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Making expressions
and
gathering terms
Sweeties
s = number of sweets in the box
If I add 2 how many?
s+2
If I add 4 more, how many?
s+2+4=s+6
If I then eat 10, how many?
s + 6 – 10 = s – 4
How many in 2 boxes?
s + s = 2 x s = 2s
How many in 11 boxes?
11 x s = 11s
How many in 3 boxes, then I eat 7?
3s -7
Algebra - the basics : “Collecting Like Terms”
h = number of biscuits in a packet of HobNobs
r = number of biscuits in a packet of Rich Tea
h
+h
+h
+h
= “6 lots of h” = 6 x h = 6h
r
+r
= 4 x r = 4r
+r
+r
+h
+h
4h
3r
h + 2r
Biscuits
Big tin of biscuits
h + 2r
3h + r
+
3h + r
Biscuits
= 4h + 3r
How many biscuits if :
- 20 in a pack of Hobnobs
- 25 in a pack of Rich Tea?
h = 20
r = 25
Big tin of biscuits
B = 4h + 3r
B = 4 x 20 + 3 x 25
= 80 + 75
= 155
Biscuits
Yum Yum
Algebra - the basics : “Collecting Like Terms - with loose biscuits”
3h + 2r + 5
h + 2r + 3
Altogether
3h + 2r + 5 + h + 2r + 3
=
4h + 4r + 8
Gather number separately
1.
a) Write an expression for a tin a 2 packets of Hobnobs and 2 packets of
Rich Teas
b) Write an expression for a tin with just 5 packets of Hobnobs
c) They are all tipped into a big tin, write an expression for the total
number of biscuits now.
2.
Simplify the following expressions by gathering like terms:
(a) h + 2r + 4h + 3r
(b) 5a + 6b + 3a + 4b
(c) x + y + 2x + 3y
(d) 7h + 4r + 5h + 4
(e) 12a + 3b – 4 + 7a + 2b
(f) 2x + 6y + 10x + 4
3.
Simplify the following expressions:
(a) 6h + 4 + 3r + 6
(b) 5a + 6b + 3a + 4b
(c) 3x + 6y + 8x – 2y
(d) 27h – 6r – 13h – 7r
(e) 21a - 33b - 4 - 7a + 21b + 7
(f) 2x + 3y + 4z + 8y –2z
a) Write an expression for a tin a 2 packets of Hobnobs and 2 packets of
Rich Teas
b) Write an expression for a tin with just 5 packets of Hobnobs 5h
c) They are all tipped into a big tin, write an expression for the total
number of biscuits now. 7h + 2r
2.
2h + 2r
Simplify the following expressions by gathering like terms:
(a) h + 2r + 4h + 3r
5h + 5r
(b) 5a + 6b + 3a + 4b 8a + 10b
(c) x + y + 2x + 3y 3x + 4y
(d) 7h + 4r + 5h + 4 12h + 4r + 4
(e) 12a + 3b – 4 + 7a + 2b
(f) 2x + 6y + 10x + 4 12x + 6y + 4
3.
19a + 5b -4
Simplify the following expressions:
8a + 10b
(a) 6h + 4 + 3r + 6 6h + 3r + 10 (b) 5a + 6b + 3a + 4b
(c) 3x + 6y + 8x – 2y 11x + 4y (d) 27h – 6r – 13h – 7r
(e) 21a - 33b - 4 - 7a + 21b + 7
14a - 12b + 3
14h - 13r
(f) 2x + 3y + 4z + 8y –2z
2x + 11y + 2z
Algebra - the basics : “Working With Powers”
w
Area = w x w =
w2
w
w x w x w x w = w4
The power tells us how many are multiplied together
a8 = a x a x a x a x a x a x a x a
Algebra - the basics : “Products”
Recall, 4h = 4 x h
Similarly, gh = g x h
Pg.153
ex 8:2 and 8:3
When letters are multiplied together, in algebra,
you don’t need to put the multiplication (x) sign
Note: always write the number first,
E.g.
then the letters in alphabetical order
f x g = fg
g x 3h = g x 3 x h = 3gh
4r x 2s = 4 x r x 2 x s = 8rs
(2p)2 = 2p x 2p = 2 x p x 2 x p = 4p2
Algebra - “Brackets”
b+5
Biscuits
+
3 (b + 5)
b+5
Biscuits
3 lots of :
‘a tin of biscuits
and 5 loose ones’
+
b+5
Biscuits
= b+5+b+5+b +5=
= b+b+b+5+5+5
3b
+
15
Algebra - “Brackets”
h + 2r + 3
+
3 (h + 2r + 3)
h + 2r + 3
+
h + 2r + 3
=h
+ 2r + 3
+ h + 2r + 3
+ h + 2r + 3 =
= h+h+h
+ 2r + 2r + 2r
+3+3+3
= 3h + 6r + 9
3h
+
6r
+ 9
Algebra - “Brackets”
“3 times”
3(4x - 6)
“3 times 4x - 3 times 6”
= 3 x 4x - 3 x 6
= 12x - 18
Everything inside the bracket must be
multiplied by the number outside
As a multiplication table:
3
4x
-6
12x
-18
Pg.155-156
ex 8:5 and 8:6
Algebra - “Brackets”
“m times”
m(4n - 6)
“m times 4n - m times 6”
= m x 4n - m x 6
= 4mn – 6m
Everything inside the bracket must be
multiplied by the number outside
As a multiplication table:
4n
m
-6
4mn -6m
Pg.155-156
ex 8:5 and 8:6
Algebra - “Brackets”
3(4x - 6) – 4(x – 1)
= (3 x 4x - 3 x 6) – (4 x x – 4 x 1)
= (12x – 18) – (4x -4)
= 12x – 18 -4x - -4 -- equals +
= 12x – 18 – 4x + 4 Gather like terms
= 8x - 14
Everything inside the bracket must be
multiplied by the number outside
Pg.155-156
ex 8:5 and 8:6