Lesson 19-5: Refine Equivalent Expressions

The fee for an overdue library book is $0.75 for the first day and $0.50 for each additional day. Rodrigo has an overdue library book. He writes the expression 0.75 + 0.5(d – 1) to represent the fee in dollars for a book that is d days overdue. Rewrite Rodrigo’s expression for the fee as a sum of two terms.

Mathematical Equivalence

ON

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CCSS.7.EE.A.1

Ana and Katrina are buying fruit to bring to their book club meeting. Ana buys 2.4 lb of oranges and 0.8 lb of cherries. Katrina buys 1.8 lb of oranges and 1.3 lb of cherries. Oranges cost r dollars per pound, and cherries cost c dollars per pound. Write an expression with exactly two terms for the total cost of the fruit Ana and Katrina buy.

Mathematical Equivalence

ON

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CCSS.7.EE.A.1

Which expression is equivalent to
3(2x + 4y) – y?

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CCSS.6.EE.A.3

Which expression is equivalent to
3(2x + 4y) – y?

Kimani chose C as the correct answer.
How might she have gotten that answer?

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CCSS.6.EE.A.3

A park meadow is planted with wildflowers. The Parks Department plans to extend the length of the rectangular meadow by x meters. Which expressions represent the total area, x, in square meters, after the meadow’s length    is increased? Select all that apply.

Groups:

(a) Equivalent

,

(b) Not Equivalent

• 15.5x + 310

• 15.5 (20 + x)

• 310 + x

• 20x + 15.5

• 15.5 (20x)

• 35.5 + x

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CCSS.6.EE.B.6

Use the distributive property to write two different expressions equal to 72. Each expression should be the product of a number and a sum. Show your work.

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KS.MA.6.NS.4

Look at each pair of expressions. Select Equivalent or Not Equivalent for each pair.

Groups:

(a) Equivalent

,

(b) Not Equivalent

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CCSS.6.EE.A.4

Show how to use the greatest common factor of 84 and 72 to rewrite 84m – 72n as a product of two factors. Label the step that shows the distributive property.

Mathematical Equivalence

ON

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CCSS.7.EE.A.1

A wading pool holds g gallons of water. A swimming pool holds 15 times as much water as the wading pool. Which expressions represent the total number of gallons of water in both pools? Select all that apply.

• 15g

• 16g

• 15 + g

• 2g +15

• g +15g

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CCSS.6.EE.B.6

Are the expressions   (4c + 8) + 3c – 2 and

4c + 2(0.5c + 1) equivalent? Explain

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CCSS.6.EE.A.4