1 1/4 As A Fraction

Functioning on Fractions: Definition, Nomenclature, Examples

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A fraction is a part of a whole quantity. When we divide a whole quantity into equal parts, each part is called a fraction. A fraction has 2 parts, the numerator and the denominator. A fraction is written as \(\frac{a}{b}, a\) and \(b\) are whole numbers, and \(b\) should not be zero. The dissimilar operations on fractions are addition, subtraction, multiplication, and partitioning on fractions.

Operating fractions is different from operating whole numbers, natural numbers, and integers. Let's wait at the steps involved in performing the diverse mathematical operations on fractions. Continue reading to learn more!

Definition of Fractions

A fraction is a number that represents a part of the whole. The whole may be a unmarried object or multiple objects. A fraction is written as \(\frac{x}{y}\) where \(x\) and \(y\) are whole numbers and \(y \neq 0\). Numbers such every bit \(\frac{1}{9}, \frac{2}{15}, \frac{xiv}{9}, 2 \frac{eleven}{7}\) are known as the fractions.

Classification of Fractions

The classification of fractions are as follows:

1. Proper Fractions and Improper Fractions

In a proper fraction, the numerator is e'er smaller than the denominator. For example, \(\frac{7}{10}, \frac{2}{4}, \frac{ane}{six}, \frac{3}{20}, \frac{21}{25}\) are the proper fractions.

In an improper fraction, the numerator is always greater than or equal to the denominator. For case, \(\frac{xiii}{2}, \frac{17}{four}, \frac{6}{5}, \frac{15}{eleven}, \frac{10}{ten}\) are the improper fractions.

ii. Mixed Fractions

A mixed fraction is a fraction that is a combination of both whole and part fractions in the same fraction. A mixed fraction has a value that is e'er greater than one.

For example, \(one \frac{1}{2}, two \frac{iii}{four}, 5 \frac{5}{6}\) are the mixed fractions.

3. Similar Fractions and Unlike Fractions

The group of two or more fractions with the aforementioned denominators or identical denominators are called like fractions. For examples, \(\frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{4}{half-dozen}, \frac{7}{half-dozen}\), etc., are all like fractions.

The grouping of ii or more fractions that have dissimilar denominators are dissimilar fractions. For examples, \(\frac{1}{6}, \frac{2}{4}, \frac{2}{5}, \frac{4}{7}, \frac{v}{eight}\), etc., are all unlike fractions.

Add-on of Fractions

The add-on is one of the fundamental operations that are also applicable to fractions. In that location are several methods of addition of fractions. Let us know about them.

Addition of Like Fractions

We know that the like fractions have identical denominators. To add together the like fractions, add the values of the numerators, keeping the denominators the same.

Case: \(\frac{3}{5}+\frac{1}{5}\)

Here, given fractions have the same denominator, \(5\). We will keep the denominator the aforementioned for the result and add the numerator to find the numerator of the result.

Therefore, \(\frac{iii}{5}+\frac{1}{5}=\frac{3+1}{5}=\frac{4}{v}\)

Addition of Unlike Fractions

We know that unlike fractions have dissimilar denominators. So, we need to convert the, dissimilar fractions into like fractions. It means the fractions must have identical denominators.

To add together the different fractions, we need to follow some steps.

Detect the LCM of the denominators of the given unlike fractions
Change the denominators into the obtained LCM. This procedure tin change the numerators of the given, unlike fractions.
Now, add together the numerators.

Example: \(\frac{4}{7}+\frac{two}{three}\)

LCM of \((7,three)\) is \(21\).
To brand the denominator \(21\), nosotros need to multiply the numerator and the denominator of \(\frac{4}{vii}\) by \(iii\). Then, we become
\(\frac{four}{7} \times \frac{3}{3}=\frac{12}{21}\)
To make the denominator of \(\frac{2}{3}\) to \(21\), we need to multiply the numerator and the denominator by \(7\). And then, nosotros get
\(\frac{two}{3} \times \frac{seven}{7}=\frac{xiv}{21}\)
Now, \(\frac{4}{7}, \frac{ii}{iii}\) are converted to similar fractions that is \(\frac{12}{21}, \frac{14}{21}\) respectively.
Now, we tin add together them in a similar way to adding like fractions.
\(\frac{12}{21}+\frac{xiv}{21}=\frac{12+xiv}{21}=\frac{26}{21}\)

Subtraction of Fractions

We have discussed the addition of fractions. Similarly, nosotros can subtract fractions. Let us see the subtraction of like and unlike fractions.

