Skip to content Skip to navigation

Connexions

You are here: Home » Content » Algebraic Expressions and Equations: Combining Like Terms Using Addition and Subtraction

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • CCQ display tagshide tags

    This module is included in aLens by: Community College of QatarAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Used as supplemental materials for developmental math courses."

    Click the "CCQ" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

  • College Open Textbooks display tagshide tags

    This module is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook CollaborativeAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Reviewer's Comments: 'I would recommend this text for a basic math course for students moving on to elementary algebra. The information in most chapters is useful, very clear, and easily […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Fundamentals of Mathematics"

    Comments:

    "Fundamentals of Mathematics is a work text that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • UniqU content

    This module is included inLens: UniqU's lens
    By: UniqU, LLCAs a part of collection: "Fundamentals of Mathematics"

    Click the "UniqU content" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Algebraic Expressions and Equations: Combining Like Terms Using Addition and Subtraction

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to combine like terms using addition and subtraction. By the end of the module students should be able to combine like terms in an algebraic expression.

Section Overview

  • Combining Like Terms

Combining Like Terms

From our examination of terms in (Reference), we know that like terms are terms in which the variable parts are identical. Like terms is an appropriate name since terms with identical variable parts and different numerical coefficients represent different amounts of the same quantity. When we are dealing with quantities of the same type, we may combine them using addition and subtraction.

Simplifying an Algebraic Expression

An algebraic expression may be simplified by combining like terms.

This concept is illustrated in the following examples.

  1. 8 records + 5 records = 13 records.8 records + 5 records = 13 records. size 12{"8 records "+" 5 records "=" 13 records" "." } {}

    Eight and 5 of the same type give 13 of that type. We have combined quantities of the same type.

  2. 8 records + 5 records + 3 tapes = 13 records + 3 tapes.8 records + 5 records + 3 tapes = 13 records + 3 tapes. size 12{"8 records "+" 5 records "+" 3 tapes "=" 13 records "+" 3 tapes" "." } {}

    Eight and 5 of the same type give 13 of that type. Thus, we have 13 of one type and 3 of another type. We have combined only quantities of the same type.

  3. Suppose we let the letter x x represent "record." Then, 8 x+ 5 x = 13 x8 x+ 5 x = 13 x size 12{"8x "+" 5x "=" 13x"} {}. The terms 8 x8 x size 12{"8x"} {} and 5 x5 x size 12{"5x"} {} are like terms. So, 8 and 5 of the same type give 13 of that type. We have combined like terms.
  4. Suppose we let the letter x x represent "record" and y y represent "tape." Then,

    8x + 5x + 3y = 13x + 5y 8x + 5x + 3y = 13x + 5y size 12{"8x "+" 5x "+" 6y "=" 13x "+" 5y"} {}

    We have combined only the like terms.

After observing the problems in these examples, we can suggest a method for simplifying an algebraic expression by combining like terms.

Combining Like Terms

Like terms may be combined by adding or subtracting their coefficients and affixing the result to the common variable.

Sample Set A

Simplify each expression by combining like terms.

Example 1

2m+6m-4m2m+6m-4m. All three terms are alike. Combine their coefficients and affix this result to mm: 2+6-4=42+6-4=4.

Thus, 2m+6m-4m=4m2m+6m-4m=4m .

Example 2

5x+2y−9y.5x+2y−9y. size 12{5x+2y-9y "." } {} The terms 2y2y size 12{2y} {} and −9y−9y size 12{-9y} {} are like terms. Combine their coefficients: 2−9= -72−9= -7 size 12{2-9"=-"7} {}.

Thus, 5x+2y−9y=5x−7y5x+2y−9y=5x−7y size 12{5x+2y-9y=5x-7y} {} .

Example 3

- 3a+2b−5a+a+6b. - 3a+2b−5a+a+6b. size 12{-3a+2b-5a+a+6b "." } {} The like terms are

- 3a, - 5a, a ︸ - 3-5+1=- 7 - 7a - 3a, - 5a, a ︸ - 3-5+1=- 7 - 7a 2b, 6b ︸ 2+6=8 8b 2b, 6b ︸ 2+6=8 8b

Thus, −3a+2b−5a+a+6b= - 7a+8b.−3a+2b−5a+a+6b= - 7a+8b. size 12{-3a+2b-5a+a+6b"=-"7a+8b "." } {}

Example 4

r−2s+7s+3r−4r−5sr−2s+7s+3r−4r−5s size 12{r-2s+7s+3r-4r-5s} {} . The like terms are

Two bracketed lists. The first list is r, 3r, and -4r. Below this is the equation, 1+3-4=0. Below this is the expression, 0r. The second list is -2s, 7s, and -5s. Below this is the equation -2+7-5=0. Below this is the expression, 0s. The results of the two lists can be simplified to 0r + 0s = 0.

Thus, r−2s+7s+3r−4r−5s=0r−2s+7s+3r−4r−5s=0 size 12{r-2s+7s+3r-4r-5s=0} {} .

Practice Set A

Simplify each expression by combining like terms.

