What is Subtracting a Negative Number?

S1-SA1-0766

Grade Level:

Class 5

Maths, Computing, AI, Physics

Definition

What is it?

Subtracting a negative number means you are actually adding its positive opposite. Think of it like removing a debt – when you remove a debt, you become richer. So, 'minus a minus' always turns into a 'plus'.

Simple Example

Quick Example

Imagine your friend owes you 5 rupees, but then they decide to 'subtract' that 'negative debt' of 5 rupees by paying you back. Instead of owing you, they've now effectively given you 5 rupees, so you gain 5 rupees. So, 0 - (-5) becomes 0 + 5 = 5.

Worked Example

Step-by-Step

Let's solve: 10 - (-3)
---Step 1: Identify the operation. We are subtracting a negative number.
---Step 2: Remember the rule: Subtracting a negative number is the same as adding its positive opposite. So, - (-3) becomes + 3.
---Step 3: Rewrite the expression with the new operation: 10 + 3.
---Step 4: Perform the addition: 10 + 3 = 13.
---Answer: 13

Why It Matters

Understanding this concept is key for advanced maths, especially when dealing with equations and graphs. It's used by software engineers to write code, by data scientists to analyze complex information, and even in physics to calculate forces and directions. It's a fundamental building block for many exciting careers!

Common Mistakes

MISTAKE: Students often think 5 - (-2) is the same as 5 - 2 and get 3. | CORRECTION: Remember 'minus a minus is a plus'. So, 5 - (-2) = 5 + 2 = 7.

MISTAKE: Forgetting to change the sign of the number being subtracted. For example, doing -4 - (-3) as -4 - 3 = -7. | CORRECTION: The minus sign outside the bracket changes the sign inside. So, -4 - (-3) = -4 + 3 = -1.

MISTAKE: Confusing - (-x) with + (-x). For example, thinking 7 + (-2) is 7 + 2. | CORRECTION: 7 + (-2) is 7 - 2 = 5. Only 'minus a minus' becomes a plus. 'Plus a minus' remains a minus.

Practice Questions

Try It Yourself

QUESTION: What is 8 - (-5)? | ANSWER: 13

QUESTION: Solve: -6 - (-4) | ANSWER: -2

QUESTION: A submarine was 100 meters below sea level (-100m). It then 'subtracted' a 'negative' dive of 20 meters (-20m). What is its new depth? | ANSWER: -80 meters (because -100 - (-20) = -100 + 20 = -80)

MCQ

Quick Quiz

Which of the following expressions is equal to 12?

10 - 2

10 - (-2)

10 + (-2)

2 - 10

The Correct Answer Is:

Option B, 10 - (-2), correctly applies the rule 'minus a minus is a plus', making it 10 + 2 = 12. The other options result in 8, 8, and -8 respectively.

Real World Connection

In the Real World

Imagine managing your mobile data. If you have 5 GB left, and your plan 'subtracts' a 'negative' data deduction (like a bonus you were accidentally charged for), it means you gain that data back. Or, in a cricket match, if a team's score is 150, and a penalty of -10 runs (a negative deduction) is removed, their score effectively increases: 150 - (-10) = 160.

Key Vocabulary

Key Terms

NEGATIVE NUMBER: A number less than zero, like -1, -5, -100 | SUBTRACT: To take away one quantity from another | OPPOSITE: The number that is the same distance from zero on the number line but in the opposite direction (e.g., the opposite of -5 is 5) | EXPRESSION: A mathematical statement that contains numbers and operations, but no equals sign

What's Next

What to Learn Next

Great job mastering this! Next, you can explore 'Multiplying and Dividing Negative Numbers'. This will build on your understanding of how positive and negative signs interact, preparing you for more complex algebra and problem-solving.