Subtraction of Like Fractions

Subtraction of like fractions is similar to the addition of the similar fractions. To subtract the like fractions, subtract the values of the numerators, keeping the denominators the same.

Case: \(\frac{3}{four}-\frac{2}{4}\)

Here, given fractions have the aforementioned denominator \(iv\). We volition go along the denominator the aforementioned for the result and subtract the numerators to find the numerator of the issue.

Therefore, \(\frac{3}{4}-\frac{2}{four}=\frac{3-2}{four}=\frac{1}{4}\)

Subtraction of Unlike fractions

Here, we volition follow the same steps which we followed in the addition of unlike fractions. Just instead of adding numerators, nosotros will subtract them.

Allow the states learn the steps:

Find the LCM of the denominators of the given different fractions
Change the denominators into the obtained LCM. This process can change the numerators of the given, unlike fractions.
Now, subtract the numerators.

Case: \(\frac{5}{8}-\frac{3}{64}\)

LCM of \((8,64)\) is \(64\).
To make the denominator \(64\), nosotros demand to multiply the numerator and the denominator of \(\frac{v}{8}\) past \(eight\). And so, we become \(\frac{5}{8} \times \frac{8}{8}=\frac{40}{64}\)

Now, \(\frac{40}{64}\) and \(\frac{iii}{64}\) are like fractions equally they take the same denominators.

Therefore, \(\frac{40}{64}-\frac{3}{64}=\frac{37}{64}\)

Multiplication of Fractions

The numerators and denominators of ii fractions are multiplied separately when they are multiplied. The first fraction's numerator will be multiplied past the 2nd's numerator, and the first fraction's denominator will be multiplied past the 2d's denominator. In the end, we will reduce the fraction to its lowest form if information technology is required.

Instance:

The production of \(\frac{two}{3}\) and \(\frac{i}{2}\) is determined by multiplying the numerators and denominators separately.
\(\Rightarrow \frac{2}{three} \times \frac{1}{2}=\frac{2}{vi}\)
Here, \(\frac{ii}{half dozen}\) is not in its simplest form equally the HCF of the numerator and the denominator is not \(1\)
HCF \((2, 6)=2\)
Nosotros can reduce the fraction to its everyman class past dividing the numerator and the denominator by \(ii\). Thus, \(\frac{ii \div 2}{6 \div 2}=\frac{one}{iii}\)

Division of Fractions

Dividing the fraction past another fraction is multiplying the first fraction by the reciprocal of the 2nd fraction. Let us larn the following steps of the division of fractions.

Nosotros will continue the showtime fraction the same, and we need to make up one's mind the reciprocal of the second fraction.
Change the partitioning sign by multiplication sign and multiply the commencement fraction with the reciprocal of the 2nd fraction.
Find the simplest form of the fraction, if needed.

Example: \(\frac{4}{15} \div \frac{2}{three}\)

Here, the reciprocal of the 2d fraction \(\left(\frac{2}{3}\right)\) is obtained by interchanging denominator and numerator and we get, \(\frac{iii}{2}\).
And then, \(\frac{4}{fifteen} \div \frac{2}{iii}\) can be written as \(\frac{four}{15} \times \frac{3}{two}=\frac{12}{thirty}\).

Hither, \(\frac{12}{30}\) is non in its simplest grade equally the HCF of the numerator and the denominator is not \(ane\)
HCF \((12,30)=vi\)
We can reduce the fraction to its lowest form by dividing the numerator and the denominator past \(six\). Thus, \(\frac{12 \div vi}{30 \div 6}=\frac{2}{v}\).

Solved Examples on Operation on Fractions

Q.1. A stick of length \(5 \mathrm{~m}\) is cutting into the small sticks of length \(\frac{ane}{5} \mathrm{~thousand}\) each. How
many small-scale sticks tin can be cut?
Ans: The number of pocket-size rods \(=v \div \frac{i}{5}\)
\(=five \times \frac{5}{1} \) (Reciprocal of \(\frac{one}{5}\) is \(five\))
\(=25\) small-scale sticks

Q.2. Solve \(\frac{9}{12}-\frac{7}{12}\)
Ans: We have \(\frac{9}{12}-\frac{vii}{12}\)
Here, given fractions have the same denominator \(12\). We will keep the denominator the aforementioned for the event and subtract the numerators to find the numerator of the issue.
\(\frac{9}{12}-\frac{7}{12}=\frac{9-7}{12}\)
\(=\frac{two}{12}\)
\( = \frac{{2 \div 2}}{{12 \div 2}}\) (Dividing the numerator and denominator past their HCF \(2\))
\(=\frac{1}{6}\)
Hence, the obtained fraction is \(\frac{1}{6}\).

