Review: Proportional reasoning

Review: Proportional Reasoning

7th Grade Math

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A rate is a comparison of two numbers with different units.

For example, a car drives 60 miles per hour for a rate of 60:1

A ratio compares two numbers with the same unit.

Multiple Choice

A carpenter lays 18 square feet of tile in  $$\frac{2}{3}$$ of an hour. How many square feet of tile does the carpenter lay per hour?

• 27 square feet per hour

• $$17\ \frac{1}{3}$$ square feet per hour

• $$18\ \frac{2}{3}$$ square feet per hour

• 12 square feet per hour

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A carpenter lays 18 square feet of tile in 2/3  of an hour. How many square feet of tile does the carpenter lay per hour?

Sq ft : hour to get from 2/3 to 1 divide by 2/3 (multiply by 3/2)
18 : 2/3 then do the same to 18
27 : 1 18 * 3/2 = 54/2 = 27

Math Response

One-quarter of a bread recipe calls for  $$\frac{2}{3}$$  cup of bread flour. How much flour is needed per recipe?

Type answer here

Correct Answer: 2\frac{2}{3}

Deg^°

Rad

Multiple Choice

A 16 in. piece of string measures 40.64 cm long. How long is a 42 in. piece of ribbon to the nearest hundredth centimeter?

• 106.68

• 82.64

• 56.64

• 16.54

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A 16 in. piece of string measures 40.64 cm long. How long is a 42 in. piece of ribbon to the nearest hundredth centimeter?

inches : centimeters
16 : 40.64
1 : 2.54 (divide both sides by 16)
42 : 106.68 (multiply both sides by 42)

Multiple Choice

A clothing store sells 3 store-brand T-shirts for $18.75. The store also sells other brands of T-shirts at the prices listed below. Which price has a unit rate that is less than the store-brand unit rate?

• 3 T-shirts for $31.25

• 7 T-shirts for $ 50.75

• 4 T-shirts for $26.00

• 6 T-shirts for $37.25

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A clothing store sells 3 store-brand T-shirts for $18.75. The store also sells other brands of T-shirts at the prices listed below. Which price has a unit rate that is less than the store-brand unit rate?

First find the price per t-shirt for the store brand (unit rate): 18.75÷3=6.25
Either multiply by the number of shirts and see if the price is less or find the unit rate for each and compare:
3@31.25 = 1@10.46 ($18.75 @ 6.25) 7@50.75= 1@7.25 (43.75 @ 6.25)
4@26.00= 1@6.50 (25.00 @ 6.25) 6@37.25 = 1@6.21 (37.50@6.25)

So the 6 at $37.25 is cheaper

Multiple Choice

The graph shows the relationship between hours spent raking and bags of leaves raked. Which statement correctly describes the relationship?

• The relationship is proportional, and the constant of proportionality is 2.5.

• The relationship is proportional, and the constant of proportionality is 5. 

• The relationship is proportional, and the constant of proportionality is 20. 

• The relationship is not proportional.

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The graph shows the relationship between hours spent raking and bags of leaves raked. Which statement correctly describes the relationship?
The relationship is proportional, and the constant of proportionality is 5. 

A proportional graph is a straight line through the origin. Where x = 1, y = k or y IS the constant of proportionality.

Multiple Select

Angela wrote the data values in the table as shown and claimed that the table shows a proportional relationship. Which changes to exactly one cell in the table result in the table showing a proportional relationship?

Select all the correct answers.

• Change x  from 10.0 to 8.0 when y=16.0.

• Change x from 14.0 to 17.5 when y=28

• Change y from 16.0 to 20.0 when x=10.0.

• Change y from 28.0 to 22.4 when x=14.0.

• Change y from 28.8 to 36.0 when x=18.0.

​Angela wrote the data values in the table as shown and claimed that the table shows a proportional relationship. Which changes to exactly one cell in the table result in the table showing a proportional relationship?

Select all the correct answers.

Remember that y = kx so to find k divide y by x.
16÷10 = 1.6; 28÷14 = 2; and 28.8÷18 = 1.6. So we are looking to maintain the 1.6 ratio. If you change 14 to 17.5 or 28 to 22.4 you get the 1.6:1 ratio.

Multiple Choice

Renting a canoe costs $5 per hour for each adult and $3 per hour for each child. One adult and two children decide to rent a canoe. Which equation shows the relationship between cost, c, in dollars and time, t, in hours?

• c = 11t

• c = 5 + 3t

• c = 8t

• c = 5t + 3

Multiple Select

Select all the equations that do not represent a proportional relationship.

• y = 12x -2.2

• y = 3x + 7

• y = 1.99x

• $$y\ =\ \frac{2}{9}x$$

• $$y\ =2+\frac{7}{8}x$$