Unit Rate with Fractions - Pre Algebra

1. Rain falls $\frac{1}{4}$ inch in $\frac{1}{6}$ hour. What is the rate in inches per hour?

   $1\frac{1}{2}$ inches per hour. $\frac{1}{4} \div \frac{1}{6} = \frac{1}{4} \times 6 = \frac{3}{2}$.

2. How do you find the unit rate for $\frac{a}{b}$ of one quantity per $\frac{c}{d}$ of another?

   Divide: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$. The result is the amount of the first quantity per 1 unit of the second.

3. Cheese costs 3.60 dollars for 1.2 pounds. What is the price per pound?

   3 dollars per pound. $3.6 \div 1.2 = 3$.

4. A painter covers $\frac{2}{3}$ of a wall in $\frac{1}{3}$ hour. How many walls per hour is that?

   2 walls per hour. $\frac{2}{3} \div \frac{1}{3} = \frac{2}{3} \times 3 = 2$.

5. A cyclist rides $2\frac{1}{2}$ miles in $\frac{1}{2}$ hour. What is the speed in miles per hour?

   5 miles per hour. $\frac{5}{2} \div \frac{1}{2} = \frac{5}{2} \times 2 = 5$.

6. A trip covers $a$ miles in $b$ hours. What do the two unit rates $\frac{a}{b}$ and $\frac{b}{a}$ mean?

   $\frac{a}{b}$ is miles per hour, and $\frac{b}{a}$ is hours per mile. Both describe the same rate from opposite directions.

7. A snail moves 1.5 feet in 0.5 minute. What is its speed in feet per minute?

   3 feet per minute. $1.5 \div 0.5 = 3$.

8. A pump fills $\frac{3}{8}$ of a tank in $\frac{3}{4}$ hour. How many hours does it take to fill the whole tank?

   2 hours. The rate is $\frac{3}{8} \div \frac{3}{4} = \frac{1}{2}$ tank per hour, so one tank takes 2 hours.

9. Two people share $\frac{5}{6}$ pound of cheese equally. How many pounds does each person get?

   $\frac{5}{12}$ pound. $\frac{5}{6} \div 2 = \frac{5}{6} \times \frac{1}{2} = \frac{5}{12}$.

10. A person walks $\frac{1}{2}$ mile in $\frac{1}{4}$ hour. What is the speed in miles per hour?

    2 miles per hour. $\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times 4 = 2$.

11. Half of a recipe uses $\frac{3}{4}$ cup of sugar. How many cups of sugar does the full recipe use?

    $1\frac{1}{2}$ cups. $\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times 2 = \frac{3}{2}$.

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