3 10 In Simplest Form

Fraction in Simplest Form: Definition, Examples, Verification

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Fraction in Simplest Course: The simplest form of a fraction is ane with a reasonably prime numerator and denominator. It signifies that the numerator (upper portion or elevation) and the denominator (lower part or bottom) of the fraction have no common component other than \(i\). A fraction is a value that represents a portion of a whole. The simplest grade of the fraction is besides known as the reduced grade of a fraction. For instance, \(\frac{3}{four}\) is the simplest form of a fraction with a common component of one. Yet, \(\frac{2}{four}\) is non the simplest form because \(\frac{ii}{iv}\) may be reduced further and expressed as \(\frac{1}{2}\). In this case, nosotros tin also say that \(\frac{one}{ii}\) and \(\frac{2}{4}\) are equivalent fractions. Finding the simplest class of whatsoever fraction is a simple process. Nosotros need to simplify the fraction'southward numerator and denominator by dividing them both by the biggest common factor that divides them entirely. Both the numerator and denominator should exist entire integers afterward division. This arroyo of fractional simplification is too known as reducing fractions.

This post will tell you everything about fractions in their simplest form, their definition, examples, and verification. Read further to find more.

Definition of Fractions

If a certain quantity of rice is divided into four equal parts, each office obtained is said to be i-quaternary \(\left( {\frac{1}{4}} \right)\) of the whole quantity of the rice. Similarly, if an orange is divided into five equal parts, each function is ane-fifth \(\left( {\frac{i}{5}} \right)\) of the whole orange. Now, if two parts of these v equal parts are eaten, three parts are left and we say three-fifths \(\left( {\frac{3}{five}} \right)\) of the orange is left.

The numbers \(\left( {\frac{1}{4}} \right),\,\left( {\frac{1}{v}} \right),\,\left( {\frac{3}{5}} \correct)\) discussed to a higher place, each represents a function of the whole quantity, are called fractions.

A fraction is a quantity that expresses a part of the whole. So, the numbers of the form \(\frac{10}{y}\), where \(x\) and \(y\) are whole numbers, and \(y≠0\), are chosen fractions.

Hither, \(x→\) Numerator and \(y→\) Denominator.

Types of Fractions

There are unlike types of fractions. Permit us sympathize each type.

1. Proper Fractions

A fraction whose numerator is less than its denominator is called a proper fraction. The value of the proper fraction is always less than \(ane\).

For example, \(\frac{3}{four},\,\frac{vii}{{10}},\,\frac{one}{4},\,\frac{3}{7}\) are all proper fractions.

2. Improper Fractions

A fraction whose numerator is greater than or equal to its denominator is chosen an improper fraction.

For example, \(\frac{vii}{four},\,\frac{{13}}{5},\,\frac{{11}}{6},\,\frac{{23}}{7}\) are all improper fractions.

3. Mixed Fractions

A combination of a whole number and a proper fraction is called a mixed fraction.

For example, \(two\frac{ii}{4},\,half dozen\frac{5}{{10}},\,5\frac{1}{v},\,6\frac{2}{{thirteen}}\) are all mixed fractions.

4. Similar Fractions

The grouping of two or more fractions that have the same denominators are like fractions.

For example, \(\frac{i}{5},\,\frac{2}{5},\,\frac{3}{five},\,\frac{4}{5},\,\frac{7}{v}\) are all like fractions.

5. Unlike Fractions

The group of two or more fractions that have different denominators are unlike fractions.

For example, \(\frac{one}{vi},\,\frac{2}{4},\,\frac{2}{five},\,\frac{4}{7},\,\frac{5}{8}\) are all unlike fractions.

6. Unit Fractions

A unit fraction is whatever fraction with \(ane\) as its numerator and a non-zero whole number as the denominator.

For example, \(\frac{ane}{9},\,\frac{i}{4},\,\frac{1}{5},\,\frac{1}{3},\,\frac{ane}{8}\) are all unit of measurement fractions.

7. Decimal Fractions

A decimal fraction is a fraction whose denominator is a power of \(10\) or a multiple of \(10\) similar \(100, 1,000, ten,000\), etc.

For example, \(\frac{iii}{{x}},\,\frac{four}{{100}},\,\frac{{13}}{{ten}},\,\frac{ix}{{1000}}\) are all decimal fractions.

Simplest Class of Fraction

A fraction is said to be in its simplest form if \(1\) is the just common factor of its numerator and denominator. So, a fraction tin not be said to be in its simplest form if the numerator and the denominator accept any common factor other than \(1\).

For example, \(\frac{iii}{4}\) is in its simplest form as \(i\) is the only common factor of \(3\) and \(4\) in this fraction. We can simplify fractions every bit information technology reduces the complexities in calculations.

Rules to Find the Simplest Form of a Fraction

Allow the given fraction be \(\frac{a}{b}\) and the HCF of \(a\) and \(b\) be \(h\). Then, \(\frac{a}{b} = \frac{{a \div h}}{{b \div h}}\)is the simplest form.

For example, the simplest grade of \(\frac{8}{{24}}\).

Now, nosotros will notice the HCF of \(8, 24\). HCF of two numbers is known as the highest or the largest common cistron between two or more numbers.

HCF \((8, 24)=eight\)

\(\Rightarrow \frac{8 \div viii}{24 \div 8}=\frac{i}{three}\)

Hence, nosotros can get the simplest form of a fraction by dividing the numerator and the denominator by the same number, and the number should be the HCF of the numerator and the denominator of the fraction.

We can apply this method likewise, but here we need to do the process several times every bit later on dividing the numerator and the denominator of \(\frac{eight}{{24}}\) by \(2\), nosotros are getting \(\frac{4}{{12}}\) which is not the simplest form.

