What Is A Fractional Notation

In Mathematics, fractions are defined as the parts of a whole. The whole tin be an object or a group of objects. In existent life, when we cutting a slice of cake from the whole of it, then the portion is the fraction of the cake. A fraction is a word that is originated from Latin. In Latin, "Fractus" ways "broken".  In aboriginal times, the fraction was represented using words. Later, it was introduced in numerical class.

The fraction is too termed as a portion or section of any quantity. It is denoted by using '/' symbol, such as a/b. For example, in 2/iv is a fraction where the upper part denotes the numerator and the lower function is the denominator .  In this article, nosotros are going to acquire the definition of fractions in Maths, types of fractions, conversion from fractions to decimals, and many solved examples with consummate explanation.

What are Fractions?

Definition 1: A fraction represents a numerical value, which defines the parts of a whole.

Definition 2: A fraction is a number that represents a part of a whole.

Generally, the fraction tin be a portion of whatever quantity out of the whole thing and the whole tin can be whatever specific things or value.

The basics of fractions explain the top and bottom numbers of a fraction. The top number represents the number of selected or shaded parts of a whole whereas the lesser number represents the total number of parts.

Suppose a number has to be divided into four parts, then it is represented equally 10/4. So the fraction here, ten/four, defines 1/fourth of the number x. Hence, i/4 is the fraction here.  Information technology means one in four equal parts. It can exist read every bit ane-4th or 1/4. This is known equally fraction.

Fractions play an of import part in our daily lives. In that location are many examples of fractions yous volition come up across in real life. We accept to willingly or unwillingly share that yummy pizza among our friends and families. Three people, four slices. If you lot acquire and visualize fractions in an like shooting fish in a barrel way, it will be more than fun and heady. For example, slice an apple into 2 parts, then each function of the sliced apple will correspond a fraction (equal to one/2).

Parts of Fractions

The fractions include two parts, numerator and denominator.

• Numerator: It is the upper part of the fraction, that represents the sections of the fraction
• Denominator: It is the lower or bottom part that represents the total parts in which the fraction is divided.

Example: If 3/iv is a fraction, then iii is the numerator and 4 is the denominator.

Properties of Fractions

Similar to real numbers and whole numbers, a fractional number also holds some of the important properties. They are:

• Commutative and associative properties concur true for fractional addition and multiplication
• The identity element of fractional add-on is 0, and partial multiplication is 1
• The multiplicative inverse of a/b is b/a, where a and b should be non zero elements
• Fractional numbers obey the distributive property of multiplication over add-on

Types of Fractions

Based on the properties of numerator and denominator, fractions are sub-divided into different types. They are:

• Proper fractions
• Improper fractions
• Mixed fractions
• Like fractions
• Unlike fractions
• Equivalent fractions

Proper Fractions

The proper fractions are those where the numerator is less than the denominator. For example, 8/9 will be a proper fraction since "numerator < denominator".

Improper Fractions

The improper fraction is a fraction where the numerator happens to be greater than the denominator. For example, 9/8 will be an improper fraction since "numerator > denominator".

Mixed Fractions

A mixed fraction is a combination of the integer part and a proper fraction. These are also called mixed numbers or mixed numerals. For example:

Similar Fractions

Like fractions are those fractions, as the proper name suggests, that are alike or aforementioned.

For instance, take ½ and two/4; they are alike since if you simplify it mathematically, you lot will get the aforementioned fraction.

Unlike Fractions

Unlike fractions, are those that are dissimilar.

For example, ½ and 1/3 are unlike fractions.

Equivalent Fractions

2 fractions are equivalent to each other if afterward simplification either of two fractions is equal to the other one.

For example, ⅔ and four/half-dozen are equivalent fractions.

Since, 4/6 = (2×2)/(2×3) = 2/3

Unit Fractions

A fraction is known as a unit fraction when the numerator is equal to 1.

• One half of whole = ½
• I-tertiary of whole = 1/iii
• One-fourth of whole = ¼
• One-fifth of whole = ⅕

Fraction on a Number Line

We have already learned to represent the integers, such equally 0, 1, ii, -1, -2, on a number line. In the aforementioned way, we can stand for fractions on a number line.

