A strike has a size and a way
An integer says how far and which way.
Two strikes on a carrom board
A carrom coin starts at 0. The first strike moves it 5 units to the right. The second strike moves it 7 units to the left.
Where does the coin stop?
What this lesson covers
The idea
Taking movement along a number line as positive in one direction and negative in the other, an integer captures both the distance (magnitude) and the direction, and successive movements combine by adding the integers.
Two strikes on a carrom board
A carrom coin starts at 0. The first strike moves it 5 units to the right. The second strike moves it 7 units to the left.
Where does the coin stop?
- 2 units to the right of 0
- 2 units to the left of 0
- 12 units away from 0
Strike the coin
Set each strike with ◀ ▶, then tap Strike. Right is positive and left is negative. Try to reach each flag.
One integer tells two things
The strike −7 says how far, 7 units (its magnitude), and which way, left (its minus sign). A + strike goes right.
After two strikes a and b, the coin is at a + b: 5 + (−7) = −2. This works when both go right, both go left, or one goes each way.
Take moving right as positive and left as negative. An integer then gives the magnitude (the distance) and the direction. Strikes combine by adding the integers: P = a + b.
- Strike | How far | Which way
- 5 | 5 units | right
- −7 | 7 units | left
Notes
An integer gives the magnitude (how far) and the direction (right: +, left: −). Successive movements combine by adding: P = a + b.
Check yourself
The first strike is −4. The coin then finishes at 5. What is the second strike?
Answer: 9
−4 + 9 = 5, so the second strike is 9: nine units to the right.
What does the strike −6 tell us?
The strikes are 1, −2, 3, −4, 5, −6, 7, −8, 9, −10, one after the other from 0. Where does the coin finish?
Answer: -5
Each pair 1 + (−2), 3 + (−4), … is −1. There are 5 pairs, so the coin finishes at −5.
A coin at 0 is struck 8 units right, then 3 units left, then 9 units left. Where does it finish?
Answer: -4
8 + (−3) = 5, then 5 + (−9) = −4.
- 6 units to the right. The minus sign gives the direction: left.
- A distance of −6. A distance cannot be negative. The size is 6; the minus sign only tells the direction.
- 6 units to the left — correct. Yes! The size is 6 and the minus sign means left.