1. **State the problem:** We are given two statues, each made of three parts with given heights as mixed numbers. We need to find which statue is taller and the difference in their heights. 2. **Write down the heights:** - Statue A parts: $\frac{2}{3}$ m, $4 \frac{1}{2}$ m, $1 \frac{1}{4}$ m - Statue B parts: $1 \frac{3}{4}$ m, $3 \frac{1}{3}$ m, $1 \frac{7}{8}$ m 3. **Convert mixed numbers to improper fractions for easier addition:** - Statue A: - $\frac{2}{3}$ (already a fraction) - $4 \frac{1}{2} = \frac{9}{2}$ - $1 \frac{1}{4} = \frac{5}{4}$ - Statue B: - $1 \frac{3}{4} = \frac{7}{4}$ - $3 \frac{1}{3} = \frac{10}{3}$ - $1 \frac{7}{8} = \frac{15}{8}$ 4. **Find common denominators and add parts for each statue:** - Statue A sum: $$\frac{2}{3} + \frac{9}{2} + \frac{5}{4}$$ Common denominator is 12: $$\frac{2}{3} = \frac{8}{12}, \quad \frac{9}{2} = \frac{54}{12}, \quad \frac{5}{4} = \frac{15}{12}$$ Sum: $$\frac{8}{12} + \frac{54}{12} + \frac{15}{12} = \frac{77}{12}$$ Convert to mixed number: $$77 \div 12 = 6 \text{ remainder } 5 \Rightarrow 6 \frac{5}{12}$$ - Statue B sum: $$\frac{7}{4} + \frac{10}{3} + \frac{15}{8}$$ Common denominator is 24: $$\frac{7}{4} = \frac{42}{24}, \quad \frac{10}{3} = \frac{80}{24}, \quad \frac{15}{8} = \frac{45}{24}$$ Sum: $$\frac{42}{24} + \frac{80}{24} + \frac{45}{24} = \frac{167}{24}$$ Convert to mixed number: $$167 \div 24 = 6 \text{ remainder } 23 \Rightarrow 6 \frac{23}{24}$$ 5. **Compare heights:** - Statue A: $6 \frac{5}{12}$ m - Statue B: $6 \frac{23}{24}$ m Since $\frac{23}{24} > \frac{5}{12}$, Statue B is taller. 6. **Find the difference in height:** $$6 \frac{23}{24} - 6 \frac{5}{12} = \left(6 + \frac{23}{24}\right) - \left(6 + \frac{5}{12}\right) = \frac{23}{24} - \frac{5}{12}$$ Convert $\frac{5}{12}$ to twenty-fourths: $$\frac{5}{12} = \frac{10}{24}$$ Difference: $$\frac{23}{24} - \frac{10}{24} = \frac{13}{24}$$ **Final answers:** - Statue B is taller. - The difference in height is $\frac{13}{24}$ metres.