Adding and Subtracting Negatives in Integers

Understanding how to add and subtract negative numbers is crucial for solving problems in arithmetic, algebra, and real-life scenarios like banking or measuring temperature changes. Mastery of this concept is important for school assessments, competitive exams like JEE and NEET, and for making sense of everyday mathematics. At Vedantu, we break down the rules for adding and subtracting negatives so you can learn with confidence.

What Are Negative Numbers?

Negative numbers are values less than zero, represented with a minus sign (-). On a number line, negative numbers are placed to the left of zero, while positive numbers are to the right. Situations such as owing money, dropping temperatures, or going below sea level all make use of negative numbers. It’s key to understand how they work before adding or subtracting them.

Rules for Adding and Subtracting Negatives

Here are some straightforward rules for working with positive and negative numbers:

• Adding a negative number: This is the same as subtraction. For example, \(6 + (-3) = 6 - 3 = 3\).
• Subtracting a negative number: Subtracting a negative is the same as adding. For example, \(6 - (-3) = 6 + 3 = 9\).
• Adding two negatives: Add their absolute values and keep the negative sign. For example, \((-2) + (-3) = -5\).
• Subtracting a positive from a negative: Move further left on the number line. For example, \(-5 - 3 = -8\).
• If the signs are different (one positive, one negative): Subtract the smaller absolute value from the larger, and keep the sign of the larger number. Example: \(7 + (-10) = -3\).

Worked Examples: Step-by-Step Solutions

Let’s practice some examples to see these rules in action:

1. Example 1: \(8 + (–3)\)
   • Adding a negative is the same as subtracting.
   • \(8 – 3 = 5\)
2. Example 2: \(–6 + (–4)\)
   • Both numbers are negative; add absolute values and keep the sign.
   • \(6 + 4 = 10\), so \(–10\)
3. Example 3: \(5 – (–2)\)
   • Subtracting a negative is the same as adding.
   • \(5 + 2 = 7\)
4. Example 4: \(–8 – 5\)
   • Subtracting a positive from a negative moves us further left on the number line.
   • \(–8 – 5 = –13\)
5. Example 5: \(–3 + 7\)
   • Signs are different; subtract and keep the sign of the larger absolute value (7 is larger and positive).
   • \(7 – 3 = 4\), so \(+4\)

Practice Problems

• \(4 + (–9) = ?\)
• \(–12 + (–8) = ?\)
• \(7 – (–5) = ?\)
• \(–10 – 6 = ?\)
• \(–2 + 15 = ?\)
• \(3 – 7 = ?\)
• \(–9 + (–2) = ?\)
• \(8 – (–4) = ?\)

Try to solve each using the rules above. You can check your work on the Adding and Subtracting Integers page on Vedantu for more solutions and worksheets.

Common Mistakes to Avoid

• Confusing subtracting a negative with basic subtraction. Remember: \(– (–) = +\)
• Forgetting to keep the correct sign after subtraction—always check which is the larger (by absolute value) and use its sign for the answer.
• Mistaking adding a negative for subtraction—this is a common source of error in exams.
• Not using the number line to visualize the operation, which can help when in doubt.

Real-World Applications

Adding and subtracting negative numbers shows up everywhere: calculating bank balances (deposits and withdrawals), measuring temperature changes (up and down the scale), in sports (score differences), and tracking elevations relative to sea level. Understanding these operations is vital for solving real-world problems, not just those found in textbooks.

At Vedantu, we offer easy-to-follow lessons and interactive exercises, so you can learn the rules for adding and subtracting negatives step by step. For related topics, you can explore Integers, Integer Rules, or broaden your knowledge with Operations on Rational Numbers.

To summarize, mastering adding and subtracting negatives means knowing the sign rules, avoiding common mistakes, and recognizing how these concepts impact your daily life and exam performance. Practice regularly to become confident in handling positive and negative numbers in any situation.