Lesson 5

Comparing Numbers and Distance from Zero

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Problem 1

In the context of elevation, what would \(|\text-7|\) feet mean?

Solution

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Problem 2

Match the the statements written in English with the mathematical statements.

A:

The number -4 is a distance of 4 units away from 0 on the number line.

B:

The number -63 is more than 4 units away from 0 on the number line.

C:

The number 4 is greater than the number -4.

D:

The numbers 4 and -4 are the same distance away from 0 on the number line.

E:

The number -63 is less than the number 4.

F:

The number -63 is further away from 0 than the number 4 on the number line.

1:

\(|\text-63| > 4\)

2:

\(\text-63 < 4\)

3:

\(|\text-63| > |4|\)

4:

\(|\text-4| = 4\)

5:

\(4 > \text-4\)

6:

\(|4| = |\text-4|\)

Solution

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Problem 3

Compare each pair of expressions using >, <, or =.

  • \(\text-32\) _____ \(15\)

  • \(|\text-32|\) _____ \(|15|\)

  • \(5\) _____ \(\text-5\)

  • \(|5|\) _____ \(|\text-5|\)

  • \(2\) _____ \(\text-17\)

  • \(2\) _____ \(|\text-17|\)

  • \(|\text-27|\) _____ \(|\text-45|\)

  • \(|\text-27|\) _____ \(\text-45\)

Solution

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Problem 4

Mai received and spent money in the following ways last month. For each example, write a signed number to represent the change in money from her perspective.

  1. Her grandmother gave her $25 in a birthday card.
  2. She earned $14 dollars babysitting.
  3. She spent $10 on a ticket to the concert.
  4. She donated $3 to a local charity
  5. She got $2 interest on money that was in her savings account.

Solution

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(From Unit 7, Lesson 3.)

Problem 5

Here are the lowest temperatures recorded in the last 2 centuries for some US cities.

  • Death Valley, CA was \(\text-45^\circ\text{F}\) in January of 1937.
  • Danbury, CT was \(\text-37^\circ\text{F}\) in February of 1943.
  • Monticello, FL was \(\text-2^\circ\text{F}\) in February of 1899.
  • East Saint Louis, IL was \(\text-36^\circ\text{F}\) in January of 1999.
  • Greenville, GA was \(\text-17^\circ\text{F}\) in January of 1940.
  1. Which of these states has the lowest record temperature?
  2. Which state has a lower record temperature, FL or GA?
  3. Which state has a lower record temperature, CT or IL?
  4. How many more degrees colder is the record temperature for GA than for FL?

Solution

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(From Unit 7, Lesson 1.)

Problem 6

Noah was assigned to make 64 cookies for the bake sale. He made 125% of that number. 90% of the cookies he made were sold. How many of Noah's cookies were left after the bake sale?

Solution

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(From Unit 6, Lesson 4.)