INTRO TO ALGEBRA:
The “term”
The basic unit of algebra is a “term”.
6a
-xy
4b2
Nelson Marlborough
Institute of Technology
TE WHARE WANANGA O TE TAU IHU
-0.7p
It has 3 parts:
1. a sign, being positive (+) or negative (-)
2. a number, called ‘the coefficient’
3. a letter, called ‘the variable’
Every term must have a sign. If there isn’t one, assume there is an unwritten positive sign.
Negative signs must always be written.
Terms must have a number. If there isn’t one, assume an unwritten coefficient of ‘one’.
Terms may or may not have a letter. If there is a variable and it has a power above the
variable (eg. 7x3), the power belongs only to the variable.
Practise with the following terms:
Sign (+ or -)
Example
8f
-10r
4xy
½m
-22
Coefficient
Variable(s)
When several basic algebraic units, or terms, are written one after the other, the sign
separates one term from the one before it. Remember that the sign belongs with the term
to its immediate RIGHT.
Put a circle around each term in the following algebraic expressions:

10b – 42de + km

m2n – a – c

-p3 + 16 – ¼ qr

-9y + 3b – 5
Library Learning Centre
LEARNING SUPPORT
Updated 6/02/2016
INTRO TO ALGEBRA:
The “term”
Nelson Marlborough
Institute of Technology
TE WHARE WANANGA O TE TAU IHU
Adding and subtracting in Algebra
This is also referred to as “simplifying terms” or “combining like terms”.
You can only simplify terms with the same variables (meaning, same letters).
B+B
2a + 3a
6y + 8ab
9G2 + 1G
really means 1B + 1B,so the answer is 2B
the answer is 5 variables called ‘a’
since the letters are all different, no simplification!
B + B = 2B
2a + 3a = 5a
6y + 8ab
9G2 + 1G
since only one variable has a power, no simplification!
It is just like adding things in real life.
4 coffees + 3 teas = 4 coffees + 3 teas
4c + 3t = 4c + 3t
4 drinks + 3 drinks = 7 drinks
4d + 3d = 7d
we can’t combine them
simplify, same variables
If any terms are negative, visualise a number line. Start at zero and then count to your
first term, by moving to the right for positive terms and to the left for negative terms. For
the next term, count from this new position and move right or left depending on the sign of
the next term.
Example: - 4z + 1z
Using a number line,
-5 -4 -3 -2 -1
0
1
2
Start at zero and count four to the LEFT:
-5
-4
-3
-2
-1
0
1
2
1
2
From –4 count one to the RIGHT:
-5
-4
-3
-2
-1
0
The answer is -3z.
Practise:
1. –2x + 4x
2. 3b – 7b + b
3. p + 2q + 3p – 3q
4. 9zy + 3zy
5. 12w + 2wz – 2w
6. 3x2 + 1x – 4x2
7. 6s + s3 + 7s2
Library Learning Centre
LEARNING SUPPORT
Updated 6/02/2016