CHAPTER 3

FRACTION:The term fraction is derived from the latin word fractus meaning broken.

TYPES OF FRACTION:

Simple fraction / Vulgar fraction :

Complex fraction:

Complex fractions are those fractions in which either numerator or denominator or both are fractions.

Decimal fraction: A fraction whose denominator is a multiple of 10, i.e of the form 10n , n N is called a decimal fraction.

Like fractions: Fractions having the same denominator but different numerators are called like fractions.

Unlike fractions :Fractions having different denominators are called unlike fractions.

Equivalent fractions:When numerator anddenominator of a fraction are multiplied or divided by the same non- zero number,we get equivalent fraction.

SIMPLEST FORM OF A FRACTION: If the fraction is in the form in which a and b have no common factor other than 1 and b ≠ 0 then the fraction is said to be in its simplest or lowest form.

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In order to convert unlike fractions into like fractions,following steps must be performed:1.Find the LCM of the denominators.2.Convert each fraction into an equivalent fraction having denominator equal to the LCMobtained in step 1.

Comparison Of Fractions: While comparing like fractions, we simply compare their numerators as the denominators are the same.

Note: When two fractions having the same denominator are compared, then the fraction with the greater numerator will be greater fraction.

If the fractions are unlike then wefirst convert unlike fractions intolike fractions and then compare.

INSERTING A FRACTION BETWEEN TWO FRACTIONS:If and are two fractions, then lies between these two fractions.We observe that the numerator of the required fraction is the sum of the numerators of the given fraction and the denominators is the sum of the denominators of the given fractions.

similarly, we can again find a fraction lying between and by this process. Thus there is no end to it. hence, the number of fractions lying between any two given fractions is infinite.

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EXAMPLE:

OPERATIONS ON FRACTIONS:Addition of Fractions:

In order to add fractions, follow these steps:1.Convert the mixed fraction( if any) into improper fractions.2. Convert the fractions into like fractions and then add the numerators, keeping the same denominator.

Subtraction of Fractions:In order to subtract fractions, follow these steps:1.Convert the mixed fraction( if any) into improper fractions.2. Convert the fractions into like fractions and then subtract thenumerators , keepingthe same denominator.

Multiplication of Fractions:In order to multiply fractions, follow these steps:1.Convert the mixed fraction( if any) into improper fraction.2.The product = numerator x numerator / denominator x denominator.3.Reduce the fraction into lowest form.4. Convert the fraction into mixed fraction in case the product is an improper fraction.

Reciprocal of a Fraction:

Two fractions are said to be the reciprocal of each other if their product is 1.

Note: Reciprocal is the multiplicative inverse and not the additive inverse.

Division of Fractions:In order to divide fractions, follow these steps:1.Convert the mixed fraction( if any) into improper fraction.2.Multiply the dividend by the reciprocal of the divisor.3.Reduce the fraction into its lowest form.4. Convert the fraction into mixed fraction in case the fraction is an improper fraction

CONVERSION OF COMPLEX FRACTIONS INTO SIMPLE FRACTIONS:

SIMPLIFICATION OF EXPRESSIONS INVOLVING FRACTIONS:In order to simplify expressions invoving fractions, we use the rule of 'BODMAS'. All the operations are to be done in order of the letters of the word.The brackets are to be removed in order as given below.

FOR MORE REFERENCE REFER THE FOLLOWING LINKS:https://youtu.be/iZteNiM1PUshttps://youtu.be/RNt8CKGnPkohttps://youtu.be/DMo7W9rE85Yhttps://youtu.be/a5YIPjhY6ykhttps://youtu.be/QyxXqP5y2wI

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