This lowest term calculator will help you find the simplified form or the lowest term of any fraction, whether in the standard form of a fraction or mixed number form. Learning how to find the lowest term can help us easily visualize a ratio or to compare different fractions. Keep on reading to start exploring the following:
- What lowest term is;
- How to reduce fractions to their lowest terms;
- How to use this lowest term calculator;
- A short quiz on which fraction is expressed in the lowest term; and
- Some examples to show how to find the lowest term of a fraction.
🙋 This calculator is a quick-read version of our simplify fractions calculator, which you can also visit for more information on reducing fractions to their simplest form.
What is lowest term?
The lowest term, a term we usually use for fractions, is the simplified form of a fraction. For example,
3/4 is the lowest term of the fraction
18/24. If we only need to tell the overall ratio of objects, we can use its fraction's lowest term to make it easier for us to visualize.
If we want to lessen the number of divisions of things we want to distribute (for example, a pizza), going for the lowest term can make life easier.
For example, we usually slice a pizza into eight slices, right? Let's say only four people will share the pizza, and they all agree they can eat two slices each.🍕🍕 That means one person will have 2/8 of the pizza. But if we divided the pizza into four pieces, each person can now easily take one part each (even though it might now be a little bit tricky to eat). That gives us portions of 1/4 for each – which is also the lowest term of 2/8.
In the next section of this text, we'll discuss how to find the lowest terms of fractions. So keep on reading. 😊
💡 If you're craving more knowledge on fractions, then our fraction calculator is for you.
How to reduce fractions to their lowest terms
The first step in reducing fractions to their lowest term is to determine the greatest common factor (or the GCF) of the fraction's numerator and denominator. You can learn more about how to find GCFs by checking out our greatest common factor calculator.
Say, for example, we consider the fraction we mentioned earlier: 18/24. We get its numerator and denominator's GCF by first determining all their factors, as shown below:
- Factors of
1, 2, 3, 6, 9, 18
- Factors of
1, 2, 3, 4, 6, 8, 12, 24
We can see that the greatest common factor is
6. Now that we know their GCF, we then divide both the numerator and denominator by their GCF to find the lowest term of our given fraction, as we can see below:
Divide the numerator and denominator by their GCF
18 / 6 = 3
24 / 6 = 4
For other fractions, like improper fractions and mixed numbers, we first express our mixed number as an improper fraction. Then we follow the same two steps discussed earlier on how to get the lowest term of a fraction. You can also revert the fraction to a mixed number if you like your fraction that way.
How to use this lowest term calculator
Using our lowest term calculator is very easy. To get the lowest term with our tool, you need to follow these two simple steps:
- Select the form your fraction is in – which is either
mixed number form.
- Enter the whole number (for a mixed number form fraction), the numerator, and the denominator of your fraction into our calculator.
That's it! Our lowest term calculator will already show you the lowest term of your entered fraction. 😊
Which fraction is expressed in lowest term?
Now that we know how to find the lowest term of a fraction, why don't we have a short one-item quiz? Are you ready?
Which of these fractions is expressed in its lowest term?
💡 The secret to this problem is to determine if the GCF of the numerator and denominator of a fraction is equal to 1. If their GCF is equal to 1, then our given fraction is already in the lowest term.
After consistent practice, we can see that by inspection, we can divide the numerator and denominator of the first fraction (12/15) by 3 (12 and 15 are both divisible by 3). Its lowest term is 4/5.
On the other hand, for the second fraction, 6 and 10 are both divisible by 2. Its lowest term fraction is equal to 3/5.
Lastly, the common factor of 8 and 11 of the last fraction is 1.
Therefore our answer to this question is C. 8/11 is already in its lowest term.
What is the lowest term of a fraction?
The lowest term of a fraction is also its simplified form. That said, we can no longer simplify a fraction if it is already in the lowest term. That happens when we use the numerator and denominator's greatest common factor to simplify the fraction.
How do I find the lowest term?
To find the lowest term of a fraction
Determine the prime factors of its numerator and denominator. For example, in the fraction
14/35, we find their factors:
1, 2, 7, 14
1, 5, 7, 35
7is the greatest common factor of these two numbers.
Then, divide both the numerator and denominator by their greatest common factor to get:
14 / 7 =
35 / 7 =
Finally, form the fraction from these quotients to have:
What is the lowest term of 4/20?
The lowest term of 4/20 is 1/5. We get that value by dividing both the numerator and denominator by their greatest common factor, which is 4. Dividing the numerator and denominator by 4, we get 1 and 5, respectively. By combining these results, we arrive at the lowest term for that fraction which is 1/5.
What is the lowest term of 3/16?
3/16 is already in its lowest term. To get that conclusion, we first take the factors of 3, which are
3, and the factors of 16, which are
1, 2, 4, 8, 16. Clearly, their greatest (in fact, only) common factor is
1. This means the fraction
3/16 cannot be simplified.