Ratios and Proportional Relationships Worksheet

Question 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.

Accepted Answer

The ratio of flour to sugar can be written as 3 to 2, 3:2, or 3/2.

Question 2

A car travels 180 miles in 3 hours at a constant speed. What is the unit rate in miles per hour?

Accepted Answer

The unit rate is 60 miles per hour because 180 divided by 3 equals 60.

Question 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

Accepted Answer

The relationship is proportional because each cost divided by the number of notebooks equals $2.50 per notebook.

Question 4

A trail mix has 4 cups of peanuts and 6 cups of raisins. Simplify the ratio of peanuts to raisins.

Accepted Answer

The ratio 4:6 simplifies to 2:3 because both numbers can be divided by 2.

Question 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?

Accepted Answer

The cities are 112.5 miles apart because 4.5 times 25 equals 112.5.

Question 6

Solve the proportion: 5/8 = x/40.

Accepted Answer

The value of x is 25 because 8 times 5 equals 40, so 5 times 5 equals 25.

Question 7

A store sells 12 markers for $9.60. What is the price per marker?

Accepted Answer

The price per marker is $0.80 because $9.60 divided by 12 equals $0.80.

Question 8

The points (1, 3), (2, 6), (3, 9), and (4, 12) are on a graph. Do they show a proportional relationship? Explain.

Accepted Answer

Yes, the points show a proportional relationship because the ratio y/x is always 3 and the graph would pass through the origin.

Question 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?

Accepted Answer

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.

Question 10

A runner completes 7.5 kilometers in 30 minutes. What is the runner's speed in kilometers per hour?

Accepted Answer

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.

Question 11

A class has 18 girls and 12 boys. What is the ratio of boys to total students in simplest form?

Accepted Answer

The ratio of boys to total students is 12:30, which simplifies to 2:5.

Question 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

Accepted Answer

The constant of proportionality is 14, and the equation is y = 14x, where x is hours worked and y is money earned in dollars.

Question 13

A school survey shows that 3 out of every 8 students prefer soccer. If 240 students are surveyed, how many prefer soccer?

Accepted Answer

90 students prefer soccer because 3/8 of 240 is 90.

Question 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?

Accepted Answer

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.

Question 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?

Accepted Answer

There are 21 red beads because the ratio has 12 total parts, each part is 3 beads, and 7 parts times 3 equals 21.

Ratios and Proportional Relationships

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