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How to Simplify Mixed Fractions?

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Last updated date: 04th Mar 2024
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Introduction to Mixed Fractions

As kids progress in higher classes, they are introduced to various new concepts in science and literature. Learning these concepts and understanding them can really help kids excel academically as well as develop a better understanding of the concepts of how things work. One such concept introduced to kids is the simplification of mixed fractions. The introduction to mixed fractions and the methods to solve them is a very interesting topic. In this article, we aim to help kids develop an understanding of what mixed fractions is. The article also discusses how to simplify mixed fractions by providing appropriate examples.


What is a Mixed Fraction?

A mixed fraction is a type of fraction that has a whole number and a fraction. The mixed fraction contains more than one whole number. The mixed fraction is in turn calculated from improper fractions. An improper fraction is defined as the one which has the numerator greater than the denominator. The concept of mixer fraction can be better understood by the example given below.


Image illustrating the mixed fraction


In the image shown above the mixed fraction 2\[\frac{1}{4}\] is represented in the pictorial form. As mentioned earlier, the mixed fractions can be derived from the improper fraction and vice versa due to their interchangeable nature. It is important to note that during the simplification of mixed fraction (conversion from mixed to improper), only the fraction part is reduced. Another point to note is that mixed fractions often represent the simplest form of representing a number. Simplification of mixed fractions results in improper fractions.


Steps to Simplify Mixed Fractions

As we have learnt about what is a mixed fraction and how they are represented, let us look into the steps that are required to simplify the mixed fractions. The simplification is an easy process that requires the understanding of basic division and factoristation concepts. They are mentioned in the following points.

  • Find the numerator and denominator

  • Find the highest common factor of numerator and denominator.

  • Divide the numerator and denominator with the highest common factor.

  • The resultant number is the simplified representation of the mixed number.

The simplified representation of the mixed fraction usually represents an improper fraction with high numerator and lower denominator. The steps to simplify a mixed fraction can be easily understood by the following examples.


Examples of Simplification of Mixed Fractions

Example 1: Simplify the fraction 2\[\frac{9}{15}\].

Solution: As mentioned earlier to simplify a mixed fraction, only the fraction part is reduced. Let us calculate the highest common factor of the numerator and denominator.

Factors of numerator are 1, 3, 9.

Factors of denominator are 1, 3, 5, and 15.

The highest common factor is 3.

Let us divide the numerator and denominator by 3.

\[\frac{9\div3}{15\div3}\]=\[\frac{3}{5}\]

Hence, the simplified representation of the mixed fraction 2 \[\frac{9}{15}\] is 2 \[\frac{3}{5}\].


Example 2: Simplify the mixed fraction 4\[\frac{15}{27}\].

Solution: Let us calculate the highest common factor of 15 and 27.

The factors of 15 are 1,3, 5, 15.

The factors of 27 are 1, 3,9, and 27.

The highest common factor is 3.

Dividing numerator and denominator by 3, we get

\[\frac{15\div3}{27\div3}\]=\[\frac{5}{9}\]

Hence, the simplified representation of mixed fraction is4 \[\frac{5}{9}\].


Conclusion

This was the complete discussion of how to simplify mixed fractions. We have learnt about what is a mixed fraction and their simplification steps. Fractions are a very fascinating concept of Mathematics. A small tip to students will be to practise as many questions as possible. As by regularly solving the problems on mixed fractions, students can develop better understanding of the concept.

FAQs on How to Simplify Mixed Fractions?

1. What is the highest common factor?

The highest common factor (HCF) is defined as the highest value number that can divide two numbers completely with a remainder of 0. HCF is also commonly termed as the greatest common divisor (GOD).

2. Convert \[\frac{9}{5}\] into a mixed fraction.

\[\frac{9}{5}\] can be converted into a mixed fraction by following the below steps.

 

Let us divide the fraction. Upon dividing \[\frac{9}{5}\], we get 4 as the remainder. 1 is written as the whole number of the mixed fraction. 4 is written as the numerator and 5, the divisor, as the denominator. Upon assembling, the mixed fraction is represented as  1 \[\frac{4}{5}\].