1. **Understanding the problem:** We need to find missing numerators or denominators in equivalent fractions. 2. **Recall the rule:** Two fractions are equivalent if their cross products are equal, or equivalently, the numerator and denominator are multiplied or divided by the same number. 3. **Solve each fraction equivalency:** **Problem 2:** Given: $\frac{3}{5} = \frac{7}{15} = \frac{?}{25}$ a) Check equivalency between $\frac{3}{5}$ and $\frac{7}{15}$. - $5 \times 3 = 15$ and $3 \times 3 = 9$ (not equal to 7), so the middle fraction is not equivalent to the first. But given, we proceed with the last equivalence: b) To find numerator for $\frac{?}{25}$ equivalent to $\frac{3}{5}$: Multiply numerator and denominator of $\frac{3}{5}$ by 5: $$3 \times 5 = 15$$ $$5 \times 5 = 25$$ So, missing numerator is **15**. 4. **Problem 3:** Given: $\frac{5}{9} = \frac{?}{18} = \frac{?}{45}$ a) Find numerator for denominator 18: $9 \times 2 = 18$, so multiply numerator by 2: $$5 \times 2 = 10$$ b) Find numerator for denominator 45: $9 \times 5 = 45$, so multiply numerator by 5: $$5 \times 5 = 25$$ 5. **Problem 4:** Given: $\frac{1}{6} = \frac{?}{24} = \frac{?}{30}$ a) Find numerator for denominator 24: $6 \times 4 = 24$, numerator: $$1 \times 4 = 4$$ b) Find numerator for denominator 30: $6 \times 5 = 30$, numerator: $$1 \times 5 = 5$$ 6. **Problem 5:** Given: $\frac{4}{9} = \frac{?}{18} = \frac{?}{27}$ a) Denominator 18: $9 \times 2 = 18$, numerator: $$4 \times 2 = 8$$ b) Denominator 27: $9 \times 3 = 27$, numerator: $$4 \times 3 = 12$$ 7. **Problem 6:** Given: $\frac{1}{4} = \frac{?}{24} = \frac{?}{40}$ a) Denominator 24: $4 \times 6 = 24$, numerator: $$1 \times 6 = 6$$ b) Denominator 40: $4 \times 10 = 40$, numerator: $$1 \times 10 = 10$$ **Final answers:** - 2) $\frac{3}{5} = \frac{7}{15} = \frac{15}{25}$ - 3) $\frac{5}{9} = \frac{10}{18} = \frac{25}{45}$ - 4) $\frac{1}{6} = \frac{4}{24} = \frac{5}{30}$ - 5) $\frac{4}{9} = \frac{8}{18} = \frac{12}{27}$ - 6) $\frac{1}{4} = \frac{6}{24} = \frac{10}{40}$