How to Convert Fractions to Lowest Terms

In the Civil Service Examination and in many mathematics examinations, results that are fractions are usually required to be converted to their lowest terms.  The numerator and the denominator of a fraction in lowest terms cannot be divided by any  similar integer. Knowledge of divisibility rules can be helpful in this process.

Example 1: Convert $\frac{6}{9}$ to lowest terms.

In the first example, we can see that the numerator and the denominator are both divisible by 3. Dividing both the numerator and the denominator by 3 gives us 2/3.

$\displaystyle \frac{6 \div 3}{9 \div 3} = \frac{2}{3}$

Note that dividing both the numerator and the denominator by the same integer does not change the value of the fraction.

Example 2: Convert $\frac{24}{42}$ to lowest terms.

Sometimes, it is hard to find the largest common divisor of fractions with large numerator and denominator so you need to perform division repeatedly. In this example, the most obvious clue is that both numbers are divisible by 2. Dividing both the numerator and denominator by 2 gives us $\frac{12}{21}$. Again, both the denominator and the denominator are divisible by 3, making the lowest term $\frac{4}{7}$. Of course, you could have divided the numerator and the denominator by 6 in the first step.

Example 3: Convert $\frac{51}{21}$ to lowest terms.

There are cases where you are asked to convert an improper fractions (fractions whose numerator is greater than the numerator) to lowest terms. In some cases, you have also to convert them to mixed form. The answer to the third example which is an improper fraction can be obtained by dividing both the numerator and denominator by 3.

$\displaystyle \frac{51 \div 3}{21 \div 3} = \frac{17}{7}$

The value of $\frac{17}{7}$ in mixed form is $\displaystyle 2 \frac{3}{7}$.

It takes time and practice to master converting fractions to lowest terms. Knowledge on divisibility and familiarity of characteristics of numbers will help you perform the computation faster.

Now that you know how to convert fractions to lowest terms, you might want to try the practice test and check your solution and answer.

6 Responses

1. October 22, 2013

[…] simple. Multiply the numerator and then the denominator. Of course, if the given fractions can be converted to lowest terms, the easier the multiplication will […]

2. January 6, 2014

[…] Reducing to lowest terms by dividing both the numerator and the denominator of the preceding fraction by , we get or . […]

3. January 30, 2014

[…] We reduce the answer to lowest terms by dividing both the numerator and denominator by 5 resulting to . […]

4. April 6, 2014

[…] reducing to lowest term we […]

5. July 22, 2014

[…] In the solutions below, all answers were also reduced to lowest terms. […]

6. August 24, 2014

[…] If Ariel can finish the job in 5 days, then if he were to work one day, he would have completed 1/5 of the job. If he works for two days, then he would have completed 2/5 of the job. Similarly, if Ben can finish the same job in 6 days, if he were to work for one day, then he would have completed 1/6 of the job. If he works for 2 days, he would have completed 2/6 of the job (or 1/3 of the job if reduced to lowest terms).  […]