Question

lesson 24 lesson 2
explain different ways to compare positive and negative numbers.
on a winter day, adrian noted the current temperatures in three nearby cities. the temperatures are ( 2.5^circ \text{f} ), ( -1.5^circ \text{f} ), and ( -5^circ \text{f} ). adrian chooses two of the cities and writes a comparison. what are all the possible comparisons between the two cities (use words and/or symbols)?
model it
we can use a number line to compare positive and negative numbers.
model it
we can write an inequality to compare positive and negative numbers.
( 2.5 > -3.5 )
( 2.5 > -5 )
( -3.5 > -5 )
analyze it
you can use inequalities to interpret the meaning of an inequality in a real - world situation.
( 2.5^circ \text{f} ) is warmer than ( -3.5^circ \text{f} )
( 1.5^circ \text{f} ) is warmer than ( -5^circ \text{f} )
( -3.5^circ \text{f} ) is warmer than ( -5^circ \text{f} )
connect it
use the problem from the previous page to help you understand how to compare positive and negative numbers.

1. look at the two model its. how can you use a number line to help you write an inequality?
2. look at analyze it. how can the inequalities help to determine which of two temperatures is warmer?
3. use the symbol > to rewrite the comparison between ( -3.5^circ \text{f} ) and ( -5^circ \text{f} ). then interpret the meaning of the inequality using the words “colder than” or “warmer than.”
4. what are all the possible inequality statements adrian might write? use > and <.
5. when given a pair of numbers in a real - world situation, how can you compare the numbers using > and <? how can an inequality help you interpret the comparison in the real - world situation?
6. reflect think about all the models and strategies you have discussed today. describe how one of them helped you better understand how to compare positive and negative numbers.

Explanation:

Step1: Analyze the numbers

We have -35°F and 25°F. On a number line, positive numbers are to the right of zero, and negative numbers are to the left. 25 is a positive number, -35 is negative. Positive numbers are greater than negative numbers.

Step2: Write the inequality

Since 25 is greater than -35, we write \( 25 > -35 \).

Step3: Interpret the inequality

Using "colder than", we know that a lower temperature (more negative or smaller positive) is colder. Since -35 is less than 25, -35°F is colder than 25°F, which matches the inequality \( 25 > -35 \) (25 is warmer, so -35 is colder, meaning 25 is greater than -35).

Answer:

The inequality is \( 25 > -35 \). The meaning is: -35°F is colder than 25°F (or 25°F is warmer than -35°F).