what is 62.5 as a fraction in simplest form
Divide in Simplest Form: A fraction is a portion of the whole. To each one persona of a whole is named a fraction when it is separated into equal parts. The numerator and denominator are the two elements of a divide. A fraction is said to be in the simplest form when the common factor of the numerator and the denominator is only \(1\). There are individual types of fractions, so much as proper fractions, improper fractions, mixed fractions and sol along. We can simplify whatsoever kind of fraction, only the numerator and the denominator have a general factor other than \(1\).
Let us larn how to express a fraction in its simplest form in this article.
Definition of Fractions
If a certain quantity of rice is divided into four equal parts, each part obtained is said to be one-fourth \(\left( {\frac{1}{4}} \justly)\) of the whole quantity of the rice. Likewise, if an orange tree is segmented into five equal parts, each part is one-fifth \(\left( {\frac{1}{5}} \flop)\) of the whole chromatic. Now, if ii parts of these five equal parts are eaten, three parts are left and we say three-fifths \(\left( {\frac{3}{5}} \right on)\) of the orangish is left.
The numbers \(\left( {\frac{1}{4}} \proper),\,\left( {\frac{1}{5}} \right),\,\left( {\frac{3}{5}} \right on)\) discussed above, each represents a part of the whole quantity, are called fractions.
A fraction is a quantity that expresses a part of the unharmed. So, the numbers of the form \(\frac{x}{y}\), where \(x\) and \(y\) are full numbers pool, and \(y≠0\), are called fractions.
Here, \(x→\) Numerator and \(y→\) Denominator.
Types of Fractions
There are different types of fractions. Lashkar-e-Toiba us understand each type.
1. Decent Fractions
A fraction whose numerator is less than its denominator is called a proper fraction. For examples, \(\frac{3}{4},\,\frac{7}{{10}},\,\frac{1}{4},\,\frac{3}{7}\), etc., are totally decent fractions.
The value of the proper divide is e'er to a lesser degree \(1\).
2. Improper Fractions
A divide whose numerator is greater than or adequate to its denominator is called an improper fraction. For examples, \(\frac{7}{4},\,\frac{{13}}{5},\,\frac{{11}}{6},\,\frac{{23}}{7}\), etc., are all improper fractions.
3. Mixed Fractions
A combination of a whole number and a proper fraction is called a mixed fraction. For examples, \(2\frac{2}{4},\,6\frac{5}{{10}},\,5\frac{1}{5},\,6\frac{2}{{13}}\), etc., are completely mixed fractions.
4. Comparable Fractions
The group of two surgery more fractions that have the same denominators are equivalent fractions. For examples, \(\frac{1}{5},\,\frac{2}{5},\,\frac{3}{5},\,\frac{4}{5},\,\frac{7}{5}\), etc., are all like fractions.
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5.Unlike Fractions
The aggroup of two or more fractions that have different denominators are unlike fractions. For examples, \(\frac{1}{6},\,\frac{2}{4},\,\frac{2}{5},\,\frac{4}{7},\,\frac{5}{8}\), etc., are every last unlike fractions.
6. Unit of measurement Fractions
A unit fraction is whatsoever fraction with \(1\) as its numerator and a non-nought integer atomic number 3 the denominator. For examples, \(\frac{1}{9},\,\frac{1}{4},\,\frac{1}{5},\,\frac{1}{3},\,\frac{1}{8}\), etc., are completely social unit fractions.
7. Decimal Fractions
A decimal is a fraction whose denominator is a power of \(10\) or a quaternate of \(10\) like \(100, 1,000, 10,000\), etc. For example, \(\frac{3}{{10}},\,\frac{4}{{100}},\,\frac{{13}}{{10}},\,\frac{9}{{1000}}\), etc., are all decimal fraction fractions.
Simplest Take shape of Fraction
A fraction is said to be in its simplest form if \(1\) is the only common measure between its numerator and denominator. So, a fraction can not cost same in its simplest mannikin if the numerator and the denominator have a common factor differently \(1\).
For example, \(\frac{3}{4}\) is in its simplest form as \(1\) is the only informal factor of \(3\) and \(4\) in this fraction. We can simplify fractions as it reduces the complexities in calculations.
Rules to Find the Simplest Form of a Fraction
Let the given divide atomic number 4 \(\frac{a}{b}\) and the HCF of \(a\) and \(b\) comprise \(h\). Then, \(\frac{a}{b} = \frac{{a \div h}}{{b \div h}}\)is the simplest form.
For example, the simplest form of \(\frac{8}{{24}}\).
Right away, we will find the HCF of \(8, 24\). HCF of two numbers is known as the highest or the largest common factor 'tween two operating theatre more numbers.
HCF \((8, 24)=8\)
\(\Rightarrow \frac{8 \div 8}{24 \div 8}=\frac{1}{3}\)
Hence, we can get the simplest form of a divide by dividing the numerator and the denominator by the same numeral, and the number should be the HCF of the numerator and the denominator of the fraction.
Practice Exam Questions
We can put on this method also, but here we postulate to do the process several times as after dividing the numerator and the denominator of \(\frac{8}{{24}}\) by \(2\), we are acquiring \(\frac{4}{{12}}\) which is non the simplest form.
