What addition and subtraction mean
Addition is combining numbers. On the number line, you start at the first number and move by the second:
- Add a positive → move right.
3 + 2lands at5. - Add a negative → move left.
3 + (−2)lands at1.
Subtraction is taking away. Once negatives are on the line, subtraction is addition with the second number's sign flipped:
So 5 − 3 is the same as 5 + (−3). 5 − (−3) is the same as
5 + 3. Drop the subtraction, flip the sign — now it's an addition.
The − symbol does two jobs. It can mark a negative number (like
−5) or tell you to subtract (like 5 − 3). If those two
meanings get tangled, rewrite the problem as an addition.
Try it
Drag the dots — the equation updates as you move them.
Drag with the mouse, or focus a dot and use ←/→.
Where it shows up in real life
A Calgary chinook day. Morning starts at −10°C. The chinook rolls
in over the Rockies and warms the city to +12°C by mid-afternoon.
Then the chinook ends, and the temperature drops 35 degrees by
late evening:
Try it
Drag the marker around the dial. The equation updates as you move.
Drag with the mouse, or focus the marker and use ←/→.
From +12 °C, a 35-degree drop lands at −23 °C — through zero
and into the negatives. Drag the marker to test other drops: a
smaller one keeps the evening above zero, a bigger one ends up
further below.
Worksheet
These aren't graded. Get them right, get them wrong — the goal is to feel out where the idea works.
Question 1 of 3
Try it
What is 5 + (−7)?
Multiple choice: what is five plus negative seven? Four answer cards: minus twelve, minus two, plus two, plus twelve.Drag the orange marker to figure out where you land.
Going further
Multiplication and division of integers come next. The sign rules
look different, but the question is the same: what does the − in
front of a number mean?
The same idea carries straight over to decimals and fractions — same number line, finer ticks.