For example, if we have to represent 1/5 and iii/v parts of a whole, and so information technology can be represented equally shown in the below effigy.

Since the denominator is equal to 5, thus ane is divided into 5 equal parts, on the number line. Now the first section is ane/5 and the 3rd section is 3/5.

Similarly, you can practice marking more than of the fractions on the number line, such as 1/ii, 1/four, ii/11, 3/7, etc.

Rules for Simplification of Fractions

There are some rules we should know earlier solving the bug based on fractions.

Rule #ane: Before calculation or subtracting fractions, we should make sure that the denominators are equal. Hence, the add-on and subtraction of fractions are possible with a common denominator.

Dominion #two: When we multiply two fractions, then the numerators are multiplied too as the denominators are multiplied. After simplify the fraction.

Dominion #iii: When we dissever a fraction from some other fraction, nosotros have to detect the reciprocal of another fraction and and then multiply with the first one to get the answer.

Adding Fractions

The improver of fractions is like shooting fish in a barrel when they have a mutual denominator.

For example, ⅔ + viii/3 = (2+viii)/three = 10/iii

Hence, we need to merely add the numerators hither.

Calculation Fractions with Different Denominators

If the denominators of the two fractions are dissimilar, nosotros have to simplify them by finding the LCM of denominators so making it common for both fractions.

Example: ⅔ + ¾

The two denominators are 3 and 4

Hence, LCM of three and 4 = 12

Therefore, multiplying ⅔ by iv/iv and ¾ by 3/3, we become;

8/12 + 9/12

= (8+9)/12

= 17/12

Subtracting Fractions

The rule for subtracting 2 or more fractions is the same as for improver. The denominators should be mutual to decrease two fractions.

Example: 9/ii – 7/2 = (ix-7)/2 = 2/two = 1

Subtracting with Different Denominators

If the denominators of the two fractions are different, we accept to simplify them by finding the LCM of denominators and and then making it common for both fractions.

Example: ⅔ – ¾

The two denominators are iii and four

Hence, LCM of 3 and 4 = 12

Therefore, multiplying ⅔ by 4/four and ¾ by 3/3, we get;

8/12 – 9/12

= (8-nine)/12

= -1/12

Multiplication of Fractions

As per rule number 2, nosotros have discussed in the previous section, when ii fractions are multiplied, so the top part (numerators) and the bottom office (denominators) are multiplied together.

If a/b and c/d are two unlike fractions, then the multiplication of a/b and c/d will exist:

(a/b) x (c/d) = (axc)/(bxd) = (air-conditioning/bd)

Example: Multiply ⅔ and 3/vii.

(⅔) 10 (three/vii) = (ii×3)/(3×vii) = 2/7

Division of Fractions

If nosotros have to split whatever two fractions, then nosotros will use here dominion three from the higher up department, where we need to multiply the get-go fraction to the reciprocal of the second fraction.

If a/b and c/d are two different fractions, and so the division a/b by c/d tin exist expressed every bit:

(a/b)÷(c/d) = (a/b)x(d/c) = (ad/bc)

Case: Split up ⅔ by 3/7.

(⅔) ÷ (iii/7) = (⅔) x (7/3) = (two×7)/(3×3) = fourteen/nine

Real-Life Examples of Fractions

Permit us visualize some of the fractions examples:

1. Imagine a pie with iv slices. Taking 2 slices of pie for yourself would mean that you have ii out of the four. Hence, you represent it as 2/4.
2. Fill one-half a glass of water. What exercise you see? i/2 glass is full. Or 1/ii glass is empty. This i/ii is fractions where 1 is the numerator that is, the number of parts we take. And 2 is the denominator, the number of parts the whole drinking glass is divided into.

How to Catechumen Fractions To Decimals?

As we already learned enough about fractions, which are function of a whole. The decimals are the numbers expressed in a decimal course which represents fractions, after division.

For example, Fraction i/two tin can be written in decimal grade as 0.v.

The best part of decimals are they can be hands used for whatever arithmetic operations such as add-on, subtraction, etc. Whereas information technology is difficult sometimes to perform operations on fractions. Let us take an instance to empathize;

Case: Add together one/6 and 1/4.

solution: 1/6 = 0.17 and 1/4 = 0.25

Hence, on adding 0.17 and 0.25, we get;

0.17 + 0.25 = 0.42

How to Simplify Fractions?

