1. **Convert the fractions to decimals using equivalent fractions:** We use the formula for converting a fraction to a decimal: $$\text{Decimal} = \frac{\text{Numerator}}{\text{Denominator}}$$ **a)** $$\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} = 0.6$$ **b)** $$\frac{5}{8} = \frac{5 \times 125}{8 \times 125} = \frac{625}{1000} = 0.625$$ **c)** $$\frac{4}{10} = 0.4$$ (already with denominator 10) **d)** $$\frac{7}{8} = \frac{7 \times 125}{8 \times 125} = \frac{875}{1000} = 0.875$$ **e)** Simplify first: $$\frac{6}{16} = \frac{3}{8}$$ then convert: $$\frac{3}{8} = \frac{3 \times 125}{8 \times 125} = \frac{375}{1000} = 0.375$$ **f)** $$\frac{8}{15} = \frac{8 \times 20}{15 \times 20} = \frac{160}{300}$$ Divide numerator and denominator by 10: $$\frac{\cancel{160}}{\cancel{300}} = \frac{16}{30}$$ Divide numerator and denominator by 2: $$\frac{\cancel{16}}{\cancel{30}} = \frac{8}{15}$$ (back to original, so convert directly) Decimal: $$\frac{8}{15} \approx 0.5333$$ (repeating) 2. **Compare the number statements using <, > or =:** - Compare $$\frac{11}{25}$$ and 0.4: $$\frac{11}{25} = 0.44 > 0.4$$ so $$\frac{11}{25} > 0.4$$ - Compare $$\frac{156}{500}$$ and 0.312: $$\frac{156}{500} = 0.312 = 0.312$$ so $$\frac{156}{500} = 0.312$$ - Compare $$\frac{4}{125}$$ and 0.32: $$\frac{4}{125} = 0.032 < 0.32$$ so $$\frac{4}{125} < 0.32$$ - Compare $$\frac{180}{300}$$ and 0.06: $$\frac{180}{300} = 0.6 > 0.06$$ so $$\frac{180}{300} > 0.06$$ 3. **Mikey's mistake and correct answer:** Mikey said: "I convert 1/8 and got 8 as my answer." Mistake: He likely divided 1 by 8 incorrectly or reversed the division. Correct calculation: $$\frac{1}{8} = 0.125$$ 4. **Dean's number possibilities:** Dean's number has 2 decimal places and satisfies: $$\frac{4}{5} < \text{number} < \frac{47}{50}$$ Calculate decimal bounds: $$\frac{4}{5} = 0.8$$ $$\frac{47}{50} = 0.94$$ Numbers with 2 decimal places between 0.8 and 0.94 include: - 0.81 - 0.85 - 0.90 5. **Challenge: Who gets more muffins?** Fabia shares 3 muffins between herself and 4 friends, total 5 people: $$\text{Muffins per person} = \frac{3}{5} = 0.6$$ Amrit shares 5 muffins between herself and 7 friends, total 8 people: $$\text{Muffins per person} = \frac{5}{8} = 0.625$$ Since $$0.625 > 0.6$$, Amrit gets more muffins per person. **Final answers:** - 5) a) 0.6, b) 0.625, c) 0.4, d) 0.875, e) 0.375, f) approx 0.5333 - 6) $$\frac{11}{25} > 0.4$$, $$\frac{156}{500} = 0.312$$, $$\frac{4}{125} < 0.32$$, $$\frac{180}{300} > 0.06$$ - 7) Mikey's mistake: incorrect division; correct answer is 0.125 - 8) Possible numbers: 0.81, 0.85, 0.90 - Challenge: Amrit gets more muffins per person