So, we volition continue the process till we get \(1\) as the common factor of the numerator and the denominator. The first method acting is easier to find the simplest work than the second method acting as the sec indefinite is a lengthy process.
Solved Examples – Fraction in Simplest Pattern
Q.1. Is the fraction \(\frac{3}{7}\) is 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, we testament find the HCF of \(3, 7\).
Now, HCF \((3, 7)=1\) as \(3, 7\) are coprime numbers.
Hence, \(\frac{3}{7}\) is in its simplest form as the highest common factor of the numerator, and the denominator is \(1\).
Q.2. Find the fractions in the simplest form from the following. \(\frac{3}{6},\,\frac{1}{3},\,\frac{2}{5},\,\frac{4}{6},\,\frac{5}{{15}}\)
Ans: Given fractions are, \(\frac{3}{6},\,\frac{1}{3},\,\frac{2}{5},\,\frac{4}{6},\,\frac{5}{{15}}\)
To find the simplest form, firstborn, we will find the greatest common factor of the numerator and the denominator of each fraction. The fractions whose HCF of the numerator and the denominator is only \(1\), crapper be said the fractions are in the simplest form.
In \(\frac{3}{6}\), the HCF of \(3,\,6\) is \(3.\)
In \(\frac{1}{3}\), 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 \(\frac{5}{15}\), the HCF of \(5, 15\) is \(5.\)
Hence, \(\frac{1}{3}\) and \(\frac{2}{5}\) are in their simplest form.
Q.3. What is the simplified form of the fraction \(\frac{144}{36}\)?
Ans: The given fraction is \(\frac{144}{36}\)
We need to observe the lowest frame operating theatre the simplest form of the given fraction.
Now, the highest common factor of \(144, 36\) is \(36.\)
So, \(\frac{{144 \div 36}}{{36 \div 36}} = \frac{4}{1} = 4.\)
Thence, the simplest form is \(4.\)
Q.4. Is \(\frac{5}{15}\) the lowest form of \(\frac{25}{75}\) ?
Ans: Atomic number 102, \(\frac{5}{15}\) is the not lowest form of \(\frac{25}{75}.\)
\(\frac{5}{15}\) buttocks be easy again if we divide the numerator and the denominator away \(5\).
So, the lowest form of \(\frac{25}{75}\) is \(\frac{1}{3}\), as \(\frac{{25 \div 25}}{{75 \div 25}} = \frac{1}{3}.\)
Hence, \(\frac{5}{15}\) is not the lowest form of \(\frac{25}{75}.\)
Q.5. What is the simplest form of the fraction \(\frac{2}{5}\) ?
Ans: Presumption fractions is \(\frac{2}{5}.\)
The numerator is \(2\) and the denominator is \(5.\) To check whether the fraction is in its simplest form or not, we will find the HCF of \(2, 5.\)
Like a sho, HCF \((2, 5)=1\) as \(2, 5\) are coprime numbers.
Therefore, \(\frac{2}{5}\) is in its simplest form, and we can not reduce or simplify more.
Summary
In this article, we covered the definition of the divide, types of fractions, the simplest form of a fraction, ways to identify the fraction is in its simplest form or non and how to find the simplest anatomy of a fraction.
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Frequently Asked Questions (FAQ) – Divide in Simplest Form
Q.1. How do you express the fractions in the simplest form?
Ans: First, we will find the highest common factor (HCF) of the numerator and denominator of the given divide. If the HCF is \(1\) so, the divide is in its simplest form. If the HCF is other than \(1\) then, divide both the numerator and denominator by HCF, get the simplest take shape of the fraction.
Q.2. What is the difference between the simplest form of a fraction and the eq fractions?
Ans: The simplest form of a fraction is as wel an equivalent fraction, but the ways to find the equivalent fraction and the simplest contour of a fraction are a trifle fleck different. If we multiply or divide the numerator and the denominator of a fraction past the same cardinal turn, we will fix the equivalent fractions. Now, to find the simplest form of a fraction, we need to divide the numerator and the denominator past the HCF of the numerator and the denominator.
Q.3. Explain the fraction in simplest form with example.
Ans: A fraction is said to be in its simplest organise if \(1\) is the only common measure of its numerator and denominator. So, a fraction can not personify aforementioned in its simplest form if the numerator and the denominator have a common agent separate than \(1\). For example, \(\frac{3}{4}\) is in its simplest form as \(1\) is the only common factor of \(3\) and \(4\) in this fraction.
Q.4. Sack we find the simplest work of a fraction by multiplying the numerator and the denominator by the same not-0 number?
Ans: Nary, we arse not. We can stick the lowest or the simplest sort of a divide by dividing the numerator and the denominator by the HCF of the numerator and the denominator.
Q.5. What is the simplest fraction form of \(1.33\) ?
Ans: The divide take shape of the decimal number \(1.33\) is \(\frac{{133}}{{100}}\).
\(100\) and \(133\) are the coprime number and its HCF is \(1\).
Therefore, the simplest fraction form of the given decimal number is \(\frac{{133}}{{100}}\).
Now that you are provided with a detailed article on the simplest form of a fraction, we hope totally your doubts are clean-handed on this topic. If you have any queries or questions, you can ask them in the notice box downstairs. We will be more than happy to help you. Outflank of luck with your studies!
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what is 62.5 as a fraction in simplest form
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