Simplest Form of a Fraction

Simplest form of a fraction is the fraction, whose numerator and denominator are relatively prime. It means the numerator (upper part or top) and denominator (lower part or bottom) of the fraction does not have any common factor between them, apart from 1.

A fraction is a value representing a part of a whole. The simplest form is also called the reduced form of fraction. For example, ¾ is the simplest form of a fraction that has a common factor equal to 1. But 2/4 is not the simplest form, because 2/4 can further be simplified and written as ½. Here, we can also say, ½ and 2/4 are equivalent fractions.

Let us find out how to write the fraction into its simplest form with the help of given steps and examples, in this article.

How to Find the Simplest Form of a Fraction?

A fraction is in simplest form when the top and bottom of the fraction are whole numbers that are coprime to each other.

Finding the simplest form of any fraction is a simple method. We need to simplify the numerator and denominator of the fraction by dividing both the numerator and denominator by the greatest common factor that divides them completely. After division both the numerator and denominator should remain whole numbers. This method of simplifying fractions is also known as reducing fractions.

For example, if the fraction is ac/bc, then the simplified form of ac/bc will be a/b, because the common factor ‘c’ is divided from both numerator and denominator.

ac/bc = a/b

Steps to Find Simplest Form

Learn the step by step method to simplify fractions here:

• Find the GCF of numerator and denominator of the fraction
• Divide the numerator and denominator by the produced GCF
• Write the simplified fraction of the given fraction

Also, read: How to Simplify Fractions?

Solved Examples

Let us solve examples based on simplification of fractions.

Simplify the fractions given below:

(i) 3/6

(ii) 2/10

(iii) 15/35

(iv) 10/15

(v) 4/16

Solution:

(i) 3/6

Let us find the GCF of 3 and 6.

GCF (3,6) = 3

So, 3/6 = (3 x 1)/(3 x 2) = ½

Hence, ½ is the solution.

(ii) 2/10

GCF of 2 and 10 is 2.

Therefore, we can write,

2/10 = (1 x 2)/(5 x 2)

Dividing both numerator and denominator by 2, we get;

2/10 = ⅕

Hence, ⅕ is the solution.

(iii) 15/35

HCF of 15 and 35 is 5

Dividing numerator and denominator by 5, we get;

15/5 = 3

35/5 = 7

Hence, 15/35 = 3/7 is the required fraction.

(iv) 10/15

GCF (10, 15) = 5

Divide 10 and 15 by 5 to get;

10/5 = 2

15/5 = 3

Therefore, the simplified fraction of 10/15 is:

10/15 = ⅔

(v) 4/16

GCD of 4 and 16 = 4

Divide the numerator and denominator ( 4 and 16) by 4 to get;

4/4 = 1

16/4 = 4

Therefore, the simplified fraction of 4/16 is:

4/16 = ¼

Simplest form of Addition of Fractions

When two fractions are added together, then the sum of the fractions has to be written in the simplest form.

 For example, adding ¼ and ¼ we get; ¼ + ¼ = 2/4 But 2/4 is not in the simplest form. Therefore, the dividing numerator and denominator by the greatest common factor of 2 and 4, i.e.,2, we get; 2/4 = ½ Hence, ¼ + ¼ = ½

Note: If the denominators of the two fractions in addition are not the same, then they are unlike fractions. Thus, we have to convert these fractions into like fractions by making the denominators the same and then add them.

Simplest Form Ratio

A ratio is represented by a:b, where a and b are the whole numbers. If we write a ratio in the simplest form then we are reducing the ratio into its lowest terms.

 Example: simplify 32:40. We can use the same method to simplify the ratio, as we have used to simplify the fraction. 32 is the antecedent and 40 is the consequent here. Therefore, we need to find the highest possible factor of 32 and 40 to get the simplified form. Hence, 8 is the common factor of 32 and 40. Therefore, the simplest form of 32:40 is 4:5 (because 8 x 4 = 32 and 8 x 5 = 40)

Decimal to Simplest Form

To convert decimal into simplest form of fraction, follow the below steps:

• Remove the decimal and write it as the whole number, that will be the numerator of the fraction.
• Write the denominator as multiples of 10 equal to the digits present after the decimal point. (For example, if there is 2 digits after the decimal, then the denominator will 10 x 10 = 100)
• Now, simplify the fraction
 Example: Write 0.5 into fraction. By following the above given steps, we get; 0.5 = 5/10 [Since, there is only one digit after decimal] = ½ [ By taking out the HCF of numerator and denominator and then simplify it]

Practice Questions

1. Simplify the following fractions:
1. 10/45
2. 2/18
3. 4/60
4. 9/81
2. What is the equivalent fraction of 5/9?
3. Solve and write into simplest form:
1. ⅗ + 7/5
2. ⅘ + 8/3
4. Fill in the blanks:
1. 36/54 = 18/___
2. 30/54 = ___/9
3. ¼ = 7/___
4. 180/___ = 9/10

Frequently Asked Questions on Simplest Form of Fraction

What is the simplest form of fraction? Give an example.

The fraction is said to be in its simplest form, when the numerator (top) and denominator (bottom) of the fraction does not have any common factor. For example, the simplest form of 6/12 is ½.

How to find the simplest form of 30/70?

To find the simplest form of fraction 30/70, we have to find the highest common divisor of 30 and 70. GCD of 30 and 70 is 10. Now divide both numerator and denominator by 10 to get the simplest form. Hence,
30/70 = 3/7

How to write mixed fraction in simplest form?

Mixed fraction has two parts: whole number and a fraction. To write mixed fraction in simplest form we need to convert it into improper fraction, where the numerator is greater than the denominator.

What is the lowest form of 12/36?

The simplest form of 12/36 is ⅓.

How to express ratio in simplest form?

To express a ratio in simplest form, divide the antecedent and consequent, by their highest common factor.