Simplest Form of Fraction: Steps, Calculator, Methods and Examples

Simplest form of fraction is the fraction, whose numerator and denominator are relatively prime. The most compressed or simplified form of a fraction occurs when the numerator and denominator of the fraction have no common factor between them, other than 1. Let’s know more about simplest form of fraction with steps and various method below.

Simplest Form of Fraction

Simplest Form of a Fraction

When the top and bottom of a fraction are whole numbers that are coprime to one another that fraction is said to be in its simplest form. So, for that calculation, we have to simplify the numerator and denominator by the GCF process. Then, after dividing the numerator and denominator getting numbers will be whole numbers.

Simplest form is also known as reducing fractions.

For example: Simplify fraction 7/21

= 7/21

• 7 = 1 × 7
• 21 = 3 × 7

= 1 × 7/3 × 7

= 1/3

Simplest Fraction Calculator

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Steps to Find Simplest Form

To find the simplest form of a fraction, follow the steps given below:

Step 1: Write the given fraction in the form of a numerator and denominator.

Step 2: After that, by GCF process the greatest number that splits equally between the numerator and the denominator.

Step 3: Repeat the procedure if any common factors are still present in the denominator and numerator until only one is left.

Step 4: Lastly, we get the simplified fraction with the smallest whole numbers of the numerator and the denominator.

Reduce Fractions to their Simplest Form

If the numerator and denominator of a fraction have no common factors other than 1, or if their greatest common factor (GCF) is 1, then the fraction is in its simplest form.

For example:

5/11 is in simplest form since 5  and  11 have no common factors other than 1.

However, 6/21 is not in simplest form, since 6  and  21  share a common factor of 3.

To reduce a fraction, divide both the numerator and denominator by the GCF process.

= 6/21

= 6 ÷ 3/ 21 ÷ 3

= 2/7

Reduce Mixed Fractions in Simplest Form

To reduce a mixed number to its simpler form is to simplify it. When the fractional part of a mixed number has the highest common factor (HCF) of 1, it is considered to be in its simplest form. Even, the value of the fraction will remain the same and the simplified mixed number and the actual mixed number are equivalent fractions over here. To find mixed fractions we have to follow the steps that are given below:

Step 1: Firstly, multiply the denominator with the whole number part. 

Step 2: Then, add the numerator to the product obtained.

Step 3: After that, we will write the value obtained at the place of the numerator and the denominator will be the same.

Step 4: Lastly, if needed we can bring it down to the smallest whole numbers otherwise can remain as it is in the simplest form of fraction.

For example,

Suppose mixed number is 2(1/3)

Here, let’s multiply denominator with whole number part: 3 × 2 = 6

Then, add numerator to received product: 6 + 1 = 7

Therefore, we get the fraction 7/3

Simplest Form of Fractions with Variables

Its simplest form of fractions with variables that express the fraction in its most basic form and present with variables that are present in both the values of the denominator and the numerator. Whereas the variable over here can be any of the alphabet with the numeral. i.e., x, y.

For example,

Let’s take Fraction with variables 6x / 21y

After simplifying it we get 3x/7y

Therefore, simplest form of 6x / 21y is 3x/7y

Simplest Form of Fractions with Exponents 

Its simplest form of Fractions with Exponents is that expresses the fraction in its most basic form and simplifies the given exponents that are present in both the values of denominator and the numerator. Whereas Exponents can be present with any of the variables with the power. i.e., “x²“. Therefore, To simplify the term exponent rules must be applied as shown in the given example below.

For example:

Let’s take fraction with exponents 8x³/ 12x²

Here, we simplify fraction first 8/12 = 2/3

Now, we simplified exponents x³÷ x² = x^3-2 = x¹ that can be written as “x”

Therefore, the simplest form of 8x³/ 12x² is 2x/3

Ratio in Simplest Form

Its simplest form of Fractions with ratio indicates the number of times one number appears in another number. Additionally, it displays the proportions of two or more values. Hence, denoted between the values with the symbol of ratio “:”. It’s as same as a fraction form only. i.e., 2:6 that will be present as 2/6. Even, the ratio and fractions both represent the relationship between quantities. So, now Let’s see the example that is given below.

