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### Course: 7th grade (Illustrative Mathematics)>Unit 5

Lesson 5: Lesson 5: Representing subtraction

# 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.
• why do you need votes?
• It's
1. So people don't repeat posts, instead upvoting them, letting people know that they agree.
• 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.
• so two negatives make a positive
• It depends on the operation.
Adding two negatives always makes a negative.
Subtracting two negatives could make zero, a negative, or a positive depending on how the two negatives compare to each other.
Multiplying or dividing two negatives always makes a positive.