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Multiply and Divide
with Algebra
Nelson Marlborough
Institute of Technology
TE WHARE WANANGA O TE TAU IHU
These two operations are opposites.
63=2
and
3X2=6
How to recognise multiplication

Usually shown by ( ).

And by X.

Often shown by parts of the term sitting next to each other.
“4(2a)” means 4 times 2a.
“5 X 6” means 5 times 6.
“7ab” means 7 times
a times b.

Sometimes shown as a dot

Sometimes with the words “expand”
“7 . 6” means 7 times 6.
“Expand 8(3a)” means 8 times 3a.
How to multiply
You MUST MULTIPLY all parts of the terms
i) Multiply the signs If signs are different … answer is negative (-)
If signs are the same … answer is positive (+)
- 4 X 5 = -20
4 (2) = 8
7 X –2 = -14
-3 X –6 = 18
ii) Multiply the coefficients
2c(3d) = 6cd
3z4y = 12zy
iii) Multiply the variables
12a X 2 = 24a
If the letters are different … sit the letters beside each
other, in alphabetical order
If the letters are the same … add the indices
a X b = ab
f2 X af3 = af5
Practise:
1. –2 X 4y
2. 3b X 7b
3. 3(7de).2
4. 5.2f
5. zy2 X y
6. –2d(6abc)
7. 6s X s3 X 7s2
q X rs = qrs
s X s 2 = s3
8. m(n . n X q)
9. 5 X zy X 4
10. a X a X B X B
Updated 22/06/2017
Multiply and Divide
with Algebra
Nelson Marlborough
Institute of Technology
TE WHARE WANANGA O TE TAU IHU
How to recognise division

Usually shown by the  sign.
“15  3” means 15 divided by 3.

Also shown in fraction form.
“ ½ “ means 1 divided by 2.
How to divide
i) Divide the numbers
This can be done as simple division
If it is fraction form, you have the option of dividing by
simplifying = find a number that will go in both
numerator and denominator evenly.
24a  2 = 12a
-16  8 = -2
4/6 = 42/62 = 2/3
6/12 = 0.5
ii) Divide the variables
Any letter divided by itself is 1, so both become an
unwritten 1 (they disappear; are ‘cancelled out’)
If the letters are the same and have indices … subtract the
indices
ab  a = b
72qrs  rq = 72s
Practise:
1. 5ac / 10abc
2. 2abc / 4b
3. 8mn  2m
4. 4b (k/4)
5. –3r / r
6. –6d  2abc
-cd /d = -c
ab3 / a2 b2 = b/a
7. q3  q2
8. f4  g3
9. 15k / 15k
10. a  a X B
Answers for multiplication
1) –8y 2) 21b2 3) 42de 4) 10f 5) y3z 6) –12abcd 7) 42s6 8) mn2q 9) 20yz
10) a2B2
Answers for division
1) 1/2b = 0.5/b 2) ac/2 = 0.5ac 3) 4n 4) bK 5) –3 6) (–3d)/(abc) 7) q 8) f4g3
9) 1 10) B
Updated 22/06/2017
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