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# Simplifying Algebraic Fractions

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by

## Mr Mattock

on 4 March 2017

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#### Transcript of Simplifying Algebraic Fractions

Simplifying Algebraic Fractions
Starter
Explain why the fractions:

a) 9
12

b) 15
20

c) 24
32

all simplify to the fraction .
Activity
Example
Simplify
L.O. - Apply understanding of fraction simplification to algebra
3
4
Starter
Explain why the fractions:

a) 9
12

b) 15
20

c) 24
32

all simplify to the fraction .
3
4

9

3 x 3

3 3

3
12

3 x 4

3 4

4
= =
x
=
15

5 x 3

5 3

3
20

5 x 4

5 4

4
= =
x
=
24

8 x 3

8 3

3
32

8 x 4

8 4

4
= =
x
=
Example
Explain why the fractions:

a) 9x
12x

b) 3y
4y

c) 24(x+2)
32(x+2)

all simplify to the fraction .
3
4
2
2
Example
Explain why the fractions:

a) 9x
12x

b) 3y
4y

c) 24(x+2)
32(x+2)

all simplify to the fraction .
3
4
2
2
9x

3x x 3

3x 3

3
12x

3x x 4

3x 4

4
= =
x
=
3y

3y x 3

3y 3

3
4y

3y x 4

3y 4

4
= =
x
=
2
2
2
2
2
2
24(x+2)

8(x+2) x 3

8(x+2) 3

3
32(x+2)

8(x+2) x 4

8(x+2) 4

4
= =
x
=
8x
20

3x
5(x - 3)

10x (x+2)
2x(x+2)
2
3
Kian says

3x + 4 x + 1
6x + 12 2x + 3

because simplifies to
and simplifies to . Comment
on Kian's explanation.
simplifies to
3 1
6 2
4 1
12 3
Example
Simplify
8x
2x
20
5

3x
x
9(x - 3)
3(x - 3)

10x (x+2)
5x(x+2)
2x(x+2)
2
3
Kian says

3x + 4 x + 1
6x + 12 2x + 3

because simplifies to
and simplifies to . Comment
on Kian's explanation.
Kian is incorrect, 3x + 4 has no common factor with 6x + 12, and so the fraction doesn't simplify.
simplifies to
3 1
6 2
4 1
12 3
2
Example
Simplify

6x + 15
6 - 9x

x + 2x
5x

x + x - 6
x - 4
2
2
2
Example
Simplify

6x + 15
6 - 9x

x + 2x
5x

x + x - 6
x - 4
2
2
2
3(2x + 5) 2x + 5
3(2 - 3x) 2 - 3x

x(x + 2) x + 2
5x 5

(x - 2)(x + 3) x + 3
(x - 2)(x + 2) x + 2
=
=
=
Activity
Activities
Activity