Solving Proportions - Pre Algebra

1. Solve $\frac{2}{x} = \frac{8}{20}$.

   $x = 5$. Cross-multiply: $8x = 40$, so $x = 5$.

2. When writing a proportion from a word problem, what must match in the two ratios?

   The units must be in the same positions, such as miles over hours on both sides of the equals sign.

3. Solve $\frac{x}{4} = \frac{9}{12}$.

   $x = 3$. $\frac{9}{12} = \frac{3}{4}$, so $x = 3$.

4. Solve $\frac{7}{x} = \frac{21}{9}$.

   $x = 3$. Cross-multiply: $21x = 63$, so $x = 3$.

5. A printer prints 45 pages in 3 minutes. At the same rate, how many minutes does it take to print 75 pages?

   5 minutes. It prints $45 \div 3 = 15$ pages per minute, and $75 \div 15 = 5$.

6. What equation does cross-multiplying give for the proportion $\frac{a}{b} = \frac{c}{d}$?

   $ad = bc$. The two cross products of a true proportion are equal.

7. A car travels 150 miles on 5 gallons of gas. At the same rate, how far does it travel on 8 gallons?

   240 miles. The car goes $150 \div 5 = 30$ miles per gallon, and $30 \times 8 = 240$.

8. Solve $\frac{x}{6} = \frac{5}{3}$.

   $x = 10$. Cross-multiply: $3x = 30$, so $x = 10$.

9. Solve $\frac{3}{5} = \frac{12}{x}$.

   $x = 20$. The numerator is multiplied by 4, so $x = 5 \times 4 = 20$.

10. Solve $\frac{x + 1}{4} = \frac{6}{8}$.

    $x = 2$. $\frac{6}{8} = \frac{3}{4}$, so $x + 1 = 3$.

11. Five notebooks cost 15 dollars. At the same rate, what do 8 notebooks cost?

    24 dollars. Solve $\frac{15}{5} = \frac{x}{8}$: each notebook costs 3 dollars, and $3 \times 8 = 24$.

12. Solve $\frac{1.5}{x} = \frac{3}{10}$.

    $x = 5$. Cross-multiply: $3x = 15$, so $x = 5$.

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