Ratios and Proportional Relationships
Using ratios, unit rates, tables, graphs, and proportions
Ratios and Proportional Relationships
Using ratios, unit rates, tables, graphs, and proportions
Math - Grade 6-8
- 1
A recipe uses 3 cups of flour for every 2 cups of sugar. Write the ratio of flour to sugar in three different ways.
Keep the order the same: flour first, sugar second.
The ratio of flour to sugar can be written as 3 to 2, 3:2, or 3/2. - 2
A car travels 180 miles in 3 hours at a constant speed. What is the unit rate in miles per hour?
The unit rate is 60 miles per hour because 180 divided by 3 equals 60. - 3
The table shows the number of notebooks and the total cost. Is the relationship proportional? Explain. Notebooks: 2, 4, 6, 8 Cost: $5, $10, $15, $20
Check whether the cost per notebook is the same for every pair of values.
The relationship is proportional because each cost divided by the number of notebooks equals $2.50 per notebook. - 4
A trail mix has 4 cups of peanuts and 6 cups of raisins. Simplify the ratio of peanuts to raisins.
The ratio 4:6 simplifies to 2:3 because both numbers can be divided by 2. - 5
A map uses a scale of 1 inch = 25 miles. If two cities are 4.5 inches apart on the map, how far apart are they in real life?
Multiply the map distance by the number of miles represented by each inch.
The cities are 112.5 miles apart because 4.5 times 25 equals 112.5. - 6
Solve the proportion: 5/8 = x/40.
The value of x is 25 because 8 times 5 equals 40, so 5 times 5 equals 25. - 7
A store sells 12 markers for $9.60. What is the price per marker?
A unit rate tells the cost for 1 item.
The price per marker is $0.80 because $9.60 divided by 12 equals $0.80. - 8
The points (1, 3), (2, 6), (3, 9), and (4, 12) are on a graph. Do they show a proportional relationship? Explain.
Yes, the points show a proportional relationship because the ratio y/x is always 3 and the graph would pass through the origin. - 9
A punch recipe uses 5 cups of juice for every 2 cups of sparkling water. How many cups of sparkling water are needed for 20 cups of juice?
Use the same scale factor for both parts of the ratio.
You need 8 cups of sparkling water because 5 cups of juice is multiplied by 4 to get 20, so 2 cups of sparkling water is also multiplied by 4. - 10
A runner completes 7.5 kilometers in 30 minutes. What is the runner's speed in kilometers per hour?
The runner's speed is 15 kilometers per hour because 30 minutes is 0.5 hour, and 7.5 divided by 0.5 equals 15. - 11
A class has 18 girls and 12 boys. What is the ratio of boys to total students in simplest form?
First find the total number of students.
The ratio of boys to total students is 12:30, which simplifies to 2:5. - 12
The table shows hours worked and money earned. Find the constant of proportionality and write an equation. Hours: 1, 2, 5, 8 Money earned: $14, $28, $70, $112
The constant of proportionality is 14, and the equation is y = 14x, where x is hours worked and y is money earned in dollars. - 13
A school survey shows that 3 out of every 8 students prefer soccer. If 240 students are surveyed, how many prefer soccer?
You can divide 240 by 8 and then multiply by 3.
90 students prefer soccer because 3/8 of 240 is 90. - 14
A rectangle in a scale drawing is 6 centimeters long and 4 centimeters wide. The actual rectangle is 18 meters long. What is its actual width?
The actual width is 12 meters because the scale factor from the drawing to the real rectangle is 18 divided by 6, which is 3, and 4 times 3 equals 12. - 15
A bag contains red and blue beads in a ratio of 7:5. There are 36 beads in all. How many red beads are in the bag?
Add the ratio parts first, then divide the total number of beads by that sum.
There are 21 red beads because the ratio has 12 total parts, each part is 3 beads, and 7 parts times 3 equals 21.