# Fractions Simplest Form

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```					Simplifying Fractions
Equivalent Fractions

1                  2                  3                     4
2                  4                  6                     8
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.

5                 6                  10                    50
10                12        1/2       20                   100
Equivalent Fractions

1        2                3          4
2        4                6          8
2
2   x½         3
3   x½       4
4   x½

5        6             10        50
10       12             20       100
5
5   x½   6
6   x½          10
10   x½    50
50   x½
Equivalent Fractions

1                   2                    3                   4
3                   6                    9                  12
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.

5                  6                   10                   30
15                 18      1/3          30                   90
Equivalent Fractions

1             2              3             4
3             6              9            12
2
2    x   1
3
3
3    x   1
3
4
4    x    1
3

5            6             10            30
15           18             30            90
5
5   x    1
3
6
6   x   1
3
10
10   x   1
3
30
30   x    1
3
Equivalent Fractions

1                                 2                                 4
4                                 8                                16
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.

8                                       16
32
1/4                     64
Equivalent Fractions

1                          2                               4
4                          8                              16
2
2   x   1
4
4
4    x   1
4

8                                   16
32                                   64
8
8   x    1
4
16
16   x    1
4
Equivalent Fractions

2                      4                     6                      8
5                     10                    15                     20
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.

10                                                   12
25                   2/5                             30
Equivalent Fractions

2                    4              6                         8
5                   10             15                        20
2
2   x    2
5
3
3   x    2
5
4
4   x    2
5

10                                      12
25                                      30
5
5   x   2
5
6
6   x    2
5
Equivalent Fractions

3                       6                     9                     12
8                      16                    24                     32
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.

15                       18                    30
40                       48                    80      3/8
Equivalent Fractions

3                     6                         9                         12
8                    16                        24                         32
2
2    x   3
8
3
3   x    3
8
4
4   x    3
8

15                        18                         30
40                        48                         80
5
5   x    3
8
6
6   x    3
8
10
10   x    3
8
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).

6
18
Simplest Form
Writing Fractions in their Simplest Form

1
3

6        HCF of 6 and 18 = 6 so    1
Example: Simplify             dividing top and bottom
18        by 6 gives:               3

6
18
Writing Fractions in their Simplest Form

1                                      3
9
3
                                      
6   Note that dividing by a factor (in this     3
Example 1: Simplify        case 2) that is not the HCF will not give
18   you the fraction in simplest form.          9

6
18
Writing Fractions in their Simplest Form

2
5

HCF of 10 and 25 = 5 so   2
Example 2: Simplify
10   dividing top and bottom
25   by 5 gives:               5

10
25
Writing Fractions in their Simplest Form

3
8

HCF of 18 and 48 = 6 so   3
Example 3: Simplify   18   dividing top and bottom
48   by 6 gives:               8

18
48
Writing Fractions in their Simplest Form

3                      6
8                     16
                  
18   Again, dividing by a factor (in this case    6
Example 3: Simplify        3) that is not the HCF will not give you
48   the fraction in simplest form.              16

18
48
Writing Fractions in their Simplest Form

Express the following fractions in their simplest form.

4             9            15             8           20
(a )         (b )          (c )          (d )         (e )
6            12            35            12           24
2             3              3            2              5
3             4              7            3              6

5            9            15            24           24
(f )         (g )          (h )          (i )         (j )
15           15            18            40           30
1             3              5            3              4
3             5              6            5              5
Questions
Writing Fractions in their Simplest Form

Express the following fractions in their simplest form.

4             9            15             8           20
(a )         (b )          (c )          (d )         (e )
6            12            35            12           24

5            9            15            24           24
(f )         (g )          (h )          (i )         (j )
15           15            18            40           30

Worksheet

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