So, nosotros will proceed the procedure till we get \(i\) every bit the common factor of the numerator and the denominator. The kickoff method is easier to find the simplest course than the 2nd method as the second one is a lengthy process.

Solved Examples – Fraction in Simplest Form

Q.1. Is the fraction \(\frac{3}{vii}\) in its simplest form?
Ans: Given fractions is \(\frac{3}{7}\).
The numerator is \(3\), and the denominator is \(7\). To check whether the fraction is in its simplest form, nosotros volition detect the HCF of \(three, 7\).
Now, HCF \((3, seven)=1\) as \(3, vii\) are coprime numbers.
Therefore, \(\frac{3}{7}\) is in its simplest class as the highest common gene of the numerator, and the denominator is \(1\).

Q.2. Find the fractions in the simplest form from the following. \(\frac{three}{6},\,\frac{one}{3},\,\frac{2}{v},\,\frac{4}{6},\,\frac{5}{{15}}\).
Ans: Given fractions are, \(\frac{3}{6},\,\frac{1}{iii},\,\frac{2}{5},\,\frac{4}{6},\,\frac{5}{{15}}\)
To observe the simplest form, first, we will find the highest common factor of the numerator and the denominator of each fraction. The fractions whose HCF of the numerator and the denominator is only \(1\), tin can be said the fractions are in the simplest form.
In \(\frac{3}{vi}\), the HCF of \(3,\,6\) is \(3.\)
In \(\frac{one}{3}\), the HCF of \(1, 3\) is \(1.\)
In \(\frac{2}{5}\), the HCF of \(2, 5\) is \(1.\)
In \(\frac{4}{6}\), the HCF of \(4,6\) is \(2.\)
In \(\frac{five}{15}\), the HCF of \(5, 15\) is \(v.\)
Hence, \(\frac{1}{iii}\) and \(\frac{ii}{5}\) are in their simplest grade.

Q.three. What is the simplified form of the fraction \(\frac{144}{36}\)?
Ans: The given fraction is \(\frac{144}{36}\)
We need to find the lowest form or the simplest grade of the given fraction.
Now, the highest mutual cistron of \(144, 36\) is \(36.\)
So, \(\frac{{144 \div 36}}{{36 \div 36}} = \frac{4}{1} = iv.\)
Hence, the simplest course is \(four.\)

Q.four. Is \(\frac{5}{15}\) the lowest form of \(\frac{25}{75}\)?
Ans: No, \(\frac{v}{fifteen}\) is the non everyman grade of \(\frac{25}{75}.\)
\(\frac{5}{15}\) tin can be simplified again if we dissever the numerator and the denominator by \(5\).
So, the lowest course of \(\frac{25}{75}\) is \(\frac{1}{3}\), as \(\frac{{25 \div 25}}{{75 \div 25}} = \frac{1}{3}.\)
Hence, \(\frac{5}{15}\) is non the lowest form of \(\frac{25}{75}.\)

Q.5. What is the simplest class of the fraction \(\frac{2}{v}\) ?
Ans: Given fractions is \(\frac{2}{v}.\)
The numerator is \(two\), and the denominator is \(5.\) To check whether the fraction is in its simplest form or not, we volition find the HCF of \(2, 5.\)
At present, HCF \((2, 5)=1\) as \(2, 5\) are coprime numbers.
Therefore, \(\frac{ii}{5}\) is in its simplest grade, and we tin not reduce or simplify more.

Summary

In this article, we covered the definition of the fraction, types of fractions, the simplest form of a fraction, ways to identify if a fraction is in its simplest course or not and how to discover the simplest course of a fraction.

Frequently Asked Questions (FAQs) – Fraction in Simplest Form

Q.1. Explain the fraction in the simplest form with an example.
Ans: A fraction is said to be in its simplest course if \(1\) is the but mutual factor of its numerator and denominator. And so, a fraction can not be said in its simplest form if the numerator and the denominator have a common factor other than \(1\). For example, \(\frac{iii}{4}\) is in its simplest form every bit \(1\) is the but mutual factor of \(3\) and \(4\) in this fraction.

Q.2. What is the simplest fraction form of \(one.33\)?
Ans: The fraction form of the decimal number \(1.33\) is \(\frac{{133}}{{100}}\).
\(100\) and \(133\) are the coprime numbers and their HCF is \(ane\).
Hence, the simplest fraction form of the given decimal number is \(\frac{{133}}{{100}}\).

Q.3. How practice you express the fractions in the simplest form?
Ans: Commencement, nosotros will find the highest common factor (HCF) of the numerator and denominator of the given fraction. If the HCF is \(1\), then the fraction is in its simplest grade. If the HCF is other than \(one\), then divide both the numerator and denominator by HCF, and get the simplest class of the fraction.

Q.4. Can nosotros find the simplest class of a fraction by multiplying the numerator and the denominator by the same non-nada number?
Ans: No, nosotros can not. We tin become the lowest or the simplest form of a fraction past dividing the numerator and the denominator past the HCF of the numerator and the denominator.

Q.five. What is the departure between the simplest form of a fraction and the equivalent fractions?
Ans: The simplest form of a fraction is also an equivalent fraction, only the ways to find the equivalent fraction and the simplest grade of a fraction are slightly dissimilar. If we multiply or divide the numerator and the denominator of a fraction by the same non-cipher number, we volition get the equivalent fractions. To find the simplest form of a fraction, we need to dissever the numerator and the denominator by the HCF of the numerator and the denominator.

At present that y'all are provided with a detailed article on the simplest grade of a fraction, we hope all your doubts are cleared on this topic. If you have whatsoever queries or questions, you lot can enquire them in the comment box beneath. We will be more happy to assist you. Best of luck with your studies!