This can be written as5
6
¼
5 4
6 4
¼
20
24
.
Animproper fractionis a fraction whose numerator is greater than or equal
to its denominator. For example,^203 ,^65 , and^33 are improper fractions. Amixed
numberis a whole number and a fraction; 8^13 ,2^14 , and 3^56 are mixed numbers.
To change an improper fraction to a mixed number, divide the numerator
by the denominator and write the remainder as the numerator of a fraction
whose denominator is the divisor. Reduce the fraction if possible.
EXAMPLE:Change^216 to a mixed number.
SOLUTION:
6 Þ 21
3
18
3
21
6
¼ 3
3
6
¼ 3
1
2
To change a mixed number to an improper fraction, multiply the
denominator of the fraction by the whole number and add the numerator.
This will be the numerator of the improper fraction. Use the same number for
the denominator of the improper fraction as the number in the denominator
of the fraction in the mixed number.
EXAMPLE:Change 5^23 to an improper fraction.
SOLUTION:
5
2
3
¼
3 5 þ 2
3¼
17
3
In order to add or subtract fractions, you need to find thelowest common
denominatorof the fractions. The lowest common denominator (LCD) of the
fractions is the smallest number that can be divided evenly by all the
denominator numbers. For example, the LCD of^16 ,^23 , and^79 is 18, since 18
can be divided evenly by 3, 6, and 9. There are several mathematical methods
for finding the LCD; however, we will use the guess method. That is,
just look at the denominators and figure out the LCD. If needed, you can
look at an arithmetic or prealgebra book for a mathematical method to find
the LCD.
REFRESHER II Fractions 19