Ratios & Ratio Tables
You make flubber using:
3/2 cups of cold water
4/3 cups of hot water
2 cups of glue
3 teaspoons of borax
Write the ratio of cold water to glue. Find and interpret the value of this ratio.
3/2 : 2
The amount of cold water in the recipe is 3/4 the amount of glue.
A nutrition label shows that every 1/4 cup of tuna has 1/2 gram of fat.
How many grams of fat are there for every cup of tuna?
How many cups of tuna are there for every gram of fat?
There are 2 grams of fat for every cup of tuna.
There is 1/2 cup of tuna for every graph of fat.
Does the ratio form a proportion? Justify your answer by comparing the ratio values:
6 : 4 and 8 : 12
3/2 is not equal to 2/3, so... No.
Solve using mental math. Explain:
5/8 = 20/x
x = 32
5x4 = 20, so 8x4 = 32
Use a graph to tell whether x & y are proportional. Explain:
x 1 2 3 4
y -2 0 2 4
The graph forms a straight line that does NOT pass through the origin, so x & y are NOT proportional.
Find the missing values in the ratio table:
Cups: 3 12 15 ?
Quarts: 3/4 ?? ?? 5/4
Cups: 3 12 15 5
Quarts: 3/4 3 15/4 5/4
A scientist estimates that a jet of liquid iron in the Earth's core travels 9 feet every half hour. How far does the liquid iron travel in one day?
The liquid iron travels about 432 feet in one day.
Does the ratio form a proportion? Justify your answer by using the Cross Products Property:
6 : 9 and 12 : 18
6x18 = 108
9x12 = 108
So... Yes.
Solve by using multiplication to isolate the variable, x:
5/7 = x/21
21(5/7) = 15
Use a graph to tell whether the relationahip is proportional. Explain:
Cucumbers: 2 3 4
Tomatoes: 4 6 8
The graph forms a straight line that passes through the origin, so the relationship IS proportional.
Find the missing values in the ratio table. Then write the equivalent ratios:
Calories: 20 ?? 10 90
Miles: 1/6 2/3 ?? ??
Calories: 20 80 10 90
Miles: 1/6 2/3 1/12 3/4
20 : 1/6 80 : 2/3 10 : 1/12 90 : 3/4
Find the unit rates:
$9.60 for 4 pounds
297 words in 5.5 minutes
5/8 ounce per 1/4 pint
$2.40 per pound
54 words per minute
2 1/2 ounces per pint
Tell whether x & y are proportional. Justify your answer:
x 2 4 6 8 10
y 4 2 1 1/2 1/4
2/4 = 1/2
4/2 = 2
6/1 = 6
8/(1/2) = 16
10/(1/4) = 40
So... No.
Solve the proportion using the Cross Products Property:
9/y = 3/17
9x17 = 3y
153 = 3y
y = 51
A graph of the time, x, in minutes that it takes for a robotic vacuum cleaner to cover y square feet of carpet passes through the orgin, the point (1/2, 8) and the point (2, 32). Find the area of carpet covered by the vacuum in 10 minutes.
The carpet covers 160 square feet of carpet in 10 minutes.
You mix 0.25 cups of juice concentrate for every two cups of water to make 18 cups of juice. How much juice concentrate do you use? How much water do you use?
2 cups of juice concetrate
16 cups of water
You hike up a mountain at a rate of 1/4 mile every 10 minutes. You hike 5 miles every 2 hours on the way down the trail. How much farther do you hike in 3 hours on the way down than you do in 3 hours on the way up?
You walk 3 miles further on the way down than you do on the way up.
You do 90 situps in 2 minutes, and your friend does 126 situps in 2.8 minutes. Do these rates form a proportion? Explain.
90/2 = 45 situps per minute
126/2.8 = 45 situps per minute
So... Yes.
A titanosaur's heart pumped 50 gallons of blood for every 2 heartbeats. How many heartbeats did it take to pump 850 gallons of blood?
2/50 = x/850
x = 34
So... 34 heartbeats.
A graph of hours worked (x) vs. total earnings (y) passes through the points: (3, 45) and (5, 75). Interpret these two points, and identify the unit rate.
You earn $45 in 3 hours.
You earn $75 in 5 hours.
You earn $15 per hour.
A store sells 2 1/4 pounds of mulch for every 1 1/2 pounds of gravel sold. The store sells 180 pounds of much and gravel combined. How many pounds of each item does the store sell?
108 pounds of mulch
72 pounds of gravel
A shuttle leaving Earth's atmosphere travels 15 miles every 2 seconds. When entering the Earth's atmosphere, it travels 2 3/8 miles every 1/2 second. Find the difference in the distances traveled after 15 seconds when leaving and entering the atmosphere.
41.25 miles
You earn $56 walking your neighbor's dog for 8 hours. Your friend earns $36 painting your neighbor's fence for 4 hours. Are the pay rates equivalent? Explain.
$56/8 = $7 per hour
$36/4 = $9 per hour
So... No.
A dance team has 80 dancers. The ratio of 7th grade dancers to all dancers is 5 : 16. How many 7th grade dancers are on the team?
There are 25 7th grade dancers.
A car travels 240 feet every 3 seconds. Find the value of the ratio, the unit rate, and the constant of proportionality.
Value of Ratio = 80
Unit Rate = 80 feet per second
Constant of Proportionality = 80