1/2
Equivalent Fractions
12
24
36
48
510
612
1020
50100
All these fractions are equivalent to ½ since they take up the same proportion of the shape. They are the result of multiplying ½ by 2/2, 3/3. 4/4, etc.
Equivalent Fractions
12
24
36
48
510
612
1020
50100
x ½ 22 x ½ 3
3 x ½ 44
x ½ 55 x ½ 6
6 x ½ 1010
x ½ 5050
1/3
13
26
39
412
515
618
1030
3090
Equivalent Fractions
All these fractions are equivalent to 1/3 since they take up the same proportion of the shape. They are the result of multiplying 1/3 by 2/2, 3/3. 4/4, etc.
13
26
39
412
515
618
1030
3090
Equivalent Fractions
x 22
13 x 3
313 x 4
413
x 55
13 x 6
613 x 1
01013 x 30
3013
14
28
416
832
1664
Equivalent Fractions
1/4
All these fractions are equivalent to ¼ since they take up the same proportion of the shape. They are the result of multiplying ¼ by 2/2, 3/3. 4/4, etc.
14
28
416
832
1664
Equivalent Fractions
x 22
14 x 4
414
x 88
14 x 1
616
14
25
410
820
615
1025
1230
Equivalent Fractions
2/5
All these fractions are equivalent to 2/5 since they take up the same proportion of the shape. They are the result of multiplying 2/5 by 2/2, 3/3. 4/4, etc.
25
410
820
615
1025
1230
Equivalent Fractions
x 22
25 x 3
325 x 4
425
x 55
25 x 6
625
38
616
1232
924
1540
1848
3080
Equivalent Fractions
3/8
All these fractions are equivalent to 3/8 since they take up the same proportion of the shape. They are the result of multiplying 3/8 by 2/2, 3/3. 4/4, etc.
38
616
1232
924
1540
1848
3080
Equivalent Fractions
x 22
38 x 3
338 x 4
438
x 55
38 x 6
638 x 1
01038
618
Writing Fractions in Simplest Form
If a fraction can be simplified then we know that it’s numerator and denominator are both multiples of some number. To get the fraction in its simplest form we divide both the numerator and denominator by their highest common factor (HCF).
Simplest Form
618
Writing Fractions in their Simplest Form
Example: Simplify
618
HCF of 6 and 18 = 6 so dividing top and bottom by 6 gives: 3
1
31
618
Writing Fractions in their Simplest Form
Example 1: Simplify
618 9
3
31
93
Note that dividing by a factor (in this case 2) that is not the HCF will not give you the fraction in simplest form.
1025
HCF of 10 and 25 = 5 so dividing top and bottom by 5 gives: 5
2
52
Example 2: Simplify
1025
Writing Fractions in their Simplest Form
1848
HCF of 18 and 48 = 6 so dividing top and bottom by 6 gives: 8
3
83
Example 3: Simplify
1848
Writing Fractions in their Simplest Form
1848
166
83
Example 3: Simplify
1848
Again, dividing by a factor (in this case 3) that is not the HCF will not give you the fraction in simplest form.
166
Writing Fractions in their Simplest Form
Questions
Express the following fractions in their simplest form.
Writing Fractions in their Simplest Form
64
)(a129
)(b3515
)(c128
)(d2420
)(e
155
)(f159
)(g1815
)(h4024
)(i3024
)( j
32
43
73
32
65
31
53
65
53
54
Worksheet
Express the following fractions in their simplest form.
Writing Fractions in their Simplest Form
64
)(a129
)(b3515
)(c128
)(d2420
)(e
155
)(f159
)(g1815
)(h4024
)(i3024
)( j
