**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

=

=

=

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