1. **Problem:** Determine if the proportion $\frac{4}{5} = \frac{20}{25}$ is true. 2. **Formula:** Two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equal if $ad = bc$. 3. **Check:** Calculate cross products: $$4 \times 25 = 100$$ $$5 \times 20 = 100$$ Since $100 = 100$, the proportion is true. --- 1. **Problem:** Determine if the proportion $\frac{5}{9} = \frac{7}{11}$ is true. 2. **Check:** Calculate cross products: $$5 \times 11 = 55$$ $$9 \times 7 = 63$$ Since $55 \neq 63$, the proportion is false. --- 1. **Problem:** Determine if the proportion $\frac{6}{7} = \frac{24}{28}$ is true. 2. **Check:** Calculate cross products: $$6 \times 28 = 168$$ $$7 \times 24 = 168$$ Since $168 = 168$, the proportion is true. --- 1. **Problem:** Determine if the proportion $\frac{8}{9} = \frac{72}{81}$ is true. 2. **Check:** Calculate cross products: $$8 \times 81 = 648$$ $$9 \times 72 = 648$$ Since $648 = 648$, the proportion is true. --- 1. **Problem:** Determine if the proportion $\frac{7}{16} = \frac{42}{90}$ is true. 2. **Check:** Calculate cross products: $$7 \times 90 = 630$$ $$16 \times 42 = 672$$ Since $630 \neq 672$, the proportion is false. --- 1. **Problem:** Determine if the proportion $\frac{13}{19} = \frac{26}{38}$ is true. 2. **Check:** Calculate cross products: $$13 \times 38 = 494$$ $$19 \times 26 = 494$$ Since $494 = 494$, the proportion is true. --- 1. **Problem:** Determine if the proportion $\frac{3}{14} = \frac{21}{98}$ is true. 2. **Check:** Calculate cross products: $$3 \times 98 = 294$$ $$14 \times 21 = 294$$ Since $294 = 294$, the proportion is true. --- 1. **Problem:** Determine if the proportion $\frac{12}{17} = \frac{50}{85}$ is true. 2. **Check:** Calculate cross products: $$12 \times 85 = 1020$$ $$17 \times 50 = 850$$ Since $1020 \neq 850$, the proportion is false. --- 1. **Problem:** Solve the proportion $\frac{12}{7} = \frac{36}{m}$ for $m$. 2. **Formula:** Cross multiply: $$12 \times m = 7 \times 36$$ 3. **Calculate:** $$12m = 252$$ 4. **Divide both sides by 12:** $$\cancel{12}m = \frac{252}{\cancel{12}}$$ $$m = 21$$ --- 1. **Problem:** Solve the proportion $\frac{6}{23} = \frac{y}{69}$ for $y$. 2. **Formula:** Cross multiply: $$6 \times 69 = 23 \times y$$ 3. **Calculate:** $$414 = 23y$$ 4. **Divide both sides by 23:** $$\cancel{23}y = \frac{414}{\cancel{23}}$$ $$y = 18$$ --- 1. **Problem:** Hue’s boat used 5 gallons of gasoline in 4 hours. At this rate, how many gallons will it use in 10 hours? 2. **Formula:** Use proportion $\frac{5}{4} = \frac{x}{10}$ where $x$ is gallons used in 10 hours. 3. **Cross multiply:** $$5 \times 10 = 4 \times x$$ $$50 = 4x$$ 4. **Divide both sides by 4:** $$\cancel{4}x = \frac{50}{\cancel{4}}$$ $$x = 12.5$$ **Answer:** The boat will use 12.5 gallons in 10 hours. --- This completes the solution for the first problem (checking and solving proportions).