Q.three. Harsha was given \(\frac{3}{v}\) of a basket of apples. What portion of apples has been left in the basket?
Ans: Harsha was given \(\frac{3}{v}\) of a basket of apples.
We need to observe the fraction of apples was left in the basket.
Then, \(ane-\frac{3}{5}=\frac{one}{1}-\frac{3}{5}\)
\(=\frac{i \times v}{one \times 5}-\frac{iii}{5}=\frac{5}{5}-\frac{iii}{five}\)
\(=\frac{five-3}{5}=\frac{2}{5}\)
Hence, the fraction of apples left in the basket was \(\frac{ii}{v}\).

Q.four. Solve \(\frac{five}{6} \times \frac{9}{10}\).
Ans: Given \(\frac{5}{six} \times \frac{9}{10}\)
The product of \(\frac{five}{six}\) and \(\frac{nine}{10}\) is determined by multiplying the numerators and denominators separately.
\(\frac{five}{6} \times \frac{9}{x}=\frac{5 \times nine}{6 \times 10}=\frac{45}{lx}\)
HCF \((45,60)=15\)
Therefore, \(\frac{45 \div 15}{60 \div 15}=\frac{3}{4}\).

Q.5. Solve \(2 \frac{3}{five}+\frac{4}{v}+1 \frac{2}{5}\)
Ans: Given, \(2 \frac{3}{v}+\frac{4}{5}+1 \frac{ii}{5}\)
\(=\frac{10+3}{v}+\frac{4}{v}+\frac{5+2}{v}\)
Hither, given fractions accept the aforementioned denominator, \(five\). We volition keep the denominator the same for the result and add the numerator to find the numerator of the effect.
\(=\frac{13}{v}+\frac{4}{v}+\frac{7}{v}\)
\(=\frac{13+4+7}{5}=\frac{24}{5}\)

Summary

In this article, we studied fractions, the different types of fractions, and the central operations of fractions like add-on, subtraction of like and unlike fractions. One can perform basic arithmetic operations similar addition, subtraction, multiplication, and partitioning on fractions. A fraction can exist defined as a number that represents a part of the whole. A fraction is represented as \(\frac{ten}{y}\) where \(ten\) and \(y\) are whole numbers. Some of the examples of fractions are \(\frac{2}{three}, \frac{iii}{xvi}, etc.

FAQs on Operations on Fractions

Q.one. What are the four operations of fractions?
Ans: The four operations of fractions are:
i. Add-on
ii. Subtraction
3. Multiplication
4. Division

Q.ii. How will y'all add like fractions?
Ans: To add two or more like fractions, nosotros may follow the following steps:
Step 1: Get the fractions.
Step ii: Add the numerators of all fractions.
Step 3: Maintain the common denominator of all fractions.
Step iv: Write down the fraction as \(\frac{\text { Result in Step 2 }}{\text { Result in Step 3. }}\).

Q.iii. How to add or decrease, dissimilar fractions?
Ans:1. Observe the LCM of the denominators of the given different fractions
2. Alter the denominators into the obtained LCM. This process tin can change the numerators of the given, different fractions.
3. Now, add or decrease the numerators.

Q.four. How to multiply two fractions?
Ans: The numerators and denominators of 2 fractions are multiplied separately when they are multiplied. The first fraction's numerator will exist multiplied past the second'southward numerator, and the first fraction'southward denominator will be multiplied by the second's denominator. In the terminate, we will reduce the fraction to its lowest form if it is required. For example, \(\frac{2}{3} \times \frac{4}{seven}=\frac{2 \times iv}{3 \times seven}=\frac{8}{21}\)

Q.five. How to separate a fraction past a fraction?
Ans: 1. Nosotros volition continue the kickoff fraction the same, and we demand to make up one's mind the reciprocal of the second fraction.
2. Change the division sign by multiplication sign and multiply the first fraction with the reciprocal of the second fraction.
3. Notice the simplest form of the fraction, if needed.

We hope this detailed article on operations on fractions helped you in your studies. If yous have whatsoever doubts, queries or suggestions regarding this article, feel free to ask united states in the comment section and we volition be more happy to assist you. Happy learning!