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(/home)EduRev (/explore?s=all)S$6 OFF (/Subscription?invite=EDUREV200&utm_medium=website&utm_source=upgrade_btn_hdr&utm_campaign=subscription_link)S$6 OFF (/Subscription?invite=EDUREV200&utm_medium=website&utm_source=upgrade_btn_hdr&utm_campaign=subscription_link)Table of Contents1.Introduction2.A Fraction3.Fractional Units as Parts of a Whole4.Measuring Using Fractional Units5.Reading FractionsView MoreIntroductionA fraction is a way to represent a part of a whole.Think of a pizza cut into two equal slices. If you divide the pizza into two equal slices, eachchild's share will be 12.Chapter Notes: FractionsLast Chance: Get S$6 off. Offer valid for today only! Usecode: EDUREV200Claim Offer(/Subscription?invite=EDUREV200&utm_source=top_banner_ad&utm_medium=edurev_website&utm_campaign=Get_additional_INR_200_off_today_with_EDUREV200_coupon_offer_banner_top)(/Subscription?invite=EDUREV200&utm_source=top_banner_ad&utm_medium=edurev_website&utm_campaign=Get_additional_INR_200_off_today_with_EDUREV200_coupon_offer_banner_top)

Now, if you divide the pizza into four equal slices, each child's share will be,  14.Fractions help us explain and understand situations where something is split into equalparts.Let us understand this concept better. A FractionA fraction means a part of a group or of a region.When we look at a fraction, it has two important numbers:1. Numerator (Top Number):

This tells us how many parts of the whole we have or are using.For example, in the fraction , the n
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(/home)EduRev (/explore?s=all)S$6 OFF (/Subscription?invite=EDUREV200&utm_medium=website&utm_source=upgrade_btn_hdr&utm_campaign=subscription_link)S$6 OFF (/Subscription?invite=EDUREV200&utm_medium=website&utm_source=upgrade_btn_hdr&utm_campaign=subscription_link)Table of Contents1.Introduction2.A Fraction3.Fractional Units as Parts of a Whole4.Measuring Using Fractional Units5.Reading FractionsView MoreIntroductionA fraction is a way to represent a part of a whole.Think of a pizza cut into two equal slices. If you divide the pizza into two equal slices, eachchild's share will be 12.Chapter Notes: FractionsLast Chance: Get S$6 off. Offer valid for today only! Usecode: EDUREV200Claim Offer(/Subscription?invite=EDUREV200&utm_source=top_banner_ad&utm_medium=edurev_website&utm_campaign=Get_additional_INR_200_off_today_with_EDUREV200_coupon_offer_banner_top)(/Subscription?invite=EDUREV200&utm_source=top_banner_ad&utm_medium=edurev_website&utm_campaign=Get_additional_INR_200_off_today_with_EDUREV200_coupon_offer_banner_top)

Now, if you divide the pizza into four equal slices, each child's share will be,  14.Fractions help us explain and understand situations where something is split into equalparts.Let us understand this concept better. A FractionA fraction means a part of a group or of a region.When we look at a fraction, it has two important numbers:1. Numerator (Top Number):

This tells us how many parts of the whole we have or are using.For example, in the fraction , the numerator is 5, meaning we have 5 partsout of the total.2. Denominator (Bottom Number):This tells us into how many equal parts the whole is divided.In , the denominator is 12, meaning the whole is divided into 12 equal parts.Let us understand fractions with the help of an example: Ethan is celebrating his birthday at home. His mother has baked a cake for his birthday.When his friends came home, she cut the cake. His mother wants to distribute the cakeequally among all his friends.There are six people (including Ethan's mother) at the party.So, his mother cuts the cake into 6 equal parts.Fractions of a CakeCan you tell what fraction of the cake Ethan gets?Total number of slices of cake = 6Ethan got (one-sixth) part of the cake. So, Ethan ate one part out of six parts of the cake.Here 1 is the numerator and 6 is the denominator.Fractional Units and Equal Shares

A fractional unit refers to a part of a whole that has been divided into equal sections.When we split something into equal parts, each part is known as a fractional unit.Understanding with ExampleConsider a chocolate bar that you wish to share with your friends. Suppose you have 1chocolate bar and 4 friends, including yourself, meaning you need to divide the chocolateinto 4 equal pieces.Each piece you receive is a fractional unit of the entire chocolate bar. In this case, asthe chocolate is split into 4 equal parts, each piece is 1/4 of the chocolate bar.

