What is Adding a Negative Number?

S1-SA1-0765

Grade Level:

Class 5

Maths, Computing, AI, Physics, Finance

Definition

What is it?

Adding a negative number means you are actually taking away from the first number. Think of it like moving backwards on a number line. Instead of making the number bigger, it makes it smaller.

Simple Example

Quick Example

Imagine you have 10 rupees in your piggy bank. You owe your friend 3 rupees (this is like having -3 rupees). When you 'add' this debt to your money, you actually pay your friend. So, 10 + (-3) means you now have 7 rupees left.

Worked Example

Step-by-Step

Let's calculate: 8 + (-5)

Step 1: Understand that adding a negative number is the same as subtracting a positive number. So, 8 + (-5) is the same as 8 - 5.
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Step 2: Start with the first number, which is 8.
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Step 3: Subtract the second number (which is 5) from the first number (8).
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Step 4: 8 - 5 = 3.
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Answer: 8 + (-5) = 3

Why It Matters

Understanding negative numbers is crucial in many fields. In finance, it helps track profits and losses. In physics, it describes direction, like movement up or down. Even in computing, it's used for data storage and calculations, opening doors to careers in data science and engineering.

Common Mistakes

MISTAKE: Thinking adding a negative number always results in a positive number. | CORRECTION: The result can be positive, negative, or zero, depending on the initial numbers. If the negative number is 'bigger' (larger absolute value) than the positive number you're adding it to, the answer will be negative.

MISTAKE: Confusing adding a negative number with subtracting a negative number. | CORRECTION: Adding a negative number means you subtract. Subtracting a negative number means you add (two negatives make a positive).

MISTAKE: Forgetting to put brackets around the negative number when writing the sum. | CORRECTION: Always use brackets, like 5 + (-2), to clearly show you are adding a negative number and not subtracting.

Practice Questions

Try It Yourself

QUESTION: What is 7 + (-4)? | ANSWER: 3

QUESTION: Your cricket team scored 15 runs, but then lost 6 runs due to a penalty. What is your team's score now? (Write as an addition problem) | ANSWER: 15 + (-6) = 9 runs

QUESTION: The temperature in Shimla was 2 degrees Celsius. Overnight, it dropped by 5 degrees. What is the new temperature? | ANSWER: 2 + (-5) = -3 degrees Celsius

MCQ

Quick Quiz

Which statement is true for 12 + (-7)?

It is the same as 12 + 7

It is the same as 12 - 7

The answer is -5

The answer is 19

The Correct Answer Is:

Adding a negative number is the same as subtracting the positive version of that number. So, 12 + (-7) is equivalent to 12 - 7, which equals 5.

Real World Connection

In the Real World

When you check your mobile phone's data usage, if you have a 2GB pack and use 500MB, you are effectively adding -500MB to your remaining data. Similarly, in a game, if you gain points but then lose some for a mistake, you're adding negative points to your score.

Key Vocabulary

Key Terms

NEGATIVE NUMBER: A number less than zero, like -1, -2, -3 | POSITIVE NUMBER: A number greater than zero, like 1, 2, 3 | NUMBER LINE: A line on which numbers are marked at regular intervals | ABSOLUTE VALUE: The distance of a number from zero, always positive (e.g., the absolute value of -5 is 5)

What's Next

What to Learn Next

Now that you understand adding negative numbers, you can explore subtracting negative numbers. This will help you master all operations with positive and negative integers, which is essential for more advanced algebra.