Compare and Order Positive and Negative Rationals

What "smaller" means on the number line

Slide your finger along the line. Further to the right is larger; further to the left is smaller. The rule doesn't change when the line crosses zero.

So $-5$ is smaller than

$-1$, even though the digit 5 is bigger than 1. More-negative does not mean larger.

−7 and +7 sit the same distance from zero — mirror images across the centre. Same absolute value, opposite signs.

A negative fraction can be written three ways:

The minus belongs to the number, not to any single digit. All three expressions live at the same point on the line.

See it on the number line

Drag the cards into ascending order — smallest on the left, largest on the right. Hit Check when you think you've got it.

Two things to watch for:

• The two negatives don't behave like positives. $-\tfrac{3}{4}$ is bigger than $-2$. Closer to zero = bigger, on the negative side.
• Convert before comparing. $-\tfrac{3}{4} = -0.75$, so it sits a touch left of $-0.6$. Without converting, you'd guess.

Where it shows up in real life

One January week, four Alberta cities posted these morning lows. Sort them from coldest to mildest.

Fort McMurray's −33 was coldest, even though 33 looks like the biggest number on the list. Bigger digit after the minus, smaller number on the line.

Worksheet

These aren't graded. Get them right, get them wrong — the goal is to feel out where the idea works.

Going further

Adding and subtracting integers comes next — the same line, now with arrows. Further right = larger becomes add a positive moves right; add a negative moves left.

The same comparison shows up later in inequalities:

$2x - 3 > 7$ asks which values of x push the left side further right than the right side?