Solve: (-302)-(-7.6) Negative Number Subtraction with Decimals

Subtraction Rules with Double Negatives

Solve the following expression:

(302)(7.6)= (-302)-(-7.6)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Negative times negative always equals positive, so we add
00:11 We'll use long subtraction to calculate addition with a negative number
00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following expression:

(302)(7.6)= (-302)-(-7.6)=

2

Step-by-step solution

Note the following rule:

(x)=+x -(-x)=+x

Now let's write the exercise in the appropriate form:

302+7.6= -302+7.6=

We'll locate -302 on the number line and go right 7.6 steps:

-302-302-302+7.6

Note that our result will be negative.

Let's solve the exercise carefully by adding a decimal point to the number 302 to avoid confusion during the solution:

302.07.6294.4 302.0\\-7.6\\294.4

Note that the final answer is negative, meaning:

294.4 -294.4

3

Final Answer

294.4 -294.4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Subtracting a negative equals adding the positive
  • Technique: Rewrite (-302)-(-7.6) as -302+7.6
  • Check: Start at -302, move right 7.6 to reach -294.4 ✓

Common Mistakes

Avoid these frequent errors
  • Treating double negatives as regular subtraction
    Don't calculate (-302)-(-7.6) as -302-7.6 = -309.6! This ignores the rule that subtracting a negative means adding. Always convert --(-7.6) to +7.6 first.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why does subtracting a negative become addition?

+

Think of it as "removing a debt"! If you owe someone 7.60(negative)andthatdebtistakenaway,youreactually7.60 (negative) and that debt is taken away, you're actually 7.60 better off (positive). So subtracting negative 7.6 adds 7.6.

How do I remember the double negative rule?

+

Use the phrase "minus a minus is plus"! The two negative signs cancel each other out, just like in grammar where "I don't know nothing" means "I know something."

Do I need to line up decimal places when adding?

+

Yes! When calculating -302 + 7.6, think of it as -302.0 + 7.6. Line up the decimal points: you're adding 7.6 to -302.0, which gives you -294.4.

How can I visualize this on a number line?

+

Start at -302 on the number line. Since you're adding 7.6 (positive), move 7.6 units to the right. You'll land at -294.4, which is closer to zero than where you started.

What if the numbers were reversed: (-7.6)-(-302)?

+

Apply the same rule: -7.6 + 302 = 294.4 (positive this time!). The order matters for the final sign - the larger absolute value determines whether your answer is positive or negative.

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