Unit 1 Proportional Relationships: Ratios & Rates

For every 1/4 mile Pascal walks, Lucien runs 2/3 miles. How many miles does Pascal walk for every 1 mile Lucien runs?

Hint: When provided two sets of fractions and determining which one is doing more, you will need to take the 1/4 ÷ 2/3. Think about what needs to be done to division and fractions.

• 3/8

• 1/2

• 4/9

• 19/31

Answer explanation

You will flip the second fraction, multiply across and will get an answer of 3/8.

The number of cups of strawberries in a shortcake recipe is proportional to the number of cups of sugar in the recipe. The recipe uses 5 cups of strawberries per 1/4 cup of sugar.

What is the constant of proportionality for the relationship of cups of strawberries to cups of sugar?

Hint: Solve the problem by dividing the cups of strawberries, by the cups of sugar. You will do what with a fraction when dividing?

• 1/20

• 4/5

• 20

• 5/4

Answer explanation

The 1/4 will get flipped, multiply across, which is 5 x 4 = 20.

Decide if the statement is True or False.

The ratio 7/9 : 2/3 has a unit rate of 14/27.

Hint: You are taking the ratio and dividing it, when you divide fractions what are you doing with the fraction?

• True

• False

Answer explanation

7/9 ÷ 2/3 would mean that we keep the first, change the sign to multiplication, and flip the last fraction. Multiply across and you would end up with 21/18. This would make the statement false.

Maggie makes a scale drawing of a deck. The scale from the actual deck to the scale drawing is 7ft to 1in. The dimensions of the deck are 28ft by 17.5ft. What are the dimensions of the deck in the drawing?

Hint: If you are going from the actual size of an object and turning it to a drawing, that would mean you have to do division.

• The dimensions on paper will be 196in by 122.5in.

• The dimensions on paper will be 196ft by 122.5 ft.

• The dimensions on paper will be 4in by 2.5in.

• The dimensions on paper will be 4ft by 2.5ft.

Answer explanation

You will have to take 28 ÷ 7 = 4in

Then take the 17.5 ÷ 7 = 2.5in.

Giancarlobuys granola. The graph shows the relationship between the weight and the cost of the granola. Which of the following are true statements about the graph? Choose all the correct answers.

Hint: There are 3 choices you need to select.

• The point (8,24) means that 8 pounds of granola costs $24.

• The point (1,3) means that the rate is $3 per pound of granola.

• The point (4,12) means that it costs $4 for 12 pounds of granola.

• Since the line passes through (1,3), 3 is the constant of proportionality.

• The graph is not a proportional relationship.

Sia makes lemon water. She uses 1/2 tablespoon of lemon juice for every 8 ounces of water. Which equation shows the relationship between ounces of water, w, and tablespoons of lemon juice, j?

Hint: The equation is asking for water as the solution, meaning it should be what your answer is equal to. The other thing, is you need to find the constant of proportionality which would be to take the numbers and divide.

• j = 16w

• w = 4j

• w = 16j

• j = 4w

Answer explanation

You would have taken the 8 ÷ 1/2 which would mean flipping the second fraction and multiply across. 8 x 2 = 16

In a recipe, for every 1/3 cup sugar, 3/4 cup flour is needed. How many cups of sugar are needed for 1 cup of flour?

Hint: You are going to have to divide your fractions. Keep in mind when you solve fractions you need to do what with the second fraction?

• 5/8

• 4/9

• 2/3

• 7/11

Answer explanation

You would have taken the 1/3 ÷ 3/4, flipped the second fraction and multiply across. It would have given you the 4/9.

The cost of 5 gallons of gasoline is $20. Write an equation to show the relationship between the cost, c, and the gallons of gasoline, g.

Hint: It wants to know the cost. If it is giving you 5 gallons you have to do something first, before you can create that equation.

• g = 4c

• g = 5c

• c = 4g

• c = 5g

Answer explanation

You have to find out what 1 gallon will cost. Take the 20÷5=4

As the equations wants to be based off cost, then you will have to use c=4g.

Perry wants to project a movie from his phone to a screen on the wall. The side length of the screen is 56 in. The scale from the screen to the phone is 7 in. to 1 in. What is the side length of Perry's phone?

Hint: You are provided a scale of 7:1, which means you need to divide that first before you could determine the length on the phone. As we are going from a large object to a small object, would you need to divide or multiply.

• 392 inches

• 7 inches

• 8 inches

• 448 inches.

Answer explanation

You would have taken the scale of 7:1, which would simply be 7. As anything multiplied or divided by 1 is itself. Then since we are going from a larger object we would have needed to divide.

56÷7=8 inches for the side length of phone.

Decide if the statement is true or false.

The ratio of 5/12 : 25/18 has a unit rate of 3/10

Hint: You have to do what with fractions when you divide. Don't forget to reduce the answer if it can be reduced.

• True

• False

Answer explanation

If the ratio is 5/12 : 25/18, you would have kept the first, changed the sign, flipped the second and multiplied.

5/12 ÷ 25/18 would now be 5/12 x 18/25. Multiply across 90/300 and then reduce for the final answer of 3/10.