Evaluate the Expression: 7.5 + (-9.5) + 5 + (-13.5)

Adding Decimals with Negative Numbers

7.5+(9.5)+5+(13.5)=? 7.5+(-9.5)+5+(-13.5)=\text{?}

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Arrange the signs in the exercise
00:02 The addition of two minuses results in a minus
00:11 The addition of two minuses results in a minus
00:21 Addition and subtraction - solve from left to right

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

7.5+(9.5)+5+(13.5)=? 7.5+(-9.5)+5+(-13.5)=\text{?}

2

Step-by-step solution

Let's begin by expanding the parentheses whilst paying attention to the minus and plus signs, which change accordingly:

+(9.5)=9.5 +(-9.5)=-9.5

+(13)=13 +(-13)=-13

We should obtain the following:

7.59.5+513.5= 7.5-9.5+5-13.5=

Now let's solve the exercise from left to right:

2+513.5= -2+5-13.5=

313.5=10.5 3-13.5=-10.5

3

Final Answer

10.5 -10.5

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Adding a negative number is the same as subtracting
  • Technique: Convert +(9.5) +(-9.5) to 9.5 -9.5 before calculating
  • Check: Verify by grouping positives and negatives: (7.5+5)+(9.5+13.5)=12.523=10.5 (7.5 + 5) + (-9.5 + -13.5) = 12.5 - 23 = -10.5

Common Mistakes

Avoid these frequent errors
  • Ignoring negative signs when adding
    Don't treat +(-9.5) as +9.5 = wrong positive result! The parentheses around negative numbers don't make them positive. Always remember that adding a negative number means subtracting that value.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do we have parentheses around negative numbers?

+

The parentheses help us see clearly that we're adding a negative number. So +(9.5) +(-9.5) means "add negative 9.5" which is the same as subtracting 9.5.

Can I just ignore the plus signs in front of the parentheses?

+

Yes! When you see +(9.5) +(-9.5) , you can simplify it to just 9.5 -9.5 . The plus sign before a negative doesn't change anything.

Is there an easier way to solve this?

+

Try grouping positive and negative numbers separately: (7.5+5)+(9.5+13.5) (7.5 + 5) + (-9.5 + -13.5) . This gives you 12.523=10.5 12.5 - 23 = -10.5 .

How do I know if my final answer should be positive or negative?

+

Look at which group is bigger! Here, the negative numbers (23 -23 ) have a larger absolute value than the positive numbers (12.5 12.5 ), so the answer is negative.

What if I make a calculation error with the decimals?

+

Double-check by adding the whole numbers and decimal parts separately, or use the grouping method as verification. Always line up decimal points when adding!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations