Ratio & Equivalent Ratios
A class has 12 students wearing sneakers and 8 students wearing sandals. Write the ratio of students wearing sneakers to students wearing sandals three different ways.
12 to 8, 12:8, 12/8
A graph contains the points (2, 4), (4, 8), and (6, 12).
The x-axis represents pencils and the y-axis represents markers.
Write the information from the graph as a ratio table.
Pencils: 2 4 6
Markers: 4 8 12
A runner travels 12 miles in 3 hours. What is the unit rate in miles per hour?
4 miles per hour because \(12 ÷ 3 = 4\).
5 feet = ___ inches
60 inches because (5 × 12 = 60).
The ratio of red balloons to blue balloons is 3:5. If there are 15 blue balloons, how many red balloons are there?
9 red balloons. 5×3=15, so 3×3=9.
At summer camp, 15 campers complete the navigation course and 20 campers go hiking. Write the ratio of navigation campers to hiking campers as a fraction in simplest form.
15/20 = 3/4
A ratio table begins with the ordered pair (3, 7).
Complete the next three ordered pairs that would belong to the same ratio relationship:
(3, 7), (6, 14), (9, ___), (12, ___)(15, ___)
(3, 7), (6, 14), (9, 21), (12, 28), (15, 35)
A machine fills 42 bottles in 6 minutes. At this rate, how many bottles does it fill per minute?
7 bottles per minute because \(42 ÷ 6 = 7\).
96 ounces = ___ pounds
6 pounds because (96 ÷ 16 = 6).
A recipe uses 4 cups of flour for every 6 cups of oats. If you use 18 cups of oats, how many cups of flour are needed?
12 cups of flour. 6×3=18, so 4×3=12.
Decide whether the ratios 8 questions correct out of 10 and 4 questions correct out of 5 are equivalent. Show or explain how you know.
Yes. 8/10 simplifies to 4/5
A point on a ratio graph is (6, 24).
The x-axis represents hours and the y-axis represents miles traveled.
What ratio does this point represent, and what would the ordered pair (9, ___) be if it is on the same line?
6 hours : 24 miles
\(24 ÷ 6 = 4\) miles per hour.
\(9 × 4 = 36\)
So the missing point is (9, 36).
A package of 8 notebooks costs $14.00. What is the unit price per notebook?
$1.75 per notebook because (14 ÷ 8 = 1.75)
A container holds 4 quarts of water. How many cups of water does it hold?
16 cups. (4 qt × 4 = 16 cups).
A car travels 156 miles using 6 gallons of gas. At the same rate, how far will it travel using 9 gallons?
156÷6=26 miles per gallon.
26×9= 234 miles.
A recipe uses 5 bananas for every 3 tablespoons of peanut butter. If the recipe uses 30 bananas, how many tablespoons of peanut butter are needed?
18 tbsp. Multiply 5 by 6 to get 30, so multiply 3 by 6: 18.
Two lines represent different ratio relationships.
Line A passes through (2, 10).
Line B passes through (3, 12).
Both lines begin at (0, 0).
Which line is steeper? Explain how you know.
Line A: \(10 ÷ 2 = 5\)
Line B: \(12 ÷ 3 = 4\)
Line A is steeper because it has the greater rate, 5 compared with 4.
At a fundraiser, 4 items cost $5 at Table A and 6 items cost $7 at Table B. Which table has the greater price per item? Show both unit rates.
Table A: (5÷4= $1.25).
Table B: (7÷6≈ $1.17).
Table A has the greater price per item.
Maria has 7 yards of ribbon. She uses 54 inches. How many feet of ribbon remain?
(7 yd × 3 = 21 ft). (54 in ÷ 12 = 4.5 ft).
21-4.5= 16.5 feet remain.
Jordan is now 5 ft 2 in. tall. Four years ago, Jordan was 4 ft 6 in. tall. What was Jordan's average growth rate in inches per year?
Current = 62 in.
Previous = 54 in.
Growth = 62-54=8 inches
8÷4=2
Answer: 2 inches per year.
Three homerooms collected canned goods. Mr. Alvarez: 25 students, 150 cans. Ms. Jensen: 28 students, 154 cans. Mrs. Saunders: 27 students, 162 cans. Determine whether any of the classes have equivalent ratios of cans per student. Explain your reasoning.
Alvarez = 6/student; Jensen = 5.5/student; Saunders = 6/student. Alvarez and Saunders are equivalent.
Three lines all begin at (0, 0).
Line A passes through (4, 28)
Line B passes through (3, 24)
Line C passes through (5, 30)
A student claims Line A is the steepest because 28 is greater than 24.
Is the student correct? Calculate the rate of each line and explain your answer.
❌ The student is not correct.
Line B is the steepest because it has the greatest rate: 8.
Store A sells 12 juice boxes for $7.80. Store B sells 18 juice boxes for $11.34. Which store has the lower unit price, and how much less does one juice box cost there?
A: (7.80÷12=$0.65).
B: (11.34÷18=$0.63).
Store B, by $0.02 per juice box.
A punch recipe uses 12 fluid ounces of juice for one batch. You make 4 batches. How many quarts of juice are needed?
12×4=48 fl oz. 48÷32= 1.5 quarts.
A school is buying markers. Pack A has 8 markers for $5.20. Pack B has 12 markers for $7.44. The school needs 48 markers. Which option costs less for 48 markers, and how much money will the school save?
A: $0.65 each → 48×.65=$31.20.
B: $0.62 each → 48×.62=$29.76.
Pack B saves $1.44.