Now, let's examine a different scenario. You still have 1 chocolate bar, but this timeyou need to share it with 9 friends.If you share the chocolate bar into 9 equal parts, each piece will be 1/9 of thechocolate bar.Comparison: Which piece is larger, 1/4 or 1/9? When you divide the chocolate into 4parts, each piece is more significant because fewer people are sharing it. Thus, 1/4 islarger than 1/9.This example illustrates that as the number of parts  (denominator)  increases, eachfractional unit (or piece) becomes smaller.Knowledge from the Past: The History of Fractions in IndiaFractions have a rich history in India, originating from ancient times when they wereacknowledged and named in various texts.In the Rig Veda, one of the oldest texts in Indian literature, fractions were referred toas "tripada."This indicates that the terms for fractions used in modern Indian languages haveroots in ancient history.Overall, the current understanding and naming of fractions in India have a profoundhistorical background.

Get additional INR 200 off today with EDUREV200 coupon.Avail OfferFractional Units as Parts of a WholeA fractional unit is a single part of something that has been split into equal pieces. Whena whole is divided into equal parts, each part is known as a fractional unit of that whole.Imagine a traditional sweet called "chikki", which is a rectangular bar made from jaggeryand nuts. Let's say you have one whole chikki and want to split it into equal parts.Dividing the Chikki into 2 Parts:If you break the chikki into 2 equal pieces, each piece is 1/2 of the whole chikki.Here, the fractional unit is 1/2, meaning each piece represents half of the originalchikki.Dividing the Chikki into 6 Parts:

If you take the same chikki and break it into 6 equal pieces, each piece is 1/6 of thewhole chikki.Here, the fractional unit is 1/6, meaning each piece is one-sixth of the original chikki.Understanding Different Shapes: Sometimes, even if the pieces look different, they canstill be the same size. For instance, if you cut the chikki into 6 equal pieces, each piecemight appear different based on the cut, but each one remains 1/6 of the whole chikki.Proper and Improper Fractions:Fractions like 1/2 and 1/6 are called proper fractions because the numerator is less thanthe denominator. When the numerator is greater than or equal to the denominator, thefraction is called an improper fraction, for example 5/4 or 3/2.Multiplying Whole Numbers with Fractions:

To multiply a whole number by a proper or improper fraction, multiply the whole numberby the numerator of the fraction and then divide by the denominator. Example: Farida has 20 marbles and Reshma has 1/5 of that number. How many marblesdoes Reshma have?Reshma has 1/5 × 20 = 4 marbles.Measuring Using Fractional UnitsMeasuring using fractional units involves dividing a whole object or quantity into smaller,equal parts to make measurement easier. When something is too large to measure in onepiece, we use fractional units like 1/2, 1/4, etc., to describe parts precisely. Example: Imagine you have a strip of paper that is one unit long. If you fold this strip intotwo equal parts, each part is now 1/2 (one-half) of the original strip. If you fold it againinto four equal parts, each part becomes 1/4 (one-quarter) of the original strip.Now, consider a whole roti (a round flatbread). If you cut the roti into two equal parts,each part is 1/2 of the whole roti. If you cut it into four equal parts, each part is 1/4 of thewhole roti.This method of using fractional units like 1/2, 1/4, and so on helps us measure anddescribe parts of a whole.Reading FractionsFractions can be read in different ways. For example, 3/4 can be read as "threequarters" or "three upon four."Reading 3/4 as "three times one-fourth" emphasises that the fractional unit is 1/4and there are 3 such units.

