9}$ to improper fraction:** $$6 \times 9 + 1 = 54 + 1 = 55$$ So, $6 \frac{1}{9} = \frac{55}{9}$. **b) Convert $\frac{12}{8}$ to mixed number:** Divide 12 by 8: $12 \div 8 = 1$ remainder $4$. So, $\frac{12}{8} = 1 \frac{4}{8}$. Simplify $\frac{4}{8}$ to $\frac{1}{2}$. Final: $1 \frac{1}{2}$. **c) Convert $\frac{60}{31}$ to mixed number:** Divide 60 by 31: $60 \div 31 = 1$ remainder $29$. So, $\frac{60}{31} = 1 \frac{29}{31}$. **d) Convert $8 \frac{4}{7}$ to improper fraction:** $$8 \times 7 + 4 = 56 + 4 = 60$$ So, $8 \frac{4}{7} = \frac{60}{7}$. 2. **Reduce fractions to lowest terms:** - Find the greatest common divisor (GCD) of numerator and denominator. - Divide numerator and denominator by the GCD. **a) Reduce $\frac{14}{16}$:** GCD of 14 and 16 is 2. $$\frac{14}{16} = \frac{14 \div 2}{16 \div 2} = \frac{7}{8}$$ **b) Reduce $\frac{56}{72}$:** GCD of 56 and 72 is 8. $$\frac{56}{72} = \frac{56 \div 8}{72 \div 8} = \frac{7}{9}$$ 3. **Complete pairs with equivalent fractions:** - Equivalent fractions have the same value when simplified. - Multiply or divide numerator and denominator by the same number to find equivalents. Since no specific pairs were given, this is the general method to complete equivalent fraction pairs. **Final answers:** - $6 \frac{1}{9} = \frac{55}{9}$ - $\frac{12}{8} = 1 \frac{1}{2}$ - $\frac{60}{31} = 1 \frac{29}{31}$ - $8 \frac{4}{7} = \frac{60}{7}$ - $\frac{14}{16} = \frac{7}{8}$ - $\frac{56}{72} = \frac{7}{9}$