Exercise 1

4x+3x+6x4x+3x+6x size 12{4x+3x+6x} {}

Solution

13x13x size 12{"13"x} {}

Exercise 2

5a+8b+6a−2b5a+8b+6a−2b size 12{5a+8b+6a-2b} {}

Solution

11a+6b11a+6b size 12{"11"a+6b} {}

Exercise 3

10m−6n−2n−m+n10m−6n−2n−m+n size 12{"10"m-6n-2n-m+n} {}

Solution

9m−7n9m−7n size 12{9m-7n} {}

Exercise 4

16a+6m+2r−3r−18a+m−7m16a+6m+2r−3r−18a+m−7m size 12{"16"a+6m+2r-3r-"18"a+m-7m} {}

Solution

- 2a−r - 2a−r size 12{-2a-r} {}

Exercise 5

5h−8k+2h−7h+3k+5k5h−8k+2h−7h+3k+5k size 12{5h-8k+2h-7h+3k+5k} {}

Solution

0

Exercises

Simplify each expression by combining like terms.

Exercise 6

4a+7a4a+7a size 12{4a+7a} {}

Solution

11a11a size 12{"11"a} {}

Exercise 7

3m+5m3m+5m size 12{3m+5m} {}

Exercise 8

6h−2h6h−2h size 12{6h-2h} {}

Solution

4h4h size 12{4h} {}

Exercise 9

11k−8k11k−8k size 12{"11"k-8k} {}

Exercise 10

5m+3n−2m5m+3n−2m size 12{5m+3n-2m} {}

Solution

3m+3n3m+3n size 12{3m+3n} {}

Exercise 11

7x−6x+3y7x−6x+3y size 12{7x-6x+3y} {}

Exercise 12

14s+3s−8r+7r14s+3s−8r+7r size 12{"14"s+3s-8r+7r} {}

Solution

17s−r17s−r size 12{"17"s-r} {}

Exercise 13

−5m−3n+2m+6n−5m−3n+2m+6n size 12{-5m-3n+2m+6n} {}

Exercise 14

7h+3a−10k+6a−2h−5k−3k7h+3a−10k+6a−2h−5k−3k size 12{7h+3a-"10"k+6a-2h-5k-3k} {}

Solution

5h+9a−18k5h+9a−18k size 12{5h+9a-"18"k} {}

Exercise 15

4x−8y−3z+x−y−z−3y−2z4x−8y−3z+x−y−z−3y−2z size 12{4x-8y-3z+x-y-z-3y-2z} {}

Exercise 16

11w+3x−6w−5w+8x−11x11w+3x−6w−5w+8x−11x size 12{"11"w+3x-6w-5w+8x-"11"x} {}

Solution

0

Exercise 17

15r−6s+2r+8s−6r−7s−s−2r15r−6s+2r+8s−6r−7s−s−2r size 12{"15"r-6s+2r+8s-6r-7s-s-2r} {}

Exercise 18

∣- 7∣m+∣6∣m+∣−3∣m∣- 7∣m+∣6∣m+∣−3∣m size 12{ lline -7 rline m+ lline 6 rline m+ lline -3 rline m} {}

Solution

16m16m size 12{"16"m} {}

Exercise 19

∣−2∣x+∣−8∣x+∣10∣x∣−2∣x+∣−8∣x+∣10∣x size 12{ lline -2 rline x+ lline -8 rline x+ lline "10" rline x} {}

Exercise 20

- 4+1k+6−3k+12−4h+5+2k - 4+1k+6−3k+12−4h+5+2k size 12{ left (-4+1 right )k+ left (6-3 right )k+ left ("12"-4 right )h+ left (5+2 right )k} {}

Solution

8h+7k8h+7k size 12{8h+7k} {}

Exercise 21

- 5+3a−2+5b−3+8b - 5+3a−2+5b−3+8b size 12{ left (-5+3 right )a- left (2+5 right )b- left (3+8 right )b} {}

Exercise 22

5⋆+2Δ+3Δ-8⋆5⋆+2Δ+3Δ-8⋆

Solution

5Δ-3⋆5Δ-3⋆

Exercise 23

9⊠+10⊞-11⊠-12⊞9⊠+10⊞-11⊠-12⊞

Exercise 24

16x−12y+5x+7−5x−16−3y16x−12y+5x+7−5x−16−3y size 12{"16"x-"12"y+5x+7-5x-"16"-3y} {}

Solution

16x−15y−916x−15y−9 size 12{"16"x-"15"y-9} {}

Exercise 25

−3y+4z−11−3z−2y+5−48−3−3y+4z−11−3z−2y+5−48−3 size 12{-3y+4z-"11"-3z-2y+5-4 left (8-3 right )} {}

Exercises for Review

Exercise 26

((Reference)) Convert 24112411 size 12{ { {"24"} over {"11"} } } {} to a mixed number

Solution

22112211 size 12{2 { {2} over {"11"} } } {}

Exercise 27

((Reference)) Determine the missing numerator: 38=?64.38=?64. size 12{ { {3} over {8} } = { {?} over {"64"} } "." } {}

Exercise 28

((Reference)) Simplify 56−1411256−14112 size 12{ { { { {5} over {6} } - { {1} over {4} } } over { { {1} over {"12"} } } } } {}.

Solution

7

Exercise 29

((Reference)) Convert 516516 size 12{ { {5} over {"16"} } } {} to a percent.

Exercise 30

((Reference)) In the expression 6 k6 k size 12{6k} {}, how many k’s are there?

Solution

6

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks