Lesson 6

Subtracting Rational Numbers

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Problem 1

Write a sentence to answer each question:

  1. How much warmer is 82 than 40?

  2. How much warmer is 82 than -40?

Solution

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Problem 2

  1. What is the difference in height between 30 m up a cliff and 87 m up a cliff? What is the distance between these positions?

  2. What is the difference in height between an albatross flying at 100 m above the surface of the ocean and a shark swimming 30 m below the surface? What is the distance between them if the shark is right below the albatross?

Solution

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Problem 3

A company produces screens of different sizes. Based on the table, could there be a relationship between the number of pixels and the area of the screen? If so, write an equation representing the relationship. If not, explain your reasoning.

square inches of screen number of pixels
6 31,104
72 373,248
105 544,320
300 1,555,200

Solution

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(From Unit 2, Lesson 8.)

Problem 4

Find each difference.

  • \((\text-5) - 6\)

  • \(35 - (\text-8)\)

  • \(\frac25 - \frac35\)

  • \(\text-4\frac38 - (\text-1\frac14)\)

Solution

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Problem 5

A family goes to a restaurant. When the bill comes, this is printed at the bottom of it:

Gratuity Guide For Your Convenience:
15% would be $4.89
18% would be $5.87
20% would be $6.52

How much was the price of the meal? Explain your reasoning.

Solution

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(From Unit 4, Lesson 10.)

Problem 6

Which is a scaled copy of Polygon A? Identify a pair of corresponding sides and a pair of corresponding angles. Compare the areas of the scaled copies.

Six L-shaped figures on a grid, labeled A, B, C, D, E, and F. 

Solution

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(From Unit 1, Lesson 2.)