Good day every one, in this post, i will teach you how to group terms in algebraic expression, this kind of branch of mathematics deals with numbers together with letters or separate into their terms. i like algebra because is all about coefficient, its select and sort things were they belong to.
Now, we have to look at some facts....
In arithmetic, 3 x 4 is a short way of writing 4 + 4 + 4 that is 4 in three places. Similarly in algebra, 3 x a is short for
(a + a + a ) that is ( a )in 3 places, that's funny,
𝑥
We say 3a = 3 x a
= a + a + a
Exercises
Write the following in the shortest possible way.
1. a + a + a
2. y + y + y + y
3. b + b + b + b +b
4 .m + m + m + m +m + m
Solution
1. a + a + a
= 3 x a
= 3a
2. y + y + y + y
= 4 x y
= 4y
3. b + b + b + b +b
= 5 x b
= 5b
5. m + m + m + m +m + m
= 6 x m
= 6m
I belief you understand that fundamental expression of the above exercises. But note, the difference between 12 in arithmetic and 5b in algebra. 12 means 1 ten and 2 units as in 10 + 2 its does not mean 1 x 2 and 5b means 5 x b..
Another important thing you must know in algebra is what is coefficient, coefficient is any number attached to a letter especially in algebraic expression, i mean...
In 3p , 3 the coefficient of p...
In 𝑥 , there is only one 𝑥 this means 𝑥 is the same as 1𝑥 , the coefficient of 𝑥 is 1..
1
1n ------- y , 1/3 is the coefficient of y which means..
3
1 y
-------- x --------
3 1
y
---------
3
Note:
1 x 𝑥 = 𝑥
not
1𝑥
Another thing to know in algebraic expression
Grouping Positive and Negative terms
Expressions such as 3𝑥 , 𝑥 , 7𝑥 , 12𝑥 , 1/2𝑥 are all terms in 𝑥. We can add terms in 𝑥 together.
Example
1. 2a + 3a
= 2a + 3a
= 5a
2. p + 4p
= p + 4p
= 5p
3. 4m - 3 m
= m ( not 1m)
W can simplify expressions that contain many terms. For example, the expression
3a - 8a + 5a + 9a - 2a
means add 3a ,5a and 9 together. Take away 8a and 2a. This gives 17a , take away 10a the result is 7a
3a - 8a + 5a + 9a - 2a
= (3a + 5a + 9a) - 8a - 2a
= 17a - 10a
= 7a
Can you see the way i grouped numbers with the same side, i applied the ruled of bodmas, then remember - 8a - 2a = - 10a.... we call this grouping positive and negative terms, it is said to be the best way of simplifying big expressions.
Another Example
Simplify 3m- 8m- 2m + 16 - 4m
3m- 8m- 2m + 16 - 4m
= (3m + 16 )- 8m- 2m -4m
= 19m - 10m -4m
=19m - 14m
=5m
Grouping like and unlike terms
This branch teach you how to recognized things that have the same surface, domains, color, smell etc. in real life . what is the sum of 3cups of rice and 4 cup of rice, is 7 cups..
4r + 3r = 7r
In other way, What is the sum of 2cups of rice and 3 cups of beans, you can see there is mixture, we cant add them. Similarly in algebra, it is impossible to simplify, this means
2r + 3y nothing , they are not the same kind....In real life we can separate things to suite its standard.
Always Remember
4r + 3r are like terms
While
2r + 3y are unlike terms
Now lets group like and unlike terms
3𝑥 + 4y + 6y +2𝑥
3𝑥 + 4y + 6y +2𝑥
= (3𝑥 +2𝑥 )+ (6y +4y)
= 5𝑥 + 10y
First of all, look at the question and point out 𝑥 terms and y terms aside, to make it professional, put the terms in bracket.
Do Not Forget
5𝑥 + 10y
cant be added....
Another Important Example
7g - 4 - 3g + 11
7g - 4 - 3g + 11
= 7g - 3g + 11 - 4
= 4g + 7
7 has no term......
Now do these
1. 9n- 5n - 3n
2. 𝑥 + 4 + 5𝑥
3. 4a - a + 5b -4b
4. 12𝑥 - 4𝑥 + 3
5. 4t - 6 - 2 + 5t
6. 8y +3 + 2 + y
7. 5c - 9c + 12c - 4
That is end of our todays class on algebraic expressions, please if you have any question, put then in the comments box.
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