Fractions
A fraction is a measure of sharing .
Example
What fraction of these counters is yellow ?
one eighth or one in eight of these counters is yellow
Common fractions are written in the form
The top number (numerator)
is divided by ÷
The bottom number ( denominator)
A proper fraction has a smaller numerator
than denominator.
Examples
3 32
4 37
An improper fraction has a larger numerator,
the top is larger than the bottom.
These are often
called
top heavy fractions.
Examples
13 39
4 37
Converting improper fractions to mixed numbers
Divide the numerator (top) by the denominator (bottom)
Write the quotient, then put the remainder over the denominator.
Example
Converting mixed numbers to improper fractions
Times the whole number by the denominator (bottom),
Add the numerator (top).
Example
Example
(This
method uses prime factors )
1. Divide by each
prime number in turn,
until you cannot divide exactly by that
number.
Continue until you reach 1.
2. Write the
number as the product of
its prime factors.
3. Cancel out
terms
4. Multiply
Example
simplify
|
Top |
÷ |
|
Bottom |
÷ |
|
84 |
2 |
|
330 |
2 |
|
42 |
2 |
|
165 |
3 |
|
21 |
3 |
|
55 |
5 |
|
7 |
7 |
|
11 |
11 |
|
1 |
|
|
1 |
|
Calculating fractions of
amounts
Example
|
Fraction |
Percentage |
Decimal |
|
1/1 |
100% |
1 |
|
1/2 |
50% |
0.5 |
|
1/3 |
33 1/3% |
0.33333… |
|
1/4 |
25% |
0.25 |
|
1/5 |
20% |
0.2 |
|
1/8 |
12.5% |
0.125 |
|
1/10 |
10% |
0.1 |
|
1/20 |
5% |
0.05 |
|
2/3 |
66 2/3% |
0.666666… |
|
2/5 |
40 % |
0.4 |
|
3/4 |
75 % |
0.75 |
|
3/5 |
60% |
0.6 |
|
3/8 |
37.5 % |
0.375 |
|
3/10 |
30 % |
0.3 |
|
4/5 |
80% |
0.8 |