What Is Fraction?

Fractions are an integral part of mathematics. Learning about fractions can teach us a lot about the quantity of any object and how much of any object is included or excluded. Fractions can be understood by imagining real-life experiences like Suppose you are cutting a birthday cake into some number of slices. These slices are nothing but a fraction or part of the cake (whole). The actual meaning of fractions is broken, even though we will learn fractions from a mathematical point of view. “/” is the symbol of fractions. For example, 3/7 means 3 is the numerator (upper part) and 7 is the denominator (lower part). 

Table Of Contents

1. Definition Of Fractions
2. Types Of Fractions
3. Operations On Fractions

• • Addition
  • Subtraction
  • Multiplication
  • Division

1. Conversion Of Fractions Into Decimal
2. FAQs
3. Conclusion
4. Reference

Definition Of Fractions

A fraction is made up of two parts. The numeric value at the top is known as a numerator, which gives us an idea about how many equal divisions of a whole object or complete value are taken. The numeric value at the bottom is known as the denominator, which gives us an idea of the total number of parts that are divisible from the whole and thus possible. 

Types Of Fractions

Equivalent Fractions

Fractions that produce the same value even after being simplified are called equivalent fractions. We can get an equivalent fraction of any fraction by either multiplying it with the same number or dividing it with the same number. 

Suppose, you find the equivalent fractions of 5/9.

Let us multiply the numerator and denominator by the same number 3.

5*3/9*3 = 15/27.

So, 15/27 is the equivalent fraction of 5/9.

Proper Fractions

A proper fraction is a term that is used by a fraction whose numerator value is numerically less than its denominator value.

For example, 3/7, 5/8, 1/5, are some proper fractions, etc. 

Improper Fractions

An improper fraction is a term that is used by a fraction whose numerator value is numerically greater than its denominator value.

For example, 8/7, 5/3, 6/5, etc. 

Mixed Fractions

A mixed fraction is formed by a whole number and a proper fraction together. These can be converted into proper or improper fractions.

For example, 3 ⅗  where 3 is a whole number, but 3/5  is a proper fraction.

Operation On Fractions

Addition

If p/q and r/s are two different fractions, then to perform the addition operation of p/q and r/s will be:

If the denominators q and s are the same, then p + r / s will be the answer.

If the denominators q and s are different, then the LCM of q and s is taken. 

For example, 2/3  + 3/4 = LCM of 4 and 3 = 12. So, now multiplying both the fractions by the LCM will give the answer. 

2/3  * 12 and 3/4  * 12 = 8/12 + 9/12 = 17/12.

Subtraction

If p/q and r/s are two different fractions, then to perform the subtraction operation of p/q and r/s will be:

If the denominators q and s are the same, then p – r / s will be the answer.

If the denominators q and s are different, then the LCM of q and s are taken. 

For example, 2/3  – 3/4 = LCM of 4 and 3 = 12. So, now multiplying both the fraction by the LCM will give the answer. 

2/3  * 12 and 3/4  * 12 = 8/12 – 9/12 = -1/12.

Multiplication

If p/q and r/s are two different fractions, then performing the multiplication operation on p/q and r/s will be:

(p/q) x (r/s) = (pxr)/(qxs) = (pr/qs)

For example, multiply 3/4 by 2/5.

(3/4) * (2/5) => 6/20 => 3/10.

Division

If p/q and r/s are two different fractions, then to perform the division operation p/q by r/s can only be done by:

(p/q)÷(r/s) = (p/q)x(s/r) = (ps/qr)

For example, divide 3/4  with 2/5.

(3/4) / (2/5) => (3/4) * (5/2) => 15/8.

Conversion Of Fractions Into Decimals

As we all know, fractions are made up of numerators and a denominator. A numerator is being divided by the denominator. If we divide the numerator with the denominator, we will get a group of numbers separated by a decimal point. This is called a decimal number. 

For example, a fraction 3/8 can be written as 0.375 in its decimal form.

There is a great advantage to using the decimal form of fractions because performing logical and arithmetic operations is very easy, like addition, subtraction, division, and multiplication between any two decimal numbers. 

For example, adding two fractions 2/3 and 1/4. 2/3  can be written as 0.66 and 1/4 can be written as 0.25, and we can easily add them 0.25 + 0.66 = 0.91. 

Conclusion

Fractions are the mathematical concepts that explain the division or sharing of any object or group of objects in between two or more people. Each one of us has witnessed the daily life use of fractions. Whenever we buy any pizza at a celebration, we share it with our friends by cutting it with a knife into an equal pie. This division of pizza slices from a whole pizza into many pieces is a fraction.