Adding and Subtracting Like Terms

Adding and subtracting like terms is the same as adding and subtracting of numbers, i.e., natural numbers, whole numbers and integers.

So, the sum and the difference of several like terms is another like term whose coefficient is the sum and the difference of the coefficient of several like terms.


Examples of adding like terms:

1. Add 7mn, -9mn, -8mn

The sum will be another like term with coefficient 7 + (-9) + (-8) = -10

Therefore, 7mn + (-9mn) + (-8mn) = -10mn


2. Sum of 5xyz, -7xyz, -9xyz and 10xyz

The sum will be another like term with coefficient 5 + (-7) + (-9) + (10) = -1

Therefore, 5xyz + (-7xyz) + (-9xyz) + 10xyz = -1xyz

Examples of subtracting like terms:

1. Subtract 12xy from 27xy

The difference will be another like term with coefficient 27 – 12 = 15

Therefore, 27xy – 12xy = 15xy


2. Difference of 15ab from 7ab

The difference will be another like term with coefficient 7 – 15 = -8

Therefore, 7ab – 15ab = -8ab


Examples of combining addition and subtraction of like terms:

1. Combine the like terms and then simplify 7a – 3b + 4ab + 9b – 6ab – 3a

= 7a – 3a – 3b + 9b + 4ab – 6ab         arrange the like terms

= (7 - 3)a + (-3 + 9)b + (4 - 6)ab       combine like terms

= (4)a + (6)b + (-2)ab                      simplify

= 4a + 6b - 2ab  


2. Combine the like terms and simplify -5z5 + 2 – 3z3 + 8z + 7z3 – 4z5 – z.

= -5z5 – 4z5 – 3z3 + 7z3 + 8z – z + 2              arrange the like terms.

= (-5 – 4)z5 + (-3 + 7)z3 + (8 - 1)z + 2           combine like terms.

= (-9)z5 + (4)z3 + (7)z + 2                            simplify.

= -9z5 + 4z3 + 7z + 2

While adding and subtracting like terms we collect different groups of like terms, then we find the sum and the difference of like terms in each group.

Terms

Like and Unlike Terms

Like Terms

Addition of Like Terms

Subtraction of Like Terms

Adding and Subtracting Like Terms

Unlike Terms

Addition of Unlike Terms

Subtraction of Unlike Terms









Algebra Page

6th Grade Page

From Adding and Subtracting Like Terms to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Counting Numbers from 1 to 50 | Match the Number | Missing Numbers

    Apr 04, 25 03:46 PM

    Math Coloring Pages on Counting Number Oredr
    In counting numbers from 1 to 50, recognize the numbers, count and then join the numbers in the correct number order. Here we mainly need eye-hand coordination to draw the picture and maintain the num

    Read More

  2. Counting Eleven to Twenty with Numbers and Words |Numbers from 11 - 20

    Apr 04, 25 03:21 PM

    Counting eleven to twenty with numbers and words are explained below. One ten and one more is eleven. Eleven comes after ten. One ten and two more is twelve. Twelve comes after eleven.

    Read More

  3. 5th Grade BODMAS Rule Worksheet | PEMDAS | Order of operations|Answers

    Apr 03, 25 03:11 PM

    5th Grade BODMAS Rule Worksheet
    In 5th Grade BODMAS Rule Worksheet you will get different types of problems on mathematical expressions involving different operations, mathematical expression with 'brackets' and 'of' and simplifying…

    Read More

  4. Worksheet on Simplification | Simplify Expressions | BODMAS Questions

    Apr 03, 25 02:58 PM

    Worksheet on Simplification
    In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet

    Read More

  5. Divisible by 2 Video |Test of Divisibility by 2 Trick| Rules| Examples

    Apr 03, 25 10:25 AM

    Divisible by 2
    A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

    Read More

Terms - Worksheets

Worksheet on Like and Unlike Terms

Worksheet on Addition of Like Terms

Worksheet on Subtraction of Like Terms

Worksheet on Adding and Subtracting Like Terms

Worksheet on Combining Like Terms

Worksheet on Addition of Unlike Terms

Worksheet on Subtraction of Unlike Terms