a − b asks how far it is from b to a, and in which direction.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
An example
4 − (−3) asks how far from −3 to 4. That is 7 steps to the right, so the answer is 7.
The same as adding the opposite
Subtracting −3 gives the same answer as adding 3, because both measure the same gap.
Why this beats the rule
"Two minuses make a plus" gives no way to check. The gap on the line always can be counted.
Subtraction measures the gap
a − b answers "how far is it from b to a, and in which direction". From 3 to 7 is +4, so 7 − 3 = 4. From 7 to 3 is −4, so 3 − 7 = −4. The sign records the direction of travel.
Subtracting a negative
3 − (−2) asks how far it is from −2 to 3: five steps to the right, so the answer is 5. Subtracting a negative gives a bigger answer, and the number-line reading makes that obvious instead of arbitrary.
The rule that follows
Subtracting is the same as adding the opposite: 3 − (−2) = 3 + 2 = 5. Rewriting every subtraction as an addition means you only ever need the addition rules, which is a real simplification once the numbers get messy.
Order matters, and the sign records it
7 − 3 and 3 − 7 differ only in sign. Subtraction is not commutative, and with signed numbers that shows up as a sign flip rather than as an obviously wrong answer — which is why it is easy to miss.
Step 2: Try It Yourself
Tap and try it out.
4 − (-3) asks how far it is from -3 to 4, and in which direction. That is 7.
Step 3: Watch an Example
One step at a time.
Watch Ana Work Out −2 − 5
Ana subtracts a positive from a negative.
- Step 1
She reads it as: how far from 5 to −2?
Step 4: Your Turn
Practice makes it stick.
The Temperatures
Problem 1 of 2
From −5 degrees to 8 degrees. How many degrees is the rise?
The Debt
Problem 2 of 2
A balance of −30 has 20 taken away. What is the new balance?
Measure the Gap
1 of 4
6 − (−2) = ?
2 of 4
−4 − 3 = ?
3 of 4
−1 − (−6) = ?
4 of 4
2 − 9 = ?
Step 5: Quick Check
Show what you know.
Question 1 of 2
3 − (−8) = ?
Question 2 of 2
What does a − b measure?
What You Learned
- Subtraction measures the gap from the second number to the first.
- Subtracting a negative is the same as adding its opposite.
- The line gives a way to check, which a sign rule does not.