How to find the simplest form of a fraction

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Simplifying a fraction means reducing a fraction to its simplest form. A fraction is in its simplest form if its numerator and denominator have no common factors other than 1. An important step that we do while we solve fraction problems is to reduce them to the simplest form. Though we simplify them, the value of the fraction is going to remain unchanged. This means the simplified fraction and the actual fraction form a pair of equivalent fractions. In this article, we will learn a few easy ways of simplifying fractions.

How to Simplify Fractions?

Simplifying a fraction implies reducing a fraction to its lowest form. A fraction is in its simplest form if its numerator and denominator are co-prime or have no common factors except 1. The simplest form of a fraction is equivalent to the given fraction. For example, the fraction 3/4 is in the simplest form because 3 and 4 have no common factor except 1. Let's try simplifying the fraction 8/24 step by step.

Simplifying Fractions Step by Step

Here is a step-by-step process for you to understand the process of simplifying a fraction. Consider the fraction, 8/24 and follow the steps mention below to understand how to simplify the fraction 8/24.

Step 1: Write the factors of 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 numerator and denominator. The common factors of 8 and 24 are 1, 2, 4, and 8.

Step 3: Divide the numerator and denominator by the common factors until they have no common factor except 1. The fraction so obtained is in the simplest form. Let's start dividing by 2, then 8/24 = (8/2)/(24/2) = 4/12. We will continue to divide by 2 until we can't go any further. So, we have (4/2)/(12/2) = 2/6 = (2/2)/(6/2) = 1/3.

Thus, 1/3 is the simplest form of the fraction 8/24.

Now, let us also discuss an easy way to simplify fractions. We can make a complicated fraction as simple as possible by following the process of simplifying the fraction. In order to find the simplified form of a fraction, take a look at an easy way to simplify the fraction. Here we have three-sixths of a pizza.

Why say three-sixths when you really mean half?

Simplifying a fraction means making a fraction as simple as possible. A quick way to find the simplest form of a fraction is to work out with the highest common factor. Follow the steps given below to learn the shortest way.

• Step 1: Write the factors of numerator and denominator.
• Step 2: Determine the highest common factor of numerator and denominator.
• Step 3: Divide the numerator and denominator by their highest common factor (HCF). The fraction so obtained is in the simplest form.

Let's get back to the same problem of simplifying the fraction 8/24. The highest common factor of 8 and 24 is 8. Dividing the numerator 8 and the denominator 24 by 8 will directly give us the simplest form of the fraction, that is, 1/3. So, the shortest way to break down a fraction into its simplest form is to divide the numerator and denominator by its highest common factor.

Simplifying Fractions with Variables

You can also simplify the fraction containing variables in the numerator and denominator. Use the expanded form of each term in the numerator and denominator to make it easy for you to simplify the fraction with variables.

Let's simply the fraction (x2y)/(xy).

Express the numerator and denominator as the product of variables.

(x2y)/(xy) = (x × x × y)/(x × y)

Cancel out the common variables.

(x2y)/(xy) = (x × x × y)/(x × y) = x

We hope simplifying fractions with variables have been easy for you.

Simplifying Fractions with Exponents

You can simplify the fraction containing exponents in the numerator and denominator. Use the expanded form of exponents in the numerator and denominator to make it easy for you to simplify the fraction with exponents. To make a number easy to read, we sometimes make use of exponents. Suppose we have the fraction 35/32. We will express the numerator and denominator as the product of numbers and then cancel out the common numbers.

35/32 = (3 × 3 × 3 × 3 × 3)/(3 × 3) = 3 × 3 × 3 = 27

So, you finally learned the way of simplifying fractions with exponents.

Simplifying Mixed Fractions

A mixed fraction is a mixture of a whole and a proper fraction. In order to simplify a mixed fraction, you need to simplify the fractional part only. For that write the numerator and the denominator in factored form and cancel out the common factors. The resultant will be the new numerator and the new denominator of the mixed fraction.

For example: Simplify the mixed fraction \(3\dfrac{4}{10}\).

To simplify the mixed fraction \(3\dfrac{4}{10}\), simplify only the fractional part. Write the numerator and denominator of the fractional part in factored form and cancel out the common factors.

4/10 = (2 × 2)/(2 × 5) = 2/5

Therefore, the mixed fraction \(3\dfrac{4}{10}\) can be simplified as \(3\dfrac{2}{5}\).

