This document provides information about simplifying algebraic expressions. It discusses combining like terms, which have the same variables and exponents, by adding or subtracting their coefficients. It also addresses simplifying expressions with rational coefficients by first writing them with a common denominator to combine like terms. Examples are provided to demonstrate identifying like and unlike terms and performing the steps to simplify expressions.

1. Simplifying
Algebraic
Expressions
G R A D E 7 M A T H E M A T I C S
INSPIRED BY

2. Combining boxes with the same fruit is the same as combining like terms.
Introduction
Suppose you have boxes of apples and oranges for which you do not know
the exact quantities. How will you simply express the total number of fruits?

3. Simplifying Algebraic Expressions with
Integer Coefficients
Today you'll
learn about...
Simplifying Algebraic Expressions with
Rational Coefficients

4. Like and Unlike Terms
2 3 3 5
5
7 k m and 4k m
2 2 3
5
7 t m and 3t m
L I K E T E R M S
3
5 4
– g h and 6h
2
7
Terms that have different variables or have the
same variables but have different exponents
Terms that have exactly the same
combination of variables
8x and -11x 10r and 10s
3 3
-3cv and -7cv
U N L I K E T E R M S
Exponents on variables should be the same to indicate that they are like terms.

5. Like terms
3x + 4y Write as it is.
5x + 4y - 2x
Rearrange and group like terms.
Identify like terms.
Add or subtract the integer coefficients
of like terms, then copy the variable.
Write the unlike term as it is.
Simplifying Expressions
with Integer Coefficients
3
2
1
(5x - 2x) + 4y
S I M P L I F Y : 5 x + 4 y - 2 x

6. Simplifying Expressions
with Rational Coefficients
1.1d + 0.2e
0.5d + 1.4e - 1.2e + 0.6d
(0.5d + 0.6d) + (1.4e - 1.2e)
Rearrange and group like terms.
Identify like terms.
Add or subtract the integer coefficients
of like terms, then copy the variable.
Write the unlike term as it is.
3
2
1
S I M P L I F Y : 0 . 5 D + 1 . 4 e - 1 . 2 e + 0 . 6 d

7. x – x – 3
)
x – 3
5
12
x – x – 3
)
x – 3 – x
2 1
3 4
How can you combine like terms with coefficients that have different denominators?
)
Use the LCM of the
denominators to
rewrite the rational
coefficients as similar
fractions, then add or
subtract.
Simplifying Expressions with
Rational Coefficients
8 3
12 12
)
2 1
3 4
Simplify:

8. y -
H
1 3 1
x + y
1 3
6 5
x -
- y
1 1
10 3
-2x + 3y + 5
- 3x + 3y
3
2
1 2x + 3y - 4x + 5
-2.6x - 10.7y + 13.7y - 0.4x
x + x
M
A
T
1 2 3
2 5 3
What's the Password?
Simplify the algebraic expressions to enter the password.
Put the letter that corresponds to the correct answer.

9. H
x + y
1 3
6 5
x -
- y
1 1
10 3
-2x + 3y + 5
- 3x + 3y
What's the Password?
Simplify the algebraic expressions to enter the password.
Put the letter that corresponds to the correct answer.
3
2x + 3y - 4x + 5
-2.6x - 10.7y + 13.7y - 0.4x
M
A
T
1 2 3
A N S W E R
K E Y
T A
M
2
1
y -
1 3 1
x + x
2 5 3

10. Recap
3
2
1
Let's check your knowledge about simplifying algebraic
expressions. Can you answer these questions?
How do you combine
like terms with different
denominators?
What are like and
unlike terms?
What are the steps in
simplifying algebraic
expressions with rational
coefficients?

11. A N S W E R
K E Y
Let's check your knowledge about simplifying algebraic
expressions. Can you answer these questions?
Recap
How do you combine
like terms with different
denominators?
What are the steps in
simplifying algebraic
expressions with rational
coefficients?
3
2
Like terms have the same
combination of variables.
Unlike terms have different
variables or have the same
variables but have
different exponents.
Use the LCM of the
denominators to rewrite
the rational coefficients
as similar fractions, then
add or subtract.
Identify like terms and
regroup them. Combine like
terms using addition or
subtraction, then write the
unlike terms as it is.
1
What are like and
unlike terms?

12. Challenge
3(5x - 2y) - x + 2y
What is the simplified form of
this algebraic expression?
Share your thoughts in the next session.

13. Reference
Mathspace. “5.0 Algebraic Expressions |
Grade 7 Math | Common Core 7 - 2023
Edition.” Accessed 12 June 2023,
https://mathspace.co/textbooks/syllabu
ses/Syllabus-1156/topics/Topic-
21898/subtopics/Subtopic-279838/

14. 3
2
1
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