Subjects ratios

Hippo Mass A6171C

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1. Problem statement: A regular hippo had mass $25\frac{1}{2}$ kg at birth and we are comparing two interpretations of the expression $25\frac{1}{2}\div5\frac{3}{10}$ to decide which makes sense in context.\n2. Formula and important rule: If the regular hippo mass equals $k$ times the pygmy hippo mass, then the pygmy mass is given by $$\text{pygmy}=\frac{\text{regular}}{k}$$ and the operation to find the pygmy mass is division.\n3. Interpretations in words: Kaipo says $25\frac{1}{2}\div5\frac{3}{10}$ could represent the pygmy mass when the regular hippo is $5\frac{3}{10}$ times the pygmy.\nNormani says that if the pygmy mass is $5\frac{3}{10}$ kg, then the regular hippo mass is $25\frac{1}{2}\div5\frac{3}{10}$ times as much as the pygmy.\n4. Convert the mixed numbers to improper fractions to compute the value of the expression; show intermediate work.\n$25\frac{1}{2}=\frac{51}{2}$\n$5\frac{3}{10}=\frac{53}{10}$\nCompute the division as multiplication by the reciprocal:$$\frac{51}{2}\div\frac{53}{10}=\frac{51}{2}\times\frac{10}{53}$$\nShow cancellation of common factors when simplifying the product:$$=\frac{51\times\cancel{10}}{\cancel{2}\times53}=\frac{51\times5}{53}=\frac{255}{53}=4\frac{43}{53}\approx4.8113$$\n5. Explain and conclude in learner-friendly language: Kaipo's interpretation matches the rule in step 2 because if regular = $5\frac{3}{10}\times$ pygmy, then pygmy = regular รท $5\frac{3}{10}$, so $25\frac{1}{2}\div5\frac{3}{10}$ would give the pygmy mass, which equals $4\frac{43}{53}\approx4.8113$ kg.\nNormani's sentence is also a true arithmetic statement: if the pygmy mass were $5\frac{3}{10}$ kg, then the multiplicative factor of how many times the regular is the pygmy is $25\frac{1}{2}\div5\frac{3}{10}\approx4.8113$, and multiplying that factor by $5\frac{3}{10}$ kg returns $25\frac{1}{2}$ kg, so her wording is consistent.\nFinal answer: C Both Kaipo's and Normani's interpretations make sense in context.\n