What is Combining Like Terms?

S3-SA1-0516

Grade Level:

Class 6

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

Definition

What is it?

Combining Like Terms means grouping and adding or subtracting terms that have the exact same variable part. It simplifies algebraic expressions by making them shorter and easier to understand. Think of it like sorting similar items together.

Simple Example

Quick Example

Imagine you have 3 cricket bats and your friend gives you 2 more cricket bats. You now have a total of 5 cricket bats. Here, 'cricket bats' is the 'like term', and you combined 3 'cricket bats' with 2 'cricket bats' to get 5 'cricket bats'.

Worked Example

Step-by-Step

Let's simplify the expression: 4x + 7y - 2x + 3y
---Step 1: Identify the 'like terms'. Look for terms with the same variable (like 'x' or 'y').
Like terms are: (4x and -2x) and (7y and 3y).
---Step 2: Group the like terms together.
(4x - 2x) + (7y + 3y)
---Step 3: Combine the coefficients (the numbers in front of the variables) for each group.
For 'x' terms: 4 - 2 = 2. So, 4x - 2x becomes 2x.
---Step 4: Combine the coefficients for the 'y' terms.
For 'y' terms: 7 + 3 = 10. So, 7y + 3y becomes 10y.
---Step 5: Write the simplified expression.
2x + 10y
Answer: The simplified expression is 2x + 10y.

Why It Matters

Combining like terms is a fundamental skill in algebra, essential for solving complex problems in fields like Data Science and Engineering. Scientists use it to simplify equations in Physics, and software developers use it to optimize code in Computer Science, making calculations faster and more efficient.

Common Mistakes

MISTAKE: Adding or subtracting terms with different variables (e.g., adding 3x and 2y) | CORRECTION: Only combine terms that have the exact same variable part. You cannot combine apples and oranges.

MISTAKE: Forgetting the sign (positive or negative) in front of a term when moving it | CORRECTION: Always take the sign with the term. For example, in 5x - 2y + 3x, the term is '-2y', not just '2y'.

MISTAKE: Not recognizing that a variable without a number in front has a coefficient of 1 (e.g., thinking 'x' has no coefficient) | CORRECTION: Remember that 'x' is the same as '1x' and '-y' is the same as '-1y'.

Practice Questions

Try It Yourself

QUESTION: Simplify: 5a + 3a | ANSWER: 8a

QUESTION: Simplify: 9p - 4p + 2q | ANSWER: 5p + 2q

QUESTION: Your mom bought 6 packets of atta and 4 packets of rice. Your dad later bought 2 more packets of atta and 1 packet of rice. Write an expression for the total items and then simplify it. (Let 'a' be atta and 'r' be rice) | ANSWER: Expression: 6a + 4r + 2a + 1r. Simplified: 8a + 5r

MCQ

Quick Quiz

Which of these expressions is correctly simplified?

3x + 2y = 5xy

7a - 3a = 4a

4p + 5 = 9p

6m + 2n = 8mn

The Correct Answer Is:

Option B is correct because 7a and 3a are like terms, so their coefficients (7 and 3) can be subtracted to get 4a. The other options incorrectly combine unlike terms.

Real World Connection

In the Real World

When a shopkeeper calculates total sales for the day, they combine 'like terms'. For example, if they sold 10 'chai' and 5 'samosas' in the morning, and 7 'chai' and 3 'samosas' in the evening, they combine the 'chai' sales (10+7=17 chai) and 'samosa' sales (5+3=8 samosas) separately to get the total. This is exactly what combining like terms does!

Key Vocabulary

Key Terms

TERM: a single number or variable, or numbers and variables multiplied together, separated by + or - signs. E.g., in 3x + 5, '3x' is a term and '5' is a term. | VARIABLE: A letter (like x, y, a) that represents an unknown number. | COEFFICIENT: The number multiplied by a variable in a term. E.g., in 5x, '5' is the coefficient. | LIKE TERMS: Terms that have the exact same variable part (including exponents). E.g., 3x and 7x are like terms; 2y and 5y are like terms.

What's Next

What to Learn Next

Great job learning to combine like terms! Next, you can explore 'Solving One-Step Equations'. This concept builds directly on combining like terms, as you'll often need to simplify expressions before finding the value of a variable.