A fraction is in the simplest form when its numerator and denominator have no common factors. The fractions have a numerator (the top number) and the denominator (the bottom number). The Conversion of a Fraction into its Smallest and Simplest Form are discussed in the below section. Let us discuss in detail about Conversion of a Fraction into its Smallest and Simplest Form with examples here.
Also, Refer:
- Reducing the Equivalent Fractions
- Simplification of Fractions
- Worksheet on Simplification of Fractions
- Fraction in Lowest Terms
Fraction into its Smallest and Simplest Form – Definition
If the numerator and denominator have no common terms then we can say that it is in the simplest form. The reduction of fractions to the simplest form involves division operation.
How to Reduce a Fraction to its Simplest Form?
Here we will learn the methods to reduce fractions to their lowest term.
Method 1: Reduce fractions the formal way
1. In order to reduce the fractions we have to know how to break down the numerator and denominator.
2. Now cross out any common factors which appear in the numerator and denominator.
3. Multiply the remaining numbers to get the simplest form.
Example: Convert \(\frac{15}{18}\) to the simplest form.
\(\frac{15}{18}\) = \(\frac{3.5}{3.3.2}\) = \(\frac{5}{6}\)
Method 2: Reduce fractions the informal way
1. If the numerator and denominator are divisible by 2 then you have to divide both the numbers by 2 until you have no common factors.
Example: Convert \(\frac{12}{24}\) to the simplest form.
\(\frac{12}{24}\) = \(\frac{1}{2}\)
Simplest form of Fraction Examples
Example 1.
Convert the fraction \(\frac{8}{24}\) into its simplest form.
Solution:
Let us solve this problem in a step by process to understand how to convert the given fraction in the simplest form.
The given fraction is \(\frac{8}{24}\)
Step 1: Write the factors for numerator and denominator.
The factors of 8 and 24 are
Factors of 8: 1, 2, 4, and 8
Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24
Step 2: Determine the common factors of the top number and bottom number. The common factors of 8 and 24 are 1, 2, 4, and 8.
Step 3: Divide the numerator and denominator by common factors until they have no common factor except 1. The fraction so obtained is in the simplest form.
\(\frac{8}{24}\) = \(\frac{8}{2}\)/\(\frac{24}{2}\) = \(\frac{4}{12}\)
\(\frac{4}{12}\) = \(\frac{4}{2}\)/\(\frac{12}{2}\) = \(\frac{2}{6}\) = \(\frac{2}{2}\)/\(\frac{6}{2}\) = \(\frac{1}{3}\)
Thus the simplest form of the fraction \(\frac{8}{24}\) is \(\frac{1}{3}\)
Example 2.
Convert the fraction \(\frac{19}{38}\) into its simplest form.
Solution:
Let us solve this problem in a step by process to understand how to convert the given fraction in the simplest form.
The given fraction is \(\frac{19}{38}\)
Step 1: Write the factors for numerator and denominator.
The factors of 19 and 38 are
Factors of 19: 19, 38, and 57
Factors of 38: 38, 76 and 114
Step 2: Determine the common factors of the top number and bottom number. The common factors of 19 and 38 are 1, 19, and 38.
Step 3: Divide the numerator and denominator by common factors until they have no common factor except 1. The fraction so obtained is in the simplest form.
\(\frac{19}{38}\) = \(\frac{19}{19}\)/\(\frac{38}{19}\) = \(\frac{1}{2}\)
Thus the simplest form of the fraction \(\frac{19}{38}\) is \(\frac{1}{2}\)
Example 3.
Convert the fraction \(\frac{24}{48}\) into its simplest form.
Solution:
Let us solve this problem in a step by process to understand how to convert the given fraction in the simplest form.
The given fraction is \(\frac{24}{48}\)
Step 1: Write the factors for numerator and denominator.
The factors of 24 and 48 are
Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 24 and 48
Step 2: Determine the common factors of the top number and bottom number. The common factors of 24 and 48 are 1, 2, 3, 4, 6, 8, 12 and 24
Step 3: Divide the numerator and denominator by common factors until they have no common factor except 1. The fraction so obtained is in the simplest form.
\(\frac{24}{48}\) = \(\frac{24}{2}\)/\(\frac{48}{2}\) = \(\frac{12}{24}\)
\(\frac{12}{24}\) = \(\frac{12}{2}\)/\(\frac{24}{2}\) = \(\frac{6}{12}\) = \(\frac{6}{2}\)/\(\frac{12}{2}\) = \(\frac{3}{6}\) = \(\frac{3}{3}\)/\(\frac{6}{3}\) = \(\frac{1}{2}\)
Thus the simplest form of the fraction \(\frac{24}{48}\) is \(\frac{1}{2}\)
Example 4.
Convert the fraction \(\frac{6}{9}\) into its simplest form.
Solution:
Let us solve this problem in a step by process to know how to convert the given fraction into the simplest form.
The given fraction is \(\frac{6}{9}\)
Step 1: Write the factors for numerator and denominator.
The factors of 6 and 9 are
Factors of 6: 1, 2, 3 and 6.
Factors of 9: 1, 3 and 9.
Step 2: Determine the common factors of the top number and bottom number. The common factors of 6 and 9 are 1 and 3.
Step 3: Divide the numerator and denominator by common factors until they have no common factor except 1. The fraction so obtained is in the simplest form.
\(\frac{6}{9}\) = \(\frac{6}{3}\)/\(\frac{9}{3}\) = \(\frac{2}{3}\)
Thus the simplest form of the fraction \(\frac{19}{38}\) is \(\frac{1}{2}\)
Example 5.
Convert the fraction \(\frac{10}{20}\) into its simplest form.
Solution:
Let us solve this problem in a step by process to know how to convert the given fraction into the simplest form.
The given fraction is \(\frac{10}{20}\)
Step 1: Write the factors for numerator and denominator.
The factors of 10 and 20 are
Factors of 10: 1, 2, 5 and 10.
Factors of 20: 1, 2, 4, 5, 10 and 20.
Step 2: Determine the common factors of the top number and bottom number. The common factors of 10 and 20 are 1, 2, 5 and 10.
Step 3: Divide the numerator and denominator by common factors until they have no common factor except 1. The fraction so obtained is in the simplest form.
\(\frac{10}{20}\) = \(\frac{10}{2}\)/\(\frac{20}{2}\) = \(\frac{5}{10}\)
\(\frac{5}{10}\) = \(\frac{5}{5}\)/\(\frac{10}{5}\) = \(\frac{1}{2}\)
Thus the simplest form of the fraction \(\frac{10}{20}\) is \(\frac{1}{2}\)
FAQs on Simplifying and Reducing Fractions to Lowest Terms
1. How do you know if a fraction is fully reduced?
Writing a fraction in the simplest form means the numerator and denominator of the given fractions should not have common factors. Then we can know the fraction is fully reduced.
2. How to Reduce a fraction to its simplest form?
1. Write down the factors for the numerator and denominator.
2. Cross the common factors in their numerator and denominator.
3. Then write the remaining numerator and denominator with no common factors.
4. And then write down the reduced form of the given fraction in the simplest form or lowest form.
3. When can you say that a fraction is already in its simplest form?
You can say that a fraction is already in its simplest form if the greatest common factors (GCF) of the numerator and denominator is just 1.