For example,

Let’s take the ratio 10:15

Here, we write it in fraction form, 10/15

Now, we simplified it with GCF process. 10 ÷ 5/ 15 ÷ 5 = 2/3

In ratio 2:3

Therefore, ratio in simplest form of given value 10:15 is 2:3

Simplest form of Addition of Fractions

Simplest form of Addition of Fractions indicates the sum of fractions represented in the simplest possible way, with the lowest terms for the denominator and numerator. Even, this involves adding the numerators after determining a common denominator.

For example:

Let’s add fractions 3/12 and 5/12

By adding numerator first, 3 + 5 = 8

Now, sum fraction with common denominator, 8/12

Therefore, sum of 3/12 and 5/12 in simplest form is 8/12 or 2/3

Decimal to Simplest Form

A decimal can be expressed as a fraction in its most simplified form by converting it to its simplest form. To simplify the decimal, it must first be written as a fraction and its numerator and denominator divided by their greatest common divisor. So, Let’s see the decimal in fraction form.

For example:

Write 0.5 into a fraction

By following above given steps, we get; 0.5

Since there is only one digit after the decimal that can be written in the form of 5/10

After Simplifying it, by taking out the HCF of the numerator and denominator that gives 1/2

Facts about Simplest Form of a Fraction

Here are some facts given below about the Simplest Form of a Fraction:

• Simplest form is the smallest possible equivalent fraction of the given number.
• It is calculated by taking the greatest common divisor (GCD) of the numerator and denominator.
• Numerators of proper fractions are less than denominators, but improper fractions are equal to or more than denominators.

Read more,

• Fractions
• Addition of Fractions
• Subtracting Fractions
• Multiplication of Fractions

Examples on the Simplest Form of a Fraction

Example 1: Reduce the fraction 15/35​ to its simplest form.

Solution:

HCF of 15 and 35 is 5

After, Dividing numerator and denominator by 5, we get;

15/5 = 3

35/5 = 7

Therefore, the simplest form of fraction 15/35 is 3/7.

Example 2: Simplify the fractions 8x⁴/ 16x²

Solution:

Let’s take the fraction with the exponents 8x³/ 16x²

Here, we simplify the fraction first 8/16 = 1/2.

Now, we simplified the exponents x⁴÷ x² = x^4-2 = x².

Therefore, the simplest form of 8x⁴/ 16x² is x²/2.

Example 3: Simplify the fraction 2(4/3).

Solution:

Let’s multiply the denominator with the whole number part: 3 × 2 = 6

Then, add the numerator to the received product: 6 + 4 = 10

Therefore, we get the fraction 10/3.

Example 4: Reduce the fraction 15/20​ to its simplest form.

Solution:

Simplest form of 15/20 by reduction method is 3/4

Example 5: Find the simplest form of 30/70.

Solution:

Simplest form of 30/70 is 3/7

Practice Questions on Simplest Form of Fraction 

Q1. Simplify the fraction 24/36​ to its simplest form.

Q2. Find the simplest form of the fraction 48/64.

Q3. Reduce the fraction 15/25​ to its simplest form.

Q4. Determine the simplest form of the fraction 42/63.

Q5. Simplify the fraction 36/48​ to its lowest terms.

Simplest Form of Fraction – FAQs

What is Simplest Form of a Fraction?

When there is no common factor between the fraction’s numerator and denominator, it is said to be in its simplest form. For example: the simplest form of 6/12 is 1/2.

How to Express Ratio in Simplest Form?

Divide the previous and subsequent by their largest common factor to express a ratio in the simplest possible way.

What is Lowest Form of 12/36?

Simplest form of 12/36 is 1/3.

What is Simplest Form of 42 by 28?

Simplest form of 42 by 28 is 3/2.

Is 49/ 64 in its Simplest Form?

Yes, 49/60 is in its simplest form.

What is Equivalent fraction of 5/9?

Equivalent fraction of 5/9 is 10/18.