What is the Difference Between Like and Unlike Terms? | Simple Explanation for Class 5

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What is the Difference Between a Like Term and an Unlike Term?

Grade Level:

Class 5

Maths, Computing, AI, Physics

Definition

What is it?

In Maths, terms are parts of an expression separated by '+' or '-' signs. Like terms are terms that have the exact same variables and powers. Unlike terms are terms that have different variables or different powers.

Simple Example

Quick Example

Imagine you are counting fruits in a basket. If you have 3 apples and 5 apples, you can easily add them to get 8 apples. Here, 'apples' is the variable. So, '3 apples' and '5 apples' are like terms because they both have 'apples'. But if you have 3 apples and 5 oranges, you cannot add them directly to say '8 apple-oranges'. '3 apples' and '5 oranges' are unlike terms because they have different fruits (variables).

Worked Example

Step-by-Step

Let's identify like and unlike terms from the following list: 4x, 7y, 2x, 5x^2, 9y, 3x. --- Step 1: Look for terms with 'x' and no power. We have 4x, 2x, 3x. These all have 'x' with a power of 1. So, (4x, 2x, 3x) are like terms. --- Step 2: Look for terms with 'y' and no power. We have 7y, 9y. These both have 'y' with a power of 1. So, (7y, 9y) are like terms. --- Step 3: Look for terms with 'x' and a power of 2. We have 5x^2. This term is different from 4x, 2x, 3x because the power of 'x' is 2, not 1. --- Step 4: Compare terms. 4x and 7y are unlike terms because they have different variables ('x' and 'y'). 4x and 5x^2 are unlike terms because 'x' has different powers (1 and 2). --- Answer: Like terms are (4x, 2x, 3x) and (7y, 9y). All other combinations like (4x, 7y) or (4x, 5x^2) are unlike terms.

Why It Matters

Understanding like and unlike terms is super important for solving algebraic equations, which are used everywhere! From designing rockets for ISRO to building AI programs that understand your voice, knowing how to combine terms helps engineers and scientists simplify complex problems. It's a foundational skill for future innovators.

Common Mistakes

MISTAKE: Students often think 3x and 3x^2 are like terms. | CORRECTION: They are unlike terms because the variable 'x' has different powers (1 and 2). For terms to be 'like', both the variable AND its power must be the same.

MISTAKE: Students sometimes add the coefficients of unlike terms, e.g., 2a + 3b = 5ab. | CORRECTION: You can only add or subtract the coefficients of like terms. For unlike terms like 2a + 3b, the expression remains as it is, you cannot simplify it further.

MISTAKE: Students might ignore the variable completely and just look at the number, thinking 5x and 5y are like terms. | CORRECTION: The variable is crucial. 5x and 5y are unlike terms because 'x' and 'y' are different variables.

Practice Questions

Try It Yourself

QUESTION: Are 6p and 8p like terms or unlike terms? | ANSWER: Like terms

QUESTION: Identify the like terms in the following list: 5m, 2n, 7m^2, 9n, 12m. | ANSWER: (5m, 12m) and (2n, 9n)

QUESTION: Can you simplify the expression: 10 chai + 5 samosa + 3 chai? If yes, what is the simplified expression? | ANSWER: Yes, you can. 13 chai + 5 samosa

MCQ

Quick Quiz

Which pair consists of like terms?

4a and 4b

7x and 7x^2

11y and 5y

2m and 3n

The Correct Answer Is:

Option C (11y and 5y) are like terms because they both have the same variable 'y' with the same power (power of 1). All other options have different variables or different powers.

Real World Connection

In the Real World

Imagine a shopkeeper using a digital billing system like those found in D-Mart or Reliance Fresh. When you buy 3 packets of biscuits and 2 packets of chips, the system treats 'packets of biscuits' and 'packets of chips' as unlike terms. It can add 5 packets of biscuits + 2 packets of biscuits to make 7 packets of biscuits (like terms), but it cannot directly add biscuits and chips together as one item type. It needs to calculate the price for each type separately.

Key Vocabulary

Key Terms

TERM: definition. | TERM: parts of an algebraic expression separated by '+' or '-' signs. | 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). | POWER: the small number written above a variable, telling how many times the variable is multiplied by itself (e.g., in x^2, 2 is the power).

What's Next

What to Learn Next

Great job understanding like and unlike terms! Your next step should be learning 'Adding and Subtracting Algebraic Expressions'. This will teach you how to use what you just learned to simplify complex math problems, which is a key skill for higher classes.