Equivalent Fractions 8B0Da9

1. **Problem statement:** Fill in the missing numbers (boxes) in the equivalent fractions for problems 12, 13, and 14. 2. **Recall the rule for equivalent fractions:** Two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent if $a \times d = b \times c$. --- ### Problem 12: $$\frac{36}{\square} = \frac{18}{54} = \frac{\square}{18}$$ 3. First, find the missing denominator in $\frac{36}{\square} = \frac{18}{54}$. Set $\frac{36}{x} = \frac{18}{54}$. Cross multiply: $$36 \times 54 = 18 \times x$$ $$1944 = 18x$$ Divide both sides by 18: $$\cancel{18} \times 108 = \cancel{18} x \Rightarrow x = 108$$ 4. Next, find the missing numerator in $\frac{18}{54} = \frac{y}{18}$. Set $\frac{18}{54} = \frac{y}{18}$. Cross multiply: $$18 \times 18 = 54 \times y$$ $$324 = 54y$$ Divide both sides by 54: $$\cancel{54} \times 6 = \cancel{54} y \Rightarrow y = 6$$ **Answer for 12:** $\boxed{108}$ and $\boxed{6}$ --- ### Problem 13: $$\frac{30}{72} = \frac{\square}{48} = \frac{35}{\square}$$ 5. Find the missing numerator in $\frac{30}{72} = \frac{x}{48}$. Cross multiply: $$30 \times 48 = 72 \times x$$ $$1440 = 72x$$ Divide both sides by 72: $$\cancel{72} \times 20 = \cancel{72} x \Rightarrow x = 20$$ 6. Find the missing denominator in $\frac{x}{48} = \frac{35}{y}$. Set $\frac{20}{48} = \frac{35}{y}$. Cross multiply: $$20 \times y = 35 \times 48$$ $$20y = 1680$$ Divide both sides by 20: $$\cancel{20} \times 84 = \cancel{20} y \Rightarrow y = 84$$ **Answer for 13:** $\boxed{20}$ and $\boxed{84}$ --- ### Problem 14: $$\frac{8}{18} = \frac{12}{\square} = \frac{\square}{45}$$ 7. Find the missing denominator in $\frac{8}{18} = \frac{12}{x}$. Cross multiply: $$8 \times x = 18 \times 12$$ $$8x = 216$$ Divide both sides by 8: $$\cancel{8} \times 27 = \cancel{8} x \Rightarrow x = 27$$ 8. Find the missing numerator in $\frac{12}{27} = \frac{y}{45}$. Cross multiply: $$12 \times 45 = 27 \times y$$ $$540 = 27y$$ Divide both sides by 27: $$\cancel{27} \times 20 = \cancel{27} y \Rightarrow y = 20$$ **Answer for 14:** $\boxed{27}$ and $\boxed{20}$ --- ### Problem 15: Which of the following is true? - A. $\frac{6}{15} = \frac{15}{75}$? Check cross multiplication: $$6 \times 75 = 450$$ $$15 \times 15 = 225$$ Since $450 \neq 225$, this is false. - C. $\frac{7}{7} = 7$? Calculate $\frac{7}{7} = 1$, which is not equal to 7, so false. **Neither A nor C is true.**