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Simplify The Subtract Expression

Grade 7
Sep 17, 2022

Key Concepts

  • Subtract expressions by using properties
  • Subtract expressions with rational coefficients
  • Subtract more complex expressions

4.7 Subtract expressions 

  • For subtracting two or more algebraic expressions, it requires categorizing the terms in an algebraic expression into two types – like and unlike terms. 
  • Then, taking up the like terms and then subtracting them accordingly.  
  • The other way is to follow the horizontal method that requires writing the expressions to be subtracted below the expression from which it is to be subtracted.  
  • Like terms are placed below each other.  
  • The sign of each term that is to be subtracted is reversed, and then the resulting expression is added normally. 


4.7.1 Subtract expressions by using properties 

Example 1: 

Lenin wants to put a tiled border around their swimming pool; what expression represents the total area of the border? 


Write an expression for the area of the pool only. 


Then write an expression for the area of the pool plus the tiled border. 

Area of the pool l width × length 

16 × (2x +16) ft 

Area of the pool and tiled border: 

20 × (2x +20) ft 


Use properties of operations to subtract the expression 

(Area of the pool + tiles) – (area of the pool) 

=20 (2x +20) – 16(2x +16) 

= 40x – 32x +400 – 256 

=8x +144 

The area of the tiled border is 8x +144 ft2.  

Example 2:  

Simplify the expression using the distributive property. 

4(x – 5) – (x + 3) 


4(x – 5) – (x + 3) 

4.7.2 Subtract expressions with rational coefficients 

Coefficient: The number multiplying by a variable.  

Rational: Can be represented by a fraction – both positive and negative numbers included.  


Subtract (0.95x- 0.04) – (0.99x – 0.13) 


(0.95x- 0.04) – (0.99x – 0.13) 

= 0.95x- 0.04 + (-1) (0.99x – 0.13) 

4.7.3 Subtract more complex expressions 

Complex expressions: 

complex expressions are mathematical expressions that include complex numbers, which contain both a real part and an imaginary part. 

Complex numbers look like binomials in that they have two terms.  

For example, 3 + 4i is a complex number as well as a complex expression. 

Example 1:  

Subtract (16+3.4m+8k) – (6.6m – 6 +3k) 


(16+3.4m+8k) – (6.6m – 6 +3k) 

(16+3.4m+8k) + (-6.6m + 6 -3k) 

=16+3.4m+8k -6.6m + 6 -3k 

=8k – 3k +3.4m – 6.6m +16+6 

=5k -3.2m + 22



  1. Subtract.
    (14x) – (–15 + 7x)
    (4y – 6) – (–y – 3)             
  2. Subtract and simplify.
    1/4  m – 2/8 m + 1/2
  3. Rewrite the expression 16m –(4+12m) without parentheses.
  4. Write an equivalent expression to 6k-(3+2k) without parentheses, then simplify.
  5. A rectangular garden has a walkway around it. Find the area of the walkway

6. Find the difference (6x – 3  ) – (–2x +4  )

7. An expression is shown (0.34 – 0.2) – (0.4n – 0. 15)
Create an equivalent expression without parentheses.

8. Subtract (16+3.5t+4s) – (2.4m- 5 +2s).

9. Subtract (0.75a – 0.03) – (0.78a-0.12).

10. A soap company has two manufacturing plants with a daily production level of 7x + 7 and 4x – 2 items, respectively, where x represents a minimum quantity. The first plant produces how many more items daily than the second plant?

Concept Map

What have we learned:

  • Understand how to subtract the expressions.
  • Understand how to subtract expressions by using properties.
  • Subtract expressions with rational coefficients.
  • Subtract more complex expressions


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