In a fraction, the top number is the numerator, and the bottom number is thedenominator. For example, in the fraction 5/6, 5 is the numerator, and 6 is thedenominator.Practical Applications of FractionsFractions are used in many everyday situations. For example:When cooking, recipes may require ingredients in fractional amounts, such as 1/2cup of sugar or 3/4 teaspoon of salt.Fractions are also important in measuring distances, like when a carpenter measuresa piece of wood to be cut into 1/3 of its length.Understanding fractions allows us to make accurate measurements and calculations indaily tasks.Marking Fraction Lengths on the Number LineFractions can be represented on a number line, just like whole numbers.To represent afraction between 0 and 1, divide the segment from 0 to 1 into as many equal parts as thedenominator of the fraction, then count the numerator number of parts from 0. Forexample, to represent 1/8 on the number line, we have to divide 0 to 1 into 8 equal partsand mark the first part as 1/8. How to place a fraction like 3/7 on a number line:1. Understand the Number Line Basics:A number line is a straight line where numbers are placed at equal distances.Whole numbers like 0, 1, 2, etc., are marked on this line.2. Identify the Fraction to Show:For example, you want to show the fraction 3/7.This fraction means you have 3 parts out of 7 equal parts.

3. Divide the Length Between 0 and 1:Since the denominator is 7, divide the length between 0 and 1 into 7 equal parts.4. Mark the Fraction:Count 3 parts from 0. The point where you stop is 3/7 on the number line.Mark this point as "P" to show 3/7.5. Mark Other Related Fractions:0/7: This is simply 0, so mark it at the starting point of the line.7/7: Since 77 is equal to 1, mark it at the point where 1 is on the number line.Examples:Consider a fraction 1/2.1/2 is greater than 0, but less than 1. Divide the space between 0 and 1 into twoequal parts. We can show one part as the fraction 1/2Consider another 1/5.1/5 fraction is greater than 0, but less than 1. Divide the space between 0 and 1 intofive equal parts. We can show the first part as 1/5 the second as 2/5 the third as3/5 the fourth as 4/5 and the fifth part as 5/5=1.

Understanding Improper FractionsA fraction where the numerator (the top number) is larger than the denominator(the bottom number). This means the fraction represents a quantity greater than orequal to 1.Example: 9/5 is an improper fraction because 9 > 5. It means 9 parts each of size 1/5;this equals 1 whole and 4/5 remaining.So, 9/5 = 1 + 4/5.Mixed FractionsA mixed fraction combines a whole number with a proper fraction. It shows howmany whole parts there are, along with a fraction of another part.For example, if you have 1 whole pizza and an additional half, it can be written as amixed fraction: 1 1/2. This means you have 1 whole pizza plus another 1/2 pizza.

Writing Fractions Greater Than One as MixedNumbers (and vice versa)When we encounter a fraction that is more than one, we can express it as a mixednumber. A mixed number combines a whole number with a fraction, which helps toillustrate how many whole parts we have and what fraction remains.Improper Fractions 1. Conversion of improper fraction into mixed fraction An improper fraction can be expressed as mixed fraction by dividing the numerator by thedenominator of the improper fraction to obtain the quotient and the remainder. Divide the Numerator by the Denominator:The numerator is the number on top, and the denominator is the number on thebottom of the fraction.Perform the division to get a quotient (the whole number part) and a remainder (thepart left over).Form the Mixed Fraction:The quotient becomes the whole number part of the mixed fraction.The remainder becomes the new numerator of the fraction, and the denominatorremains the same.

The mixed fraction is then written as:Then the mixed fraction will be.Example:2. Conversion of mixed fraction into an improper fraction:1. Multiply the whole number part by the denominator.2. Add the numerator to the product from step 1. This sum becomes the numerator ofthe improper fraction.3. The denominator remains the same.Let us convert this mixed fraction to an improper fraction using the following stepsand the explanation given below.