Simplifying Improper Fractions

Improper fractions are those in which the numerator is greater than or equal to the denominator. To simplify improper fractions we need to convert them to mixed fractions, and for that, we need to divide the numerator by the denominator. Then, we write it in the mixed number form by placing the quotient as the whole number, the remainder as the numerator, and the divisor as the denominator. Let us go through the following example to understand this better.

For example, to simplify the improper fraction 11/4, we need to divide 11 by 4 and get the values of quotient and remainder after performing division. When we divide 11/4, we get 2 as the quotient and 3 as the remainder. Therefore, the simplified form of the improper fraction 11/4 is \(2\dfrac{3}{4}\).

Related Articles

Check these interesting articles related to simplifying fractions.

1. Example 1: Sally loves growing flowers in her garden. Can you tell which flowers she grows the most? Express the part of those flowers in the form of the simplest fraction.

   

   Solution:

   The large area of the garden is filled with red flowers. So, Sally loves to grow red flowers the most. Red flowers cover 8/12 of her garden. Let's express the fraction 8/12 in its simplest form using the HCF method. Factors of 8: 1, 2, 4, and 8. And, factors of 12: 1, 2, 3, 4, 6, and 12. The highest common factor of 8 and 12 is 4, so divide 8 and 12 by 4, i.e. 8/12 = (8 ÷ 4)/(12 ÷ 4) = 2/3. Since 2 and 3 have no common factors except 1, 2/3 is the simplest form of 8/12. So, Sally loves growing red flowers the most. It is represented as 2/3.

2. Example 2: Jolly is playing with her magic disc. The disc is divided into 16 equal parts as shown. What part of the disc is colored blue? Can you express this fraction in the simplest form?

   

   Solution:

   The fraction representing the blue shaded region in the disc is 8/16. Let's find the highest common factor of 8 and 16. Factors of 8: 1, 2, 4, and 8, and factors of 16: 1, 2, 4, 8, and 16. We observe the highest common factor of 8 and 16 is 8. For simplifying the fraction, let's divide the numerator and the denominator of 8/16 by the highest common factor, that is (8/8)/(16/8) = 1/2. This means half of the disc is colored blue. So, the simplest form of 8/16 is 1/2.

3. Example 3: Find the simplest form of the fraction 11/33.

   Solution:

   Let us use the HCF method of simplifying fractions to solve this question. The highest common factor of 11 and 33 is 11. So, divide both numerator and denominator by 11, i.e 11/33 = (11 ÷ 11)/(33 ÷ 11) = 1/3. Therefore, the simplest form of 11/33 is 1/3.

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FAQs on Simplifying Fractions

Simplifying fractions mean reducing the fraction in its lowest form. It helps us to do calculations involving fractions much easily. For an instance, it is easier to add 1/2 and 1/2 as compared to 2/4 + 4/8.

What is the Rule for Simplifying Fractions?

The rule of simplifying fractions is to cancel out the common factors in the numerator and the denominator of the given fraction. In other words, we have to make sure that the numerator and denominator should be co-prime numbers.

What are the Steps in Simplifying Fractions?

Follow the steps mentioned below to reduce a fraction to its simplest form:

• Find the highest common factor of the numerator and denominator.
• Divide the numerator and denominator by the highest common factor.

The fraction so obtained is in the simplest form.

How do you Simplify Large Fractions?

Large fractions can be simplified by dividing the numerator and denominator by the common prime factors to reduce it to the simplest form.

How to Teach Simplifying Fractions?

Simplifying fractions usually come in grade 5 or 6. To teach simplifying fractions, follow the points given below:

• Allow learners to work on hands-on activities including rectangular or circular fraction models to arrive at an understanding that 2/4 is the same as 1/2.
• Use real-life examples of simplifying fractions.
• Use simplifying fractions worksheets.

How to Explain Simplifying Fractions?

A fraction is said to be in the simplest form when there is no common factor of numerator and denominator other than 1. For example, 11/23 is a simplified fraction as 11 and 23 do not have any common factors.

How to Convert an Improper Fraction to its Simplified Form?

Divide the numerator by denominator to obtain quotient and remainder. Then, the mixed fraction or the simplified fraction can be written as \(\text{Quotient}\dfrac{\text{Remainder}}{\text{Divisor}}\).

How are Fractions Reduced to their Simplified Form?

To reduce a fraction into its simplest form, divide the numerator and denominator by their highest common factor.

What is the Easiest way to Simplifying Fractions?

One of the quickest ways to reduce a fraction to its simplest form is to divide the numerator and denominator of the fraction by their highest common factor.