Adding And Subtracting Integers Sample Problems

Adding and Subtracting Integers Sample Problems

Introduction

Learning how to add and subtract integers is a foundational skill in mathematics that opens the door to more complex topics such as algebra, geometry, and data analysis. This article provides a clear, step‑by‑step guide to mastering integer operations, followed by a series of sample problems that illustrate each concept. By the end of the reading, you will be able to solve real‑world scenarios involving positive and negative numbers with confidence The details matter here..

Understanding Integers

What Are Integers?

Integers are whole numbers that include positive numbers, zero, and negative numbers. They are represented on the number line without fractional parts.

• Positive integers: 1, 2, 3, …
• Zero: 0
• Negative integers: -1, -2, -3, …

Why Integers Matter

Integers appear in everyday situations: tracking temperature changes, balancing a bank account, counting steps, or measuring elevation. Mastering addition and subtraction with integers equips you to handle these practical contexts accurately.

Adding Integers

Core Rules

1. Same Sign – When both numbers are positive or both are negative, add their absolute values and keep the common sign.

   • Example: 5 + 3 = 8 (both positive)
   • Example: -4 + -7 = -11 (both negative)

2. Different Signs – Subtract the smaller absolute value from the larger absolute value and assign the sign of the number with the larger absolute value.

   • Example: 6 + -2 = 4 (positive sign because 6 > 2)
   • Example: -9 + 4 = -5 (negative sign because |-9| > 4)

Step‑by‑Step Procedure

1. Identify the signs of the integers.
2. If the signs are the same, add the absolute values.
3. If the signs differ, subtract the smaller absolute value from the larger one.
4. Attach the appropriate sign to the result.

Visual Aid

Imagine a number line: moving right for positive numbers, left for negative numbers. Adding a positive integer means moving right; adding a negative integer means moving left.

Subtracting Integers

Core Rule

Subtracting an integer is equivalent to adding its opposite.

• a - b  =  a + (-b)

Thus, the same sign rules used for addition apply after converting subtraction into addition.

Step‑by‑Step Procedure

1. Change the subtraction sign to addition by flipping the sign of the second integer.
2. Follow the adding integers rules described above.

Example

• 7 - 3 = 7 + (-3) → signs differ → subtract absolute values (7 - 3) = 4, keep the positive sign → 4.
• -5 - (-2) = -5 + 2 → signs differ → subtract (5 - 2) = 3, keep the sign of the larger absolute value (-5) → -3.

Sample Problems

Below are 15 sample problems arranged from basic to advanced, each accompanied by a solution Not complicated — just consistent..

Basic Level

1. 5 + (-3)

   • Different signs → subtract (5 - 3) = 2, positive sign → 2.

2. -8 + (-2)

   • Same signs → add absolute values (8 + 2) = 10, keep negative → -10.

3. 12 - 5

   • Convert to 12 + (-5) → different signs → subtract (12 - 5) = 7, positive → 7.

4. -15 - (-6)

   • Becomes -15 + 6 → different signs → subtract (15 - 6) = 9, sign of larger absolute value (-15) → -9.

Intermediate Level

5. 23 + -9

   • Different signs → subtract (23 - 9) = 14, positive → 14.

6. -4 + 7

   • Different signs → subtract (7 - 4) = 3, sign of larger absolute value (7) → 3.

7. -10 - 12

   • Convert to -10 + (-12) → same signs → add (10 + 12) = 22, keep negative → -22.

8. 15 - (-8)

   • Becomes 15 + 8 → same signs → add (15 + 8) = 23, positive → 23.

9. -3 - (-7)

   • Becomes -3 + 7 → different signs → subtract (7 - 3) = 4, sign of larger absolute value (7) → 4.

Advanced Level

10. -50 + 30 - 10

    • First, -50 + 30 = -20 (different signs, keep negative).
    • Then -20 - 10 = -20 + (-10) → same signs → add (20 + 10) = 30, keep negative → -30.

11. 0 - (-15) + 5

    • 0 - (-15) = 0 + 15 = 15.
    • 15 + 5 = 20 → 20.

12. -8 + 12 - 5 + -3

    • Combine positives: 12 - 5 = 7.
    • Combine negatives: -8 + -3 = -11.
    • Add results: 7 + (-11) = -4 → -4.

13. 25 - (-30) + -15

    • 25 - (-30) = 25 + 30 = 55.
    • 55 + (-15) = 40 → 40.

14. -100 + 50 - 25 + 5

    • -100 + 50 = -50.
    • -50 - 25 = -