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If Alaska is −5∘F and Chicago is −2∘F, which city is actually warmer?
It can feel tricky because 5 is bigger than 2, but with negative numbers, standard rules flip.
The Left-to-Right Rule
A rational number is any number that can be written as a simple fraction, including whole numbers, integers, and decimals.
On a horizontal number line, value always increases from left to right.
📊Create an interactive visual diagram of a horizontal number line ranging from -6 to 6 with tick marks every 1 unit. Plot two distinct points: point A at -5 (colored coral red #ef4444, labeled '-5°F') and point B at -2 (colored sky blue #0284c7, labeled '-2°F'). Above the line, show a gradient arrow pointing right with the label 'GREATER (Warmer) ->' and an arrow pointing left with '<- LESS (Colder)'. Display an inequality badge underneath: '-2 > -5 because -2 is to the right of -5'. Clean light theme (#f8f9fa background, dark text #1e2945, rounded 12px card).
Because −2 lies to the right of −5, we know that −2>−5, meaning Chicago is warmer than Alaska.
What happens when you need to order an entire mixed set of decimals, fractions, and negative numbers?
Ordering from Least to Greatest
Let's order this set from least to greatest: {−1.5,43,−2.25,0.5}.
First, convert all fractions to decimals so they are easy to compare: 43=0.75.
📊Create a clean number line visualization from -3 to 2 with tick marks every 0.5. Plot four points clearly labeled with dots and callout tags: -2.25 (purple), -1.5 (red), 0.5 (blue), and 0.75 [labeled as '3/4 (0.75)'] (emerald green). Underneath, draw a smooth horizontal arrow sweeping from left to right with numbered step markers (1, 2, 3, 4) indicating the reading order: -2.25 -> -1.5 -> 0.5 -> 3/4. Include a final ordered list at the bottom: '-2.25 < -1.5 < 0.5 < 3/4'.
Reading the points from left to right gives our final order: −2.25,−1.5,0.5,43.