Fraction Equivalence D38Df0

1. **Problem 11:** Find the missing number in the proportion $$6/\boxed{x} = 12/32$$ given $$96 = 12/32$$. Since $$12/32$$ is a fraction, the equality $$96 = 12/32$$ is likely a typo or unrelated. We focus on $$12/32 = 6/\boxed{x}$$. Use cross multiplication: $$12 \times \boxed{x} = 6 \times 32$$ $$12\boxed{x} = 192$$ Divide both sides by 12: $$\cancel{12}\boxed{x} = \frac{192}{\cancel{12}}$$ $$\boxed{x} = 16$$ 2. **Problem 12:** Find the missing numbers in $$36/\boxed{a} = 18/54 = \boxed{b}$$. First, simplify $$18/54$$: $$18/54 = \frac{18 \div 18}{54 \div 18} = 1/3$$ So, $$36/\boxed{a} = 1/3$$. Cross multiply: $$36 \times 3 = 1 \times \boxed{a}$$ $$108 = \boxed{a}$$ The second box $$\boxed{b}$$ equals $$18/54 = 1/3$$. 3. **Problem 13:** Find the missing numbers in $$30/72 = \boxed{c}/48 = 35/\boxed{d}$$. Simplify $$30/72$$: $$30/72 = \frac{30 \div 6}{72 \div 6} = 5/12$$ So, $$\boxed{c}/48 = 5/12$$. Cross multiply: $$12 \times \boxed{c} = 5 \times 48$$ $$12\boxed{c} = 240$$ Divide both sides by 12: $$\cancel{12}\boxed{c} = \frac{240}{\cancel{12}}$$ $$\boxed{c} = 20$$ Next, $$35/\boxed{d} = 5/12$$. Cross multiply: $$5 \times \boxed{d} = 35 \times 12$$ $$5\boxed{d} = 420$$ Divide both sides by 5: $$\cancel{5}\boxed{d} = \frac{420}{\cancel{5}}$$ $$\boxed{d} = 84$$ 4. **Problem 14:** Find the missing numbers in $$8/18 = 12/\boxed{e} = \boxed{f}$$. Simplify $$8/18$$: $$8/18 = \frac{8 \div 2}{18 \div 2} = 4/9$$ So, $$12/\boxed{e} = 4/9$$. Cross multiply: $$4 \times \boxed{e} = 12 \times 9$$ $$4\boxed{e} = 108$$ Divide both sides by 4: $$\cancel{4}\boxed{e} = \frac{108}{\cancel{4}}$$ $$\boxed{e} = 27$$ The last box $$\boxed{f}$$ equals $$8/18 = 4/9$$. 5. **Problem 15:** Determine which of the following is true: A. $$6/15 = 15/75$$ Simplify both: $$6/15 = 2/5$$ $$15/75 = 1/5$$ Not equal. B. $$20/36 = 15/27$$ Simplify both: $$20/36 = 5/9$$ $$15/27 = 5/9$$ Equal. C. $$7/7 = 7$$ $$7/7 = 1$$, not 7. D. $$33/66 = 11/33$$ Simplify both: $$33/66 = 1/2$$ $$11/33 = 1/3$$ Not equal. **Answer:** Only option B is true. **Final answers:** - 11: $$\boxed{16}$$ - 12: $$\boxed{108}$$ and $$\boxed{\frac{1}{3}}$$ - 13: $$\boxed{20}$$ and $$\boxed{84}$$ - 14: $$\boxed{27}$$ and $$\boxed{\frac{4}{9}}$$ - 15: Option B is true.