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Lesson 4: Subtracting negative numbers fluently

# Subtracting negative numbers review

Review the basic of subtracting negative numbers and try some practice problems.

## Subtracting negative numbers

Subtracting a number is the same as adding the opposite of the number.
Let's look at two examples:
$-5-7=-5+\left(-7\right)$
$10-\left(-3\right)=10+3$
Note: In both examples, we change subtraction to addition and changed the sign of the second number to the opposite sign.
Want to know why this works? Check out this video.
Once we have an addition problem, we can solve.

### Example 1: negative $-$‍  negative

Lets subtract $-5-\left(-6\right)$.
Step 1: Rewrite as an addition problem
$-5-\left(-6\right)=-5+6$
Step 2: Start at the first number in the addition problem, in this case $-5$:
Step 3: Move $6$ places to the right. We move $6$ to the right because adding positive $6$ increases our number by $6$.
$-5+6$ takes us to $1$ on the number line.
$-5-\left(-6\right)=1$

### Example 2: negative $-$‍  positive

Lets subtract $-4-7$.
Step 1: Rewrite as an addition problem
$-4-7=-4+\left(-7\right)$
Step 2: Start at the first number in the addition problem, in this case $-4$:
Step 3: Move $7$ places to the left. We move $7$ to the left because adding negative $7$ decreases our number by $7$.
$-4+\left(-7\right)$ takes us to $-11$ on the number line.
$-4-7=-11$

## Practice

Problem 1
Subtract.
$-8-\left(-2\right)=$

Want to try some more subtracting negative numbers problems? Check out this exercise.

## Want to join the conversation?

• why does it say subtract when you have to add
• Because two negatives equal a positive in a subtraction when it's next to each other. 3-(-6)=9=3+6=9
• Negative minus a positive is a negative?
• Yes, subtracting a positive always makes the number smaller.
• So basically 2 negatives make a positive?
• You could be mistaking this for a multiplication problem. negative * negative = positive but in addition negative + negative = negative.
• So, correct me anyone if I'm wrong. So let's say I have
-4-(-4), wouldn't equal 0? Because instead of me subrtracting with -4, I have to add it. So, would it be 0 instead of -8?
• Yes that is correct.
• can 10 people please vote me i want the moon badge to
• I am confused that 8 - (-2) means you add up. IS that count Mr.Khan?
• Because when you do a subtraction problem with a positive taken away, you go down. 8 - 2 = 6 When that's negative, you have the opposite, so you go up. 8 - ( - 2 ) = 10 You still might wonder why it isn't - 10, but I can answer it. Subtraction and addition like this stuff are never gonna give you negative.
• I don't get why they are swiching the signs telling me to add when I have to subtract. I just don't understand at all.
• Another way to think of a negative sign is as an OPPOSITE sign. So when you are subtracting a negative, it's really telling you to do the opposite of subtracting, which ends up being adding.
Another way some people might look at it is to think of someone telling you that you no longer owe them any money you borrowed. By taking away your debt (subtracting a negative), they have given you a gift (adding a positive).