Question

practice & problem solving
leveled practice in 7 - 10, fill in the boxes to find the unit rate.

1. cups of sugar $\frac{3}{4}$

cups of butter $\frac{1}{8}$
boxes for answers
box for cups of sugar for each cup of butter

1. miles $\frac{3}{5}$

hours $\frac{1}{3}$
boxes for answers
box formiles in 1 hour

1. $\frac{7\text{ mi}}{\frac{1}{3}\text{ gal}}=\frac{7divbox}{boxdivbox}=\frac{7\timesbox}{box\timesbox}=\frac{box}{box}$

box formiles per gallon

1. $\frac{\frac{3}{4}\text{ page}}{2\text{ minutes}}$

box for page in 1 minute

1. hadley paddled a canoe $\frac{2}{3}$ mile in $\frac{1}{4}$ hour. how fast did hadley paddle, in miles per hour?
2. a box of cereal states that there are 90 calories in a $\frac{3}{4}$ - cup serving. how many calories are there in 4 cups of the cereal?
3. a robot can complete 8 tasks in $\frac{5}{6}$ hour. each task takes the same amount of time.

a. how long does it take the robot to complete one task?
b. how many tasks can the robot complete in one hour?

Explanation:

Step1: Recall unit - rate formula

The unit rate is found by dividing the quantity in the numerator by the quantity in the denominator of a ratio. For example, to find cups of sugar per cup of butter, divide the number of cups of sugar by the number of cups of butter.

Step2: Solve problem 7

We want to find the number of cups of sugar for each cup of butter. Given $\frac{3}{4}$ cups of sugar and $\frac{1}{8}$ cups of butter. The unit - rate is $\frac{\frac{3}{4}}{\frac{1}{8}}=\frac{3}{4}\times\frac{8}{1} = 6$ cups of sugar per cup of butter.

Step3: Solve problem 8

To find the number of miles in 1 hour (speed), given $\frac{3}{5}$ miles in $\frac{1}{3}$ hours. The unit - rate is $\frac{\frac{3}{5}}{\frac{1}{3}}=\frac{3}{5}\times\frac{3}{1}=\frac{9}{5} = 1.8$ miles per hour.

Step4: Solve problem 9

For $\frac{7\text{ mi}}{\frac{1}{3}\text{ gal}}$, we can rewrite it as $\frac{7\div1}{\frac{1}{3}\div1}=\frac{7}{\frac{1}{3}}=7\times\frac{3}{1} = 21$ miles per gallon.

Step5: Solve problem 10

To find the number of pages in 1 minute, given $\frac{3}{4}$ page in 2 minutes. The unit - rate is $\frac{\frac{3}{4}}{2}=\frac{3}{4}\times\frac{1}{2}=\frac{3}{8}$ page per minute.

Step6: Solve problem 11

Hadley paddled $\frac{2}{3}$ mile in $\frac{1}{4}$ hour. The speed (miles per hour) is $\frac{\frac{2}{3}}{\frac{1}{4}}=\frac{2}{3}\times\frac{4}{1}=\frac{8}{3}\approx2.67$ miles per hour.

Step7: Solve problem 12

If there are 90 calories in $\frac{3}{4}$ cup serving. First, find the number of calories per cup. Let $x$ be the number of calories per cup. Then $\frac{90}{\frac{3}{4}}=90\times\frac{4}{3}=120$ calories per cup. For 4 cups, there are $120\times4 = 480$ calories.

Step8: Solve problem 13a

A robot can complete 8 tasks in $\frac{5}{6}$ hour. To find the time for one task, divide the total time by the number of tasks. So the time per task is $\frac{\frac{5}{6}}{8}=\frac{5}{6}\times\frac{1}{8}=\frac{5}{48}$ hour per task.

Step9: Solve problem 13b

To find the number of tasks in 1 hour, divide 1 by the time per task. The number of tasks in 1 hour is $\frac{1}{\frac{5}{48}}=1\times\frac{48}{5}=\frac{48}{5} = 9.6$ tasks per hour.

Answer:

1. 6
2. 1.8
3. 21
4. $\frac{3}{8}$
5. $\frac{8}{3}$
6. 480

13a. $\frac{5}{48}$
13b. 9.6