Understanding Fraction Conversion in Maths

When a complete item is divided into equal pieces, each component is referred to as a fraction. A fraction, in other terms, is a portion of the total. A fraction is composed of two parts: the numerator and the denominator. It is written as a numerator/denominator. The numerator indicates how many total factors are taken, whereas the denominator indicates the total number of equal parts.

What is a Mixed Fraction? 

Improper fractions are represented more simply using mixed numbers. Improper Fraction: Do you know what it is? A fraction is referred to be an improper fraction if it cannot be further simplified and has a numerator that is more than or equal to the denominator. A mixed fraction is one generated by mixing a whole number and a fraction. Conversion of fraction example: if 3 is a whole number and \[\dfrac{5}{9}\] is the fraction part then, \[3\dfrac{5}{9}\] is the mixed fraction.

Conversion of Improper Fraction Into a Mixed Fraction(Mixed Number Converter)

An improper fraction has a numerator greater than a denominator. In order to convert this fraction into a mixed fraction, we can follow the following steps. 

• Step one- Divide the fraction (numerator divided by denominator) 

• Step two- Obtain the remainder. 

• Step three- The whole number part of the mixed fraction would be the quotient obtained after dividing and the numerator part will be the remainder, which we got in step two. In this, the denominator(divisor) will remain the same.

Example – \[\dfrac{12}{5}\] will have 2 as a remainder and 2 as the quotient. So, the mixed fraction would be \[2\dfrac{2}{5}\].

Converting Improper Fraction to Mixed Fraction

Conversion of Mixed Fraction Into an Improper Fraction 

The mixed fraction can be changed easily into an improper fraction by following the given steps. 

• Step one- Multiple the denominator with the whole number part of the equation. 

• Step two- The product obtained will then be added to the numerator of the given mixed fraction. 

• Step three- The result we got would be the numerator of the improper fraction and the denominator would remain. 

Example- \[7\dfrac{2}{3}\] in this mixed fraction we will multiply 3 and 7 and the product we will get is 21 which will then be added to 2 giving the result as 23. So, the improper fraction will turn out as \[\dfrac{23}{3}\].

Methods of Reduction of Different Fractions 

The methods through which the complex fraction can be changed into the simplest form so that it further can be divided. There are different methods by which the fraction can be reduced. By dividing the numerator and denominator by a common divisor until the common factor equals 1, we may simplify fractions by reducing them. To put it another way, a fraction can only be divided by 1 or another whole integer. Consider the fraction 8/24 as an illustration. Here is how to decrease the fraction step by step.

• Step 1: Write the denominator and numerator's factors in Step 1. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 while the factors of 8 are 1, 2, 4, and 8.

• Step 2: The second step is to identify the shared factors between the numerator and the denominator. 1, 2, 4, and 8 are the factors that 8 and 24 have in common.

• Step 3: Subtract the common factors from the numerator and denominator until there is only one common factor remaining: 1. This gives you the fraction in its reduced form.

Let's start dividing by 2: \[\dfrac{{8}}{{24}} = \dfrac{{8 \div 2}}{{24 \div 2}} = \dfrac{4}{12}\]. We will continue to divide by 2 until we can't go any further. So, we have \[\dfrac{{4 \div 2}}{{12 \div 2}} = \dfrac{2}{6} = \dfrac{{2 \div 2}}{{6 \div 2}} = \dfrac{1}{3}\].

Therefore, the reduced form of \[\dfrac{8}{{24}}\]is \[\dfrac{1}{{3}}\].

Tips for Reducing Fractions

So you now understand the different methods for reducing a fraction to its simplest form. Here are some tips to assist you in fast-reducing fractions. When reducing fractions to their simplest form, use these techniques.

• If a fraction's numerator or denominator is a prime number, the fraction cannot be simplified anymore.

• A fraction with 1 in the numerator cannot be further lowered.

• To simplify an improper fraction, first, express it as a mixed fraction and then simplify it as you would a proper fraction.

• For application of any arithmetic operation convert into like fraction so that they have the same denominator. 

Sample Questions

1) Convert  \[4\dfrac{1}{3}\] into an improper fraction. 

Ans) 

• The first step is to multiply the denominator by the whole number component of the equation.

• Step two is to add the resulting product to the numerator of the current mixed fraction.

• Step three- the outcome would be the improper fraction's numerator and the denominator would remain.

\[\begin{array}{l}4\dfrac{1}{3} = 3 \times 4 + 1 = 13\\ = \dfrac{{13}}{3}\end{array}\]

2) Convert \[\dfrac{16}{5}\] into a mixed fraction. 

Ans) 

• Step one: divide the numerator by the denominator  

• Step two: get the remainder

• Step three: The quotient produced after dividing the whole number component of the mixed fraction will be the numerator part, which we received in step two. The denominator (divisor) will remain constant in this case.

\[\dfrac{{16}}{5} = 16 \div 5 = 3\]

Remainder = 1 

Fraction \[3\dfrac{1}{5}\]

3) Add \[1\dfrac{3}{4}\] and \[2\dfrac{5}{6}\]. 

Ans) 

• Convert the mixed fraction into an improper fraction. 

• As the denominators are different, take LCM and make the denominator the same. 

• Now add the numerator. 

\[\begin{array}{l}1\dfrac{3}{4} = \dfrac{7}{4}\\2\dfrac{5}{6} = \dfrac{{17}}{6}\end{array}\]

LCM of 4 and 6 is 12. 

\[\dfrac{{21}}{{12}} + \dfrac{{34}}{{12}} = \dfrac{{55}}{{12}}\]

4) Multiply \[3\dfrac{4}{7}\] and   \[4\dfrac{5}{9}\] .

Ans) Convert the mixed fraction into an improper fraction and then multiply the numerators and denominators separately. 

\[\begin{array}{l}3\dfrac{4}{7} = \dfrac{{25}}{7}\\4\dfrac{5}{9} = \dfrac{{41}}{9}\\\dfrac{{25}}{7} \times \dfrac{{41}}{9} = \dfrac{{1025}}{{63}}\end{array}\]

5) Reduce the fraction \[\dfrac{18}{81}\] by GCF method.

Ans) As the highest common factor is 9 for the given fraction, it needs to be divided by 9 to reduce it. 

 \[\begin{array}{l}\dfrac{{18}}{{81}}\\ = 18 \div 9,81 \div 9\\ = \dfrac{2}{9}\end{array}\]

6) Reduce the following fractions by the GCF method. a) 16/64, b) 18/81
Solution: We will use the GCF method to reduce fractions.
a) The greatest common factor of 16 and 64 is 16. Dividing the numerator and the denominator by 16, we get the fraction reduced to \[\dfrac{1}{4}\]. 

\[\dfrac{{16}}{{64}} = \dfrac{{16 \div 16}}{{64 \div 16}} = \dfrac{1}{4}\]

 Therefore, the reduced form of \[\dfrac{{16}}{{64}}\] is \[\dfrac{1}{4}\]

b) The greatest common factor of 18 and 81 is 9. Dividing the numerator and the denominator by 9, we get the fraction reduced to \[\dfrac{2}{9}\]

 \[\dfrac{{18}}{{81}} = \dfrac{{19 \div 9}}{{81 \div 9}} = \dfrac{2}{9}\]

 Therefore, the reduced form of \[\dfrac{{18}}{{81}}\] is \[\dfrac{2}{9}\].

Conclusion 

A fraction consists of a numerator and a denominator. The fraction can be like a fraction, unlike fractions and mixed fractions. The mixed fraction can be converted into an improper fraction or unlike fraction and vice versa. Like fraction is a fraction whose denominator is the same and is greater than the numerator.