What is Adding Like Terms? | Simple Explanation for Class 5

S1-SA5-1183

What is Adding Like Terms (Simple — 2x + 3x = 5x)?

Grade Level:

Class 5

Maths, Computing, AI, Physics, Programming

Definition

What is it?

Adding Like Terms means combining terms that have the exact same variable part. For example, you can add 2 apples and 3 apples to get 5 apples, just like you can add 2x and 3x to get 5x. It helps simplify long expressions.

Simple Example

Quick Example

Imagine you have 2 cricket bats and your friend gives you 3 more cricket bats. How many bats do you have in total? You have 2 bats + 3 bats = 5 bats. Here, 'bats' is like our variable 'x', so 2x + 3x = 5x.

Worked Example

Step-by-Step

Let's simplify: 4y + 7y + 2y

1. Identify the terms: The terms are 4y, 7y, and 2y.
2. Check if they are 'like terms': Yes, all terms have the same variable 'y'. This means we can add their numbers.
3. Add the numbers (coefficients) in front of the 'y's: 4 + 7 + 2
4. Calculate the sum: 4 + 7 = 11, and 11 + 2 = 13.
5. Combine the sum with the variable: 13y

Answer: 4y + 7y + 2y = 13y

Why It Matters

Understanding like terms is crucial for solving equations in Maths and simplifying formulas in Physics. In Computing and AI, this concept helps engineers optimize algorithms and process data efficiently. It's a foundational skill for careers in data science and engineering.

Common Mistakes

MISTAKE: Adding numbers from unlike terms, e.g., 2x + 3y = 5xy | CORRECTION: You cannot add terms with different variables. 2x + 3y remains 2x + 3y.

MISTAKE: Forgetting the variable after adding, e.g., 5a + 4a = 9 | CORRECTION: Always remember to keep the common variable with the sum, so 5a + 4a = 9a.

MISTAKE: Adding the powers of variables, e.g., 2x + 3x = 5x^2 | CORRECTION: When adding like terms, only the coefficients (numbers) are added. The variable and its power remain the same, so 2x + 3x = 5x.

Practice Questions

Try It Yourself

QUESTION: Simplify: 6p + 2p | ANSWER: 8p

QUESTION: Simplify: 10m + 5m - 3m | ANSWER: 12m

QUESTION: A vegetable seller has 7 kg of potatoes (P) and buys 4 kg more. How much potatoes does he have in total? Write it as an algebraic expression. | ANSWER: 7P + 4P = 11P

MCQ

Quick Quiz

Which of these expressions can be simplified by adding like terms?

5a + 3b

4x + 7x

2y + 6z

9m + 2n + 5

The Correct Answer Is:

Option B (4x + 7x) has terms with the same variable 'x', so they are like terms and can be added to get 11x. The other options have different variables or a constant, so they cannot be combined.

Real World Connection

In the Real World

Imagine a shopkeeper tracking their inventory. If they have 5 cartons of biscuits (B) and receive 3 more cartons of biscuits, they use 'adding like terms' to know they now have 8B (8 cartons of biscuits). This simple idea helps businesses manage stock and finances, even in apps like Paytm for tracking expenses.

Key Vocabulary

Key Terms

TERM: Term: A single number, variable, or product of numbers and variables. | TERM: Variable: A letter (like x, y, a) representing an unknown value. | TERM: Coefficient: The number multiplied by a variable in a term (e.g., in 5x, 5 is the coefficient). | TERM: Like Terms: Terms that have the same variable part, including the same power.

What's Next

What to Learn Next

Great job understanding like terms! Next, you can explore 'Subtracting Like Terms' and then 'Adding and Subtracting Unlike Terms'. These concepts will help you simplify even more complex algebraic expressions, preparing you for solving equations.