1.2: Reducing Fractions
Fractions can be reduced (expressed) in their lowest terms. This simply means that the fractions can no longer be divided by any other number.
In proper fractions, if the numerator and denominator can be divided by the same number, the fraction can be reduced.
Example: \(\dfrac{2}{4}=\dfrac{1}{2}\)
In the example above, this is accomplished by dividing the numerator and denominator by the number 2. Two fourths and one half represent the same number. They are just expressed differently. One half is a reduced form of two fourths.
Example: \(\dfrac{2}{4} \div \dfrac{2}{2}=\dfrac{1}{2}\)
At times a fraction can be divided multiple times in order to reduce it.
Example: \(\dfrac{8}{12} \div \dfrac{2}{2}=\dfrac{4}{6} \div \dfrac{2}{2}=\dfrac{2}{3}\)
This can also be performed in one step as follows. Both solutions provide the same answer.
Example: \(\dfrac{8}{12} \div \dfrac{4}{4}=\dfrac{2}{3}\)
In reducing improper fractions the denominator is divided into the numerator to create a mixed number. The remainder is written as a fraction.
Example:
Remember: The resulting mixed number may also need to be reduced further.
Example:
Exercise 1.2
Reduce the following fractions to their lowest terms.
- \(\dfrac{7}{2}\)
- \(\dfrac{10}{4}\)
- \(\dfrac{18}{4}\)
- \(\dfrac{20}{4}\)
- \(\dfrac{6}{5}\)
- \(\dfrac{100}{3}\)
- \(\dfrac{39}{6}\)
- \(1\dfrac{8}{12}\)
- \(2\dfrac{9}{4}\)
- \(\dfrac{4}{3}\)
- \(\dfrac{14}{3}\)
- \(\dfrac{140}{200}\)
- \(\dfrac{10}{20}\)
- \(7\dfrac{30}{40}\)