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Grade 6 · Maths · Lessons
How far across the grid
🗺️grid📍P and Q➖subtract➕add
How far across the grid?
The big ideaSame side of zero, subtract. Opposite sides, add.

How it works

Same side of zero, subtract. Opposite sides, add.

Two points on the same horizontal or vertical line: look at the numbers that change.

Distance is never negative.

Same side• −4 and −1: 4 − 1 = 3Opposite sides• −8 and 4: 8 + 4 = 12
Same side or opposite sides?

Example 1: Same side

  1. P is at −4 and Q is at −1 along a line.
  2. Both are negative, so subtract the sizes: 4 − 1 = 3.
  3. They are 3 apart.

Example 2: Opposite sides

  1. P is at −8 and Q is at 4.
  2. They are on opposite sides of zero, so add the sizes: 8 + 4 = 12.
  3. They are 12 apart.

Example 3: Another

  1. P is at −5 and Q is at −8.
  2. Same side: 8 − 5 = 3.
  3. They are 3 apart.

Words to know

distance
How far apart.
coordinate
One of the two numbers that name a point.

Watch out

Try it

  1. How far apart are −2 and 6?
  2. How far apart are −9 and −4?
  3. How far apart are 3 and 10?
  4. Which do you do for opposite sides: add or subtract?
Answers: 1. 8 · 2. 5 · 3. 7 · 4. add
For grown-upsUse a thermometer-like line and ask how far from −3 to 5 degrees.
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