To simplify the fractions easily, start, write the factors of both numerator and denominator. Then find the largest factor that is common for both numerator and denominator. Then dissever both the numerator and the denominator by the greatest common factor (GCF) to go the reduced fraction, which is the simplest course of the given fraction. At present, permit us consider an case to detect the simplest fraction for the given fraction.

For example, take the fraction, 16/48

So, the factors of 16 are 1, 2, iv, 8, 16.

Similarly, the factors of 48 are 1, two, 3, 4, 6, 8, 12, 16, 24, 48.

Thus, the greatest common gene for sixteen and 48 is sixteen.

i.e. GCF (16, 48) = 16.

Now, divide both the numerator and denominator of the given fraction past sixteen, we get

16/48 = (sixteen/sixteen) / (48/16) = 1/3.

Hence, the simplest class of the fraction 16/48 is 1/3.

Solved Examples on Fractions

Example 1:

Is 12/6 a fraction?

Solution:

Yes, it is. Information technology is called an improper fraction.

Case two:

Catechumen 130.1200 into a fraction.

Solution:

Here will employ the concept of how to convert decimals into fractions

130.1200 = 130.1200/10000

= 13012/100

Example three:

Add together three/ 5 and ten/15.

Solution:

3 /5 + x/15

LCM of 5 and 15 is 15

= (nine + 10)/15

= nineteen/15

Example iv:

Which of the post-obit fraction is the largest?

(a) 29/23

(b) 29/27

(c) 29/25

(d) 29/30

Solution:

To detect whether the largest fractions amongst the given options, first catechumen the fractional value to the decimal value.

(a) 29/23 = i.261

(b) 29/27 = ane.074

(c) 29/25 = ane.16

(d) 29/30 = 0.967

Thus, 29/23 is the largest fraction amid the given options.

Hence, selection (a) 29/23 is the correct answer.

Example 5:

Reduce the fraction 15/65 to the simplest class.

Solution:

Given fraction: 15/65.

Factors of 15: ane, 3, 5 and 15

Factors of 65: one, five, xiii, and 65

Hence, the greatest common factor of 15 and 65 is v.

i.due east. GCF (fifteen, 65) = 5.

At present, divide both the numerator and the denominator of the given fraction (16/65) past 5, we become

15/65 = (15/5) / (65/5) = 3/13.

Hence, the simplest form of the fraction xv/65 is three/xiii.

Video Lesson

Understanding Fractions

Exercise Questions on Fractions

Solve the post-obit:

1. 3/7+9/two-8.
2. 22/7+8/eleven.
3. 32/9 ten 81/iv.
4. 44/9 ÷ 36/iv.
5. Reduce 35/84 to the simplest class.
6. Convert the fraction 81/63 to the reduced form.

Fractions Related Articles

• Fractions Worksheet
• Fractions Calculator
• Types Of Fraction
• Add-on And Subtraction Of Fractions
• Dividing Fractions
• Multiplication of fractions

Frequently Asked Questions on Fractions

What are fractions in Maths?

Fractions are the numerical values that are a part of the whole. A whole can be an object or a group of objects. If a number or a affair is divided into equal parts, so each part will be a fraction of the whole. A fraction is denoted as a/b, where a is the numerator and b is the denominator.

How to solve fractions?

To add together or decrease fractions, we have to bank check if the denominators are the same or unlike. For the same denominators, nosotros can straight add or decrease the numerators, keeping the denominator common. Just if the denominators are different, so nosotros need to simplify them past finding the LCM.

What are the 3 types of fractions in Maths?

The 3 types of fractions in Maths are Proper fractions, Improper fractions, and Mixed fractions.

Requite existent-life examples of fractions.

If a watermelon is divided into four equal parts, then each part is a fraction of ¼.
Similarly, if a pizza is divided into three equal parts, then each office shows one/3rd of pizza.

What is a unit fraction?

A fraction with numerator ane is chosen a unit of measurement fraction. Examples are ½, ⅓, ¼, ⅕, 1/seven, 1/10, etc.

What Is A Fractional Notation,

Source: https://byjus.com/maths/fractions/

Posted by: porternoust1988.blogspot.com

Share this post