What is Subtraction of Monomials? | Simple Explanation for Class 6

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What is the Subtraction of Monomials?

Grade Level:

Class 6

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

Definition

What is it?

Subtracting monomials means finding the difference between two single-term algebraic expressions. You can only subtract monomials if they have the exact same variable part (like 'x' or 'y^2'), which means they are 'like terms'. When subtracting, you only work with the numerical coefficients.

Simple Example

Quick Example

Imagine you have 7 cricket bats (7x) and your friend borrows 3 cricket bats (3x). To find out how many bats you have left, you subtract 3x from 7x. You'll be left with 4x bats.

Worked Example

Step-by-Step

Let's subtract 5y from 12y.

STEP 1: Identify the monomials. They are 12y and 5y.
---STEP 2: Check if they are 'like terms'. Both have the variable 'y' raised to the power of 1. Yes, they are like terms.
---STEP 3: Write the subtraction expression: 12y - 5y.
---STEP 4: Subtract the numerical coefficients: 12 - 5.
---STEP 5: Calculate the difference: 12 - 5 = 7.
---STEP 6: Attach the common variable part to the result. So, it becomes 7y.

ANSWER: 12y - 5y = 7y

Why It Matters

Understanding monomial subtraction helps us simplify complex problems in science and technology. Engineers use it to calculate material quantities, and data scientists use it to manage data sets efficiently. It's a foundational skill for careers in AI, Physics, and Computer Science.

Common Mistakes

MISTAKE: Subtracting coefficients of unlike terms (e.g., trying to subtract 3x from 5y). | CORRECTION: You can only subtract monomials if they have the exact same variable part. If they are unlike terms, you just write the expression as is (e.g., 5y - 3x).

MISTAKE: Forgetting to distribute the minus sign when subtracting an expression with multiple terms (though this page is about monomials, students sometimes carry over this mistake from earlier concepts). | CORRECTION: When subtracting a monomial, only its coefficient is affected. For example, 7x - (-2x) becomes 7x + 2x.

MISTAKE: Subtracting the exponents of the variables (e.g., thinking x^3 - x^2 = x^1). | CORRECTION: When subtracting like terms, the variable part (including its exponent) remains exactly the same. Only the numerical coefficients are subtracted.

Practice Questions

Try It Yourself

QUESTION: Subtract 4a from 9a. | ANSWER: 5a

QUESTION: What is the result of 15p^2 - 8p^2? | ANSWER: 7p^2

QUESTION: A shopkeeper had 25k kilos of rice. He sold 13k kilos. How many kilos of rice are left? | ANSWER: 12k kilos

MCQ

Quick Quiz

What is 10m - 3m?

13m

7m^2

The Correct Answer Is:

When subtracting like monomials, we subtract the numerical coefficients (10 - 3 = 7) and keep the variable part (m) the same. So, 10m - 3m = 7m.

Real World Connection

In the Real World

Imagine a farmer in a village who has 50x bags of wheat. If he sells 20x bags to a local merchant, he uses monomial subtraction (50x - 20x = 30x) to quickly figure out he has 30x bags left. This helps him manage his inventory and plan for future sales, much like inventory systems used by big e-commerce companies in India.

Key Vocabulary

Key Terms

MONOMIAL: An algebraic expression with only one term, like 5x or 7y^2 | COEFFICIENT: The numerical part of a monomial, like 5 in 5x | VARIABLE: The letter part of a monomial, like x in 5x | LIKE TERMS: Monomials that have the exact same variable part, like 5x and 3x

What's Next

What to Learn Next

Great job with subtracting monomials! Next, you'll learn about 'Subtraction of Polynomials'. This will build on what you've learned here, as polynomials are just sums or differences of many monomials.