Question

explain different ways to compare positive and negative numbers.
on a winter day, adrian looks up the current temperatures in hong kong cities. the temperatures are 2.5°f, -3.5°f and -5°f. explain each way of the temperatures and write a comparison. what are all the possible comparisons for each method? use one sentence and/or equations.
model 1
you can use a number line to compare positive and negative numbers.
three number line images with points labeled 2.5, -3.5, 1.5, -5, -3.5, -5
model 2
you can write an inequality to compare positive and negative numbers.
2.5 > -3.5
1.5 > -5
-3.5 > -5
analyze it
you can use words to interpret the meaning of an inequality in a real - world situation.
2.5°f is warmer than - 3.5°f.
2.5°f is warmer than - 5°f
-3.5°f is warmer than - 5°f

Explanation:

Step1: Identify Comparison Method (Number Line)

Using a number line, positive numbers are to the right of 0, negative to the left. So \( 2.5 \) (right of 0) is greater than \( -3.5 \) (left of 0), \( 2.5 > -5 \) (since \( -5 \) is further left), and \( -3.5 > -5 \) (closer to 0 than \( -5 \)).

Step2: Identify Comparison Method (Inequality)

Write inequalities: \( 2.5 > -3.5 \), \( 2.5 > -5 \), \( -3.5 > -5 \).

Step3: Interpret in Real - World (Temperature)

For temperature, a higher number (less negative or positive) means warmer. So \( 2.5^\circ\text{F} \) is warmer than \( -3.5^\circ\text{F} \), \( 2.5^\circ\text{F} \) warmer than \( -5^\circ\text{F} \), \( -3.5^\circ\text{F} \) warmer than \( -5^\circ\text{F} \).

Answer:

Ways to compare: 1. Use a number line (positive numbers are right of 0, so greater than negatives; among negatives, closer to 0 is greater). 2. Write inequalities (\( 2.5 > - 3.5 \), \( 2.5 > - 5 \), \( - 3.5 > - 5 \)). 3. Interpret in temperature context (warmer temperature means greater number).