What is Algebraic Sum? | Simple Explanation for Class 6

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What is the Algebraic Sum?

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The algebraic sum is simply the total value you get when you add a series of numbers, where each number can be positive or negative. It means we consider the 'sign' (+ or -) of each number when combining them. It's different from just adding absolute values.

Simple Example

Quick Example

Imagine you have money in your piggy bank. You put in ₹50 (+50), then take out ₹20 (-20) for a snack, and then your aunt gives you ₹10 (+10). The algebraic sum of your money changes would be +50 + (-20) + (+10).

Worked Example

Step-by-Step

Let's find the algebraic sum of the following numbers: -7, +12, -3, +5.

Step 1: Write down all the numbers with their signs: -7, +12, -3, +5.
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Step 2: Group the positive numbers together and the negative numbers together: (+12 + 5) and (-7 - 3).
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Step 3: Add the positive numbers: 12 + 5 = 17.
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Step 4: Add the negative numbers (treating them as absolute values first, then keeping the negative sign): 7 + 3 = 10. So, -7 - 3 becomes -10.
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Step 5: Now, combine the sum of positive numbers and the sum of negative numbers: +17 + (-10).
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Step 6: Perform the final addition: 17 - 10 = 7.
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The algebraic sum is 7.

Why It Matters

Understanding algebraic sums is crucial for many advanced fields like Data Science and Physics, where you deal with quantities that can increase or decrease. Engineers use it to balance forces, and economists use it to calculate profits and losses. It's a foundational skill for problem-solving in real-world scenarios.

Common Mistakes

MISTAKE: Ignoring the negative sign and adding all numbers as positive. E.g., for 5 + (-3), calculating 5 + 3 = 8. | CORRECTION: Always pay attention to the sign. A negative sign means subtraction. So, 5 + (-3) is actually 5 - 3 = 2.

MISTAKE: Getting confused when two negative signs are together. E.g., for 7 - (-2), calculating 7 - 2 = 5. | CORRECTION: Remember the rule: 'minus minus makes plus'. So, 7 - (-2) is 7 + 2 = 9.

MISTAKE: Incorrectly adding/subtracting positive and negative numbers. E.g., for -8 + 3, calculating -11. | CORRECTION: When adding numbers with different signs, subtract the smaller absolute value from the larger absolute value, and keep the sign of the number with the larger absolute value. So, -8 + 3: (8 - 3 = 5), and since 8 is larger and negative, the answer is -5.

Practice Questions

Try It Yourself

QUESTION: What is the algebraic sum of +9, -4, and +2? | ANSWER: 7

QUESTION: Find the algebraic sum of -15, +7, -3, and +10. | ANSWER: -1

QUESTION: A shopkeeper started the day with ₹500. He made sales of ₹250 and ₹180, but also had expenses of ₹100 for electricity and ₹70 for tea. What is his algebraic sum of money change for the day (excluding starting amount)? | ANSWER: ₹260

MCQ

Quick Quiz

Which of the following correctly represents the algebraic sum of -6, +10, and -2?

-18

-2

The Correct Answer Is:

To find the algebraic sum, add the positive numbers: +10. Add the negative numbers: -6 + (-2) = -8. Then combine them: +10 + (-8) = 10 - 8 = +2.

Real World Connection

In the Real World

When you check your bank balance or mobile wallet (like Paytm or Google Pay), the total amount shown is an algebraic sum. Every time you add money (+), it's a positive entry, and every time you spend money (-), it's a negative entry. The app constantly calculates the algebraic sum of all these transactions to show your current balance.

Key Vocabulary

Key Terms

Positive Number: A number greater than zero, usually with a '+' sign or no sign. E.g., 5, +12 | Negative Number: A number less than zero, always with a '-' sign. E.g., -3, -10 | Integer: Whole numbers, including positive numbers, negative numbers, and zero. E.g., -2, 0, 5 | Sign: The '+' or '-' symbol indicating if a number is positive or negative.

What's Next

What to Learn Next

Great job understanding algebraic sums! Next, you can explore 'Addition and Subtraction of Integers' in more detail. This will help you master working with positive and negative numbers even more efficiently, which is super useful for algebra and beyond.