<< Chapter < Page Chapter >> Page >
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 [link] , 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 . 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 . 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 represent "record." Then, 8 x + 5 x = 13 x size 12{"8x "+" 5x "=" 13x"} {} . The terms 8 x size 12{"8x"} {} and 5 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 represent "record" and y represent "tape." Then,

    8 x + 5 x + 3 y = 13 x + 5 y 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.

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

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Practice set a

Simplify each expression by combining like terms.

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

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

9 m 7 n size 12{9m-7n} {}

Got questions? Get instant answers now!

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

- 2 a r size 12{-2a-r} {}

Got questions? Get instant answers now!

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

0

Got questions? Get instant answers now!

Exercises

Simplify each expression by combining like terms.

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

6 h 2 h size 12{6h-2h} {}

4 h size 12{4h} {}

Got questions? Get instant answers now!

11 k 8 k size 12{"11"k-8k} {}

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

7 x 6 x + 3 y size 12{7x-6x+3y} {}

Got questions? Get instant answers now!

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

17 s r size 12{"17"s-r} {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

0

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

5 + 2 Δ + 3 Δ - 8

5 Δ - 3

Got questions? Get instant answers now!

9 + 10 - 11 - 12

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Exercises for review

( [link] ) Convert 24 11 size 12{ { {"24"} over {"11"} } } {} to a mixed number

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

Got questions? Get instant answers now!

( [link] ) Determine the missing numerator: 3 8 = ? 64 . size 12{ { {3} over {8} } = { {?} over {"64"} } "." } {}

Got questions? Get instant answers now!

( [link] ) Simplify 5 6 1 4 1 12 size 12{ { { { {5} over {6} } - { {1} over {4} } } over { { {1} over {"12"} } } } } {} .

7

Got questions? Get instant answers now!

( [link] ) Convert 5 16 size 12{ { {5} over {"16"} } } {} to a percent.

Got questions? Get instant answers now!

( [link] ) In the expression 6 k size 12{6k} {} , how many k ’s are there?

6

Got questions? Get instant answers now!

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask