Ratio Fractions In Simplest Form

Written Past Madhurima Das
Last Modified xix-10-2022

Fraction in Simplest Form: Definition, Examples, Verification

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Fraction in Simplest Course: The simplest grade of a fraction is one with a reasonably prime numerator and denominator. It signifies that the numerator (upper portion or tiptop) and the denominator (lower role or bottom) of the fraction accept no common component other than \(ane\). A fraction is a value that represents a portion of a whole. The simplest form of the fraction is also known as the reduced course of a fraction. For instance, \(\frac{3}{four}\) is the simplest form of a fraction with a common component of one. However, \(\frac{two}{4}\) is not the simplest class because \(\frac{2}{four}\) may be reduced further and expressed as \(\frac{i}{two}\). In this instance, we can as well say that \(\frac{i}{2}\) and \(\frac{2}{4}\) are equivalent fractions. Finding the simplest grade of any fraction is a elementary process. Nosotros need to simplify the fraction's 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 after division. This arroyo of fractional simplification is also known as reducing fractions.

This mail will tell yous everything about fractions in their simplest form, their definition, examples, and verification. Read further to observe more.

Definition of Fractions

If a sure quantity of rice is divided into four equal parts, each office obtained is said to be ane-fourth \(\left( {\frac{1}{four}} \right)\) of the whole quantity of the rice. Similarly, if an orange is divided into five equal parts, each part is ane-fifth \(\left( {\frac{1}{five}} \correct)\) of the whole orangish. At present, if two parts of these five equal parts are eaten, three parts are left and nosotros say three-fifths \(\left( {\frac{iii}{five}} \right)\) of the orangish is left.

The numbers \(\left( {\frac{1}{4}} \correct),\,\left( {\frac{1}{5}} \right),\,\left( {\frac{three}{v}} \right)\) discussed above, each represents a office of the whole quantity, are chosen fractions.

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

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

Types of Fractions

In that location are different types of fractions. Let united states of america understand each type.

ane. 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 \(1\).

For example, \(\frac{3}{4},\,\frac{7}{{ten}},\,\frac{1}{iv},\,\frac{3}{vii}\) are all proper fractions.

2. Improper Fractions

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

For example, \(\frac{7}{4},\,\frac{{13}}{5},\,\frac{{11}}{half-dozen},\,\frac{{23}}{7}\) are all improper fractions.

3. Mixed Fractions

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

For example, \(2\frac{two}{four},\,6\frac{5}{{10}},\,5\frac{ane}{five},\,6\frac{ii}{{13}}\) are all mixed fractions.

iv. Like Fractions

The group of two or more fractions that have the same denominators are similar fractions.

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

5. Dissimilar Fractions

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

For example, \(\frac{i}{6},\,\frac{2}{4},\,\frac{2}{5},\,\frac{4}{7},\,\frac{5}{eight}\) are all different fractions.

6. Unit Fractions

A unit fraction is any fraction with \(1\) as its numerator and a non-zippo whole number as the denominator.

For example, \(\frac{one}{9},\,\frac{ane}{iv},\,\frac{one}{5},\,\frac{ane}{three},\,\frac{1}{eight}\) are all unit of measurement fractions.

vii. Decimal Fractions

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

For example, \(\frac{3}{{10}},\,\frac{iv}{{100}},\,\frac{{13}}{{10}},\,\frac{9}{{1000}}\) are all decimal fractions.

Simplest Grade of Fraction

A fraction is said to exist in its simplest form if \(1\) is the just mutual factor of its numerator and denominator. And then, a fraction tin non be said to be in its simplest form if the numerator and the denominator have whatever common factor other than \(ane\).

For example, \(\frac{three}{4}\) is in its simplest form as \(1\) is the only mutual factor of \(3\) and \(iv\) in this fraction. We tin simplify fractions as it reduces the complexities in calculations.

Rules to Detect the Simplest Course of a Fraction

Let the given fraction exist \(\frac{a}{b}\) 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 instance, the simplest grade of \(\frac{8}{{24}}\).

Now, we will find the HCF of \(8, 24\). HCF of 2 numbers is known as the highest or the largest mutual factor between 2 or more numbers.

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

\(\Rightarrow \frac{8 \div 8}{24 \div 8}=\frac{1}{3}\)

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

We tin apply this method also, but here we demand to do the process several times as afterward dividing the numerator and the denominator of \(\frac{viii}{{24}}\) by \(ii\), we are getting \(\frac{4}{{12}}\) which is non the simplest form.

So, we will go along the process till we get \(1\) as the mutual factor of the numerator and the denominator. The showtime method is easier to find the simplest class than the second method as the 2nd one is a lengthy process.

