Adding a positive walks right. Adding a negative walks left. That is the whole rule.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
A pair that cancels has a name.
Additive inverse is the number that adds to give zero. The inverse of 7 is −7.
When the signs differ
−8 + 3 walks 3 right from −8, landing on −5. The bigger distance decides the sign.
No sign rules needed
Every case is one walk. There is nothing to memorise.
Adding is a walk along the line
Start at the first number and walk. A positive number walks right; a negative walks left. So −3 + 5 starts at −3, walks 5 right, and lands on 2. One picture handles every combination of signs.
Same signs: the walk continues
−3 + (−4) walks left, then further left, landing on −7. When both numbers share a sign, the magnitudes add and the sign stays. This is the easy case and it matches the intuition of "more of the same".
Different signs: the walk doubles back
−3 + 5 walks left then right, ending up 2 to the right of zero. When the signs differ, the smaller magnitude cancels part of the larger, and the answer takes the sign of the larger. Zero pairs are what is really happening.
Money and temperature make it concrete
Owing £3 and then receiving £5 leaves you £2 ahead. Starting at −3 degrees and warming 5 degrees gives 2 degrees. When a signed calculation feels abstract, recast it as money or temperature and the answer becomes obvious.
Step 2: Try It Yourself
The arc is the walk. Watch which way it goes.
Adding 3 walks 3 to the right.
Step 3: Watch an Example
One step at a time.
Watch Leo Work Out −6 + 10
Leo adds a positive to a negative.
- Step 1
He starts at −6 on the line.
Step 4: Your Turn
Practice makes it stick.
The Temperature
Problem 1 of 2
It is −7 degrees and rises 12. What is the temperature now?
The Account
Problem 2 of 2
An account at −40 pounds receives 15. What is the balance?
Walk the Line
1 of 4
−5 + 9 = ?
2 of 4
6 + (−10) = ?
3 of 4
−3 + (−4) = ?
4 of 4
What is the additive inverse of −11?
Step 5: Quick Check
Show what you know.
Question 1 of 2
−9 + 4 = ?
Question 2 of 2
What does adding a negative do on the line?
What You Learned
- Adding a positive walks right, a negative walks left.
- Additive inverses add to zero.
- Every case is one walk, so there are no sign rules to learn.