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In this lesson, we will learn how to identify proportional relationships and use them to solve real-world problems.

Q1:

Determine whether the quantities in the following rates are proportional: 820 calories in 5 servings and 800 calories in 4 servings.

Q2:

Mr. Amir asked his students whether the following numbers were terms of a proportion: 4, 20, 7, 35. Yara said they were, while Sarah said they were not. Who was correct?

Q3:

Does the following table show a proportional relationship between the number of pages read 𝑛 and the time 𝑡 ?

Q4:

Does the following table show a proportional relationship between the number of miles traveled on a bicycle and the time of travel?

Q5:

Mona is working as a part-time babysitter. The following table shows how much she earns and the number of hours she spends babysitting. Does the table show a proportional relationship?

Q6:

For the following square, are the perimeter and side length proportional?

Q7:

The graph below shows the relation between distance and time for a moving car. Is there a proportional relationship between the two quantities?

Q8:

Uptown Pizzeria sells medium pizzas for $7 each and charges a $3 delivery fee per order. Is the cost of an order proportional to the number of pizzas ordered?

Q9:

Consider the data shown below.

Does this show a proportional relationship?

Q10:

An adult elephant drinks about 225 litres of water each day. Is the number of days that an elephant’s water supply lasts for proportional to the number of liters the elephant drinks?

Q11:

At a certain middle school, every homeroom teacher is assigned 28 students. There are 3 teachers who do not have a homeroom. Is the number of students at this school proportional to the number of teachers?

Q12:

At the beginning of the school year, Dina had $120 in the bank. Each week, she deposits another $20. Is her account balance proportional to the number of weeks since she started school?

Q13:

MegaMart collects a sales tax equal to 1 1 6 of the retail price of each purchase and sends this money to the state government. Is the amount of tax collected proportional to the cost of an item before tax is added?

Q14:

Which of the following tables shows a proportional relationship between the prices and the number of apples?

Q15:

For the following figure, Yasmine thinks that the length of its shorter side is proportional to its area. Do you agree with her?

Q16:

The following table shows the ages and weights of three brothers.

Are the brothers’ weights proportional to their ages?

Q17:

On Saturday, Yara gave away 416 coupons for a free appetiser at a local restaurant. The next day, she gave away about 52 coupons an hour. Is the total number of coupons Yara gave away on Saturday and Sunday proportional to the number of hours she worked on Sunday?

Q18:

Does the following graph show a proportional relationship?

Q19:

Isabella is using origami sheets to make flowers. The following shows the number of flowers she makes and the number of origami sheets she uses. Is this a proportional relationship?

Q20:

Last week, Dalia bought one gallon of milk for $3.50. This week, she bought 2 gallons of milk for $7.50. Is the total money she paid proportional to the number of gallons?

Q21:

The figure below shows the number of pizzas made by Chloe and the number of tomatoes she used to make them. Does the figure show a proportional relationship?

Q22:

To convert a temperature from degrees Celsius to degrees Fahrenheit, multiply the temperature in Celsius by 9 5 and then add 3 2 ∘ . Is a temperature in degrees Celsius proportional to its equivalent temperature in degrees Fahrenheit?

Q23:

Shady earns $18 per hour for mowing lawns. Is the amount of money he earns proportional to the number of hours he spends mowing?

Q24:

Fady decided to work during the summer. The graph represents the relationship between the money he earns and the time he spends working. Is this relationship proportional?

Q25:

The table shows how many pages of a book Nabil has read at different times.

Is Nabil reading at a constant speed? Why?

What is the constant of proportionality (or unit rate)? What does it represent?

Write an equation in the form for the number of pages read in minutes.

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