 # Equivalent Expressions with Rational Numbers

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Lesson Plans and Worksheets for Grade 7
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Examples, videos, and solutions to help Grade 7 students learn how to write, evaluate, and find equivalent expressions with rational numbers.

### New York State Common Core Math Grade 7, Module 2, Lesson 18, Lesson 19

Lesson 18 & Lesson 19 Student Outcomes

Students create equivalent forms of expressions in order to see structure, reveal characteristics, and make connections to context.

Students compare equivalent forms of expressions and recognize that there are multiple ways to represent the context of a word problem.

Students write and evaluate expressions to represent real-world scenarios.

Lesson 18 Summary

• An expression is a number or a letter, which can be raised to a whole number exponent. An expression can be a product whose factors are any one of the entities described above. An expression can also be the sum and/or difference of the products described above.
• To evaluate an expression, replace each variable with its corresponding numerical value. Using order of operations, the expression can be written as a single numerical value.
• Expressions are equivalent if they evaluate to the same number for every substitution of numbers into all the letters in each expression.

Lesson 18 Example 1

John's father asked him to compare several different cell phone plans and identify which plan will be the least expensive for the family. Use the information contained in the table below to answer the following questions.
All members of the family may not want identical plans, therefore we will let represent the number of phone lines, represent the number of phone lines with unlimited texting, and represent the number of phone lines with Internet access.
Using the expressions above, find the cost to the family of each company’s phone plan if:
a. Four people want a phone line, four people want unlimited texting, and the family needs two Internet lines. Which cell phone company should John’s family use? Why?
b. Four people want a phone line, four people want unlimited texting, and all four people want internet lines. Which cell phone company should John’s family use? Why?
c. Two people want a phone line, two people want unlimited texting and the family needs two Internet lines. Which cell phone company should John’s family use? Why?

Example 2
Three friends went to the movies. Each purchased a medium-sized popcorn for dollars and a small soft drink for dollars.
a. Write the expression that represents the total amount of money (in dollars) the three friends spent at the concession stand.
b. If the concession stand charges \$6.50 for a medium-sized popcorn and \$4.00 for a small soft drink, how much did the three friends spend on their refreshments all together?

Example 3
Complete the table below by writing equivalent expressions to the given expression, and evaluating each expression with the given values.

Lesson 18 Problem Set

4. Profit is defined as earnings less expenses (earnings – expenses). At the local hot air balloon festival, the Ma & Pops Ice Cream Truck sells ice cream pops, which cost them \$0.75 each, for \$2 each. They also paid \$50 to the festival's organizers for a vendor permit. The table below shows the earnings, expenses and profit earned when 50, 75, and 100 ice cream pops were sold at the festival.
a. Write an expression that represents the profit (in dollars) Ma & Pop earned by selling ice cream pops at the festival.
b. Write an equivalent expression.
c. How much did Ma & Pops Ice Cream Truck profit if it sold 20 ice cream pops? What does this mean? Explain why this might be the case?
d. How much did Ma & Pops Ice Cream truck profit if it sold 75 Ice Cream Pops? What does this mean? Explain why this might be the case?

Lesson 19 Summary

• Two expressions are equivalent if they yield the same number for every substitution of numbers for the letters in each expression.
• The expression that allows us to find the cost of an item after the discount has been taken and the sales tax has been added is written by representing the discount price added to the discount price multiplied by the sales tax rate.

Lesson 19 Example 1: Tic-Tac-Toe Review

Fill in the 9 spaces with one expression from the list below. Use one expression per space. You will use 9 of the expressions:

Example 2:

Use your knowledge of percents and discounts to find the discount amount and new price when the original price is given.

Example 3

An item that has an original price of dollars is discounted 33%

a. Write an expression that represents the amount of the discount.
b. Write two equivalent expressions that represent the new, discounted price.
c. Use one of your expressions to calculate the new, discounted price if the original price was \$56.
d. How would the expressions you created in parts (a) and (b) have to change if the item’s price had increased by 33% instead of discounted 33%?

Example 4

Sales tax is a number added to the cost of an item and it is found by finding the sales rate (%) of the item and added to the cost.

Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers. Corresponds to NYS Module 2 Lessons 18 & 19. Lesson 19 Problem Set
2. Sally designs web pages for customers. She charges \$135.50 per web page, however she must pay a monthly rental fee of \$650 for her office. Write an expression to determine her take-home pay after expenses. If Sally designed 5 web pages last month, what was her take-home pay after expenses?

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