Halves, Quarters and Eighths
Remember the equivalent fractions for halves, quarters and eighths.
1
2
1
4
=
2
4
=
2
3
8 and 4
=
4
8
=
6
8
This will help you find the equivalent percentages.
Halving and Combining
Many equivalent percentages can be found by doubling and halving
known percentages.
½
¼
= 50%
¾
=
is half of
½
+
¼
½
so
is half of
= 25%
= 50% + 25% = 75%
We can extend this to
⅛
¼
¼
⅛, ⅜, ⅝
so
⅛
=
½
and
⅞.
of 25% = 12.5%
⅜ =¼
+
⅛
= 25% + 12.5% = 37.5%
⅝ =½
+
⅛
= 50% + 12.5% = 62.5%
⅞ =¾
+
⅛
= 75% + 12.5% = 87.5%
Fifths and Tenths
Remember the equivalent fractions for halves, fifths and tenths.
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
4
5
8
= 10
5
½ = 10
1
5
=
2
10
2
5
=
4
10
3
5
6
= 10
Halving and Combining
Fifths and tenths are mainly found by combining the required number of
1
tenths as 10 = 10%
5
=
10
½
= 50%
3
4
2
2
1
= 10 = 20%, 5 = 40%, 5 = 60%, 5 = 80%
5
1
3
7
9
=
10%,
=
30%,
=
70%,
= 90%
10
10
10
10
Thirds, Sixths and Twelfths
Remember the equivalent fractions for halves, thirds, sixths and twelfths.
1
6
1
12
3
6
2
6
3
12
2
12
4
12
⅓=
3
6
2
6
1
6
2 and 5
12
6
½=
=
=
=
5
12
4
8
4
2
and
12
3
=
10
12
4
6
6
12
=
8
12
7
12
4
6
5
6
=
8
12
9
12
6
6
10
12
11
12
12
12
Halving and Combining
Many of the equivalent percentages for thirds, sixths and twelfths use the
recurring 3333 or 6666. Use this along with halving and combining to
find the equivalent percentages.
⅓
= 33.3%,
⅔
= 66.66% rounded to 66.7%
When halving 33.3% we know half of 32 =16 and use half of 1.33 ≈ 0.67
1
so 6 = 16.7%.
Look for the best way to combine the percentages to find all
the equivalents.
Combining Twenty-Fifths
1
We know that 25 × 4 = 100 so 25 = 4%.
12
To find the equivalent percentage of 25 we multiply 12 by 4.
12
25 = 48%.
Try other twenty-fifths.
Calculating Equivalent Percentages
Equivalent percentages can be calculated by dividing the numerator by
the denominator (to find the equivalent decimal) and multiplying by 100
to give the percentage.
½
0.5
2 1.0
0.5 x 100 = 50%
⅝
0.625
8 5.000
0.625 x 100 = 62.5%