Solved Examples – Fraction in Simplest Form

Q.1. Is the fraction \(\frac{3}{7}\) in its simplest grade?
Ans: Given fractions is \(\frac{3}{7}\).
The numerator is \(3\), and the denominator is \(seven\). To check whether the fraction is in its simplest form, we will detect the HCF of \(3, 7\).
Now, HCF \((3, 7)=1\) as \(iii, seven\) are coprime numbers.
Therefore, \(\frac{3}{seven}\) is in its simplest class every bit the highest mutual gene of the numerator, and the denominator is \(1\).

Q.two. Observe the fractions in the simplest form from the following. \(\frac{3}{six},\,\frac{1}{iii},\,\frac{ii}{v},\,\frac{4}{6},\,\frac{5}{{15}}\).
Ans: Given fractions are, \(\frac{3}{half-dozen},\,\frac{ane}{3},\,\frac{2}{5},\,\frac{4}{6},\,\frac{5}{{15}}\)
To find the simplest course, beginning, 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 merely \(1\), can be said the fractions are in the simplest form.
In \(\frac{iii}{six}\), the HCF of \(3,\,6\) is \(three.\)
In \(\frac{1}{3}\), the HCF of \(1, 3\) is \(1.\)
In \(\frac{ii}{5}\), the HCF of \(ii, 5\) is \(i.\)
In \(\frac{iv}{half-dozen}\), the HCF of \(4,6\) is \(2.\)
In \(\frac{five}{xv}\), the HCF of \(5, 15\) is \(5.\)
Hence, \(\frac{1}{3}\) and \(\frac{two}{5}\) are in their simplest form.

Q.3. What is the simplified grade of the fraction \(\frac{144}{36}\)?
Ans: The given fraction is \(\frac{144}{36}\)
We demand to detect the everyman form or the simplest grade of the given fraction.
At present, the highest common factor of \(144, 36\) is \(36.\)
So, \(\frac{{144 \div 36}}{{36 \div 36}} = \frac{iv}{one} = 4.\)
Hence, the simplest form is \(4.\)

Q.4. Is \(\frac{5}{15}\) the lowest grade of \(\frac{25}{75}\)?
Ans: No, \(\frac{5}{15}\) is the not everyman form of \(\frac{25}{75}.\)
\(\frac{v}{15}\) can exist simplified once more if we divide the numerator and the denominator by \(v\).
And then, the lowest form of \(\frac{25}{75}\) is \(\frac{i}{three}\), as \(\frac{{25 \div 25}}{{75 \div 25}} = \frac{1}{3}.\)
Hence, \(\frac{five}{fifteen}\) is not the lowest course of \(\frac{25}{75}.\)

Q.five. What is the simplest form of the fraction \(\frac{2}{5}\) ?
Ans: Given fractions is \(\frac{2}{v}.\)
The numerator is \(ii\), and the denominator is \(5.\) To check whether the fraction is in its simplest grade or not, we volition find the HCF of \(2, 5.\)
Now, HCF \((2, five)=ane\) every bit \(ii, five\) are coprime numbers.
Therefore, \(\frac{2}{five}\) is in its simplest form, and nosotros can not reduce or simplify more.

Summary

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

Often Asked Questions (FAQs) – Fraction in Simplest Grade

Q.1. Explain the fraction in the simplest form with an example.
Ans: A fraction is said to exist in its simplest form if \(ane\) is the only common factor of its numerator and denominator. And so, a fraction can not be said in its simplest grade if the numerator and the denominator have a common cistron other than \(ane\). For example, \(\frac{3}{4}\) is in its simplest class as \(ane\) is the merely common factor of \(3\) and \(iv\) in this fraction.

Q.2. What is the simplest fraction form of \(1.33\)?
Ans: The fraction course of the decimal number \(ane.33\) 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 do y'all limited the fractions in the simplest form?
Ans: First, we will observe the highest mutual factor (HCF) of the numerator and denominator of the given fraction. If the HCF is \(1\), then the fraction is in its simplest form. If the HCF is other than \(1\), and then separate both the numerator and denominator by HCF, and get the simplest form of the fraction.

Q.iv. Can we notice the simplest grade of a fraction by multiplying the numerator and the denominator by the same non-zero number?
Ans: No, nosotros can non. We tin get the everyman or the simplest form of a fraction by dividing the numerator and the denominator by the HCF of the numerator and the denominator.

Q.5. What is the difference between the simplest class of a fraction and the equivalent fractions?
Ans: The simplest form of a fraction is also an equivalent fraction, but the means to find the equivalent fraction and the simplest class of a fraction are slightly unlike. If we multiply or split the numerator and the denominator of a fraction by the same non-goose egg number, we volition become the equivalent fractions. To find the simplest form of a fraction, nosotros need to divide the numerator and the denominator by the HCF of the numerator and the denominator.

At present that you are provided with a detailed article on the simplest form of a fraction, we hope all your doubts are cleared on this topic. If you have whatsoever queries or questions, you can ask them in the comment box below. We will be more than happy to help you. Best of luck with your studies!