Step 1: Multiply the denominator of the mixed fraction with the whole number part.In this case, 5 × 2 = 10Step 2: Add the numerator to the product obtained from Step 1. Here, 4 + 10 = 14.Step 3: Write the improper fraction with the sum obtained from Step 2 in thenumerator/denominator form. Here, it will be 14/5.Also watch: FractionsEquivalent FractionsThese are fractions that represent the same value or part of a whole, even though theyhave different numerators and denominators.

Using a fraction wall to find equal fractional lengths!Equivalent fractions are different fractions that represent the same amount. To see iffractions like 1/2, 2/4, and 4/8 are equal, we can use strips of paper.1/2, 2/4 and 4/8 are equivalent fractions, as shown using paper strips. You can create afraction wall to help compare and visualize different fractions more effectively.Understanding Equivalent Fractions using Equal Shares

When a roti is shared equally among four children, each child's share is 1/4. Equivalentfractions can represent the same share in different forms. The reciprocal of a fraction isobtained by swapping numerator and denominator; the reciprocal of 1/4 is 4/1.Fractions are also used in area calculations. For example, if length = 3/4 and width = 1/2,then:Area = Length × Width = 3/4 × 1/2 = 3/8 square units.How to Find Equivalent FractionsMultiplying Both Numerator and Denominator: To find an equivalent fraction, multiplyboth the numerator (top number) and the denominator (bottom number) by the samenumber.Dividing Both Numerator and Denominator: Alternatively, you can divide both thenumerator and the denominator by the same number to find equivalent fractions.

Equivalent fractions represent the same part of a whole because they are different waysof expressing the same proportion. When you multiply or divide the numerator anddenominator by the same number, you are essentially scaling the fraction but keeping thesame overall value.Expressing a Fraction in Lowest Terms (Simplest Form)Understanding Lowest TermsA fraction is in its lowest terms or simplest form when the top number (numerator) andthe bottom number (denominator) share no common factors apart from 1. This meansboth numbers are as small as they can be and  the fraction cannot be reduced anyfurther.  To put a fraction in lowest terms, divide both the numerator and denominator bytheir greatest common factor (GCF).Important Note: The greatest common divisor (GCD) is key to simplifyingfractions, as it helps find the largest number that can evenly divide both thenumerator and the denominator.Step-by-Step Example: Simplifying 36/601. Step 1: Both 36 and 60 are even, so divide by 2: 2. Step 2: Now, 18 and 30 are also even, so divide by 2 again: 

3. Step 3: Next, 9 and 15 are multiples of 3, so divide both by 3: 4. Now, 3/5 is in its simplest form since 3 and 5 have no common factors other than 1.Example: Find the simplest form of the fraction 11/33Comparing Fractions1. Comparing Like FractionsComparing fractions involves figuring out which of two or more fractions is larger orsmaller. A simple way to do this is by turning them into equivalent fractions that have thesame denominator. When the fractions share a denominator, we can directly compare thenumerators (the top numbers) to establish which fraction is greater.It's also useful to know about reciprocals when dealing with fractions. The reciprocal of afraction is found by flipping its numerator and denominator.Here's how to compare the fractions 4/9 and 5/7:

1. Step 1: Identify a common denominator. This is a number that both denominators (9and 7) can divide into. Here, the common denominator is 63.2. Step 2: Adjust each fraction to match the common denominator:4/9 changes to 28/63 since 4 × 7 = 28 and 9 × 7 = 63.5/7 changes to 45/63 since 5 × 9 = 45 and 7 × 9 = 63.3. Step 3: Now, compare the numerators (28 and 45):Since 45 > 28, it shows that 5/7 is greater than 4/9.2. Comparing Unlike FractionsIf two fractions have the same numerator but different denominators, the fractionwith the smaller denominator is greater.To compare fractions with unlike denominators generally, convert them to likedenominators using the Least Common Multiple (LCM) of the denominators, thencompare numerators.Comparing Unlike FractionsClaim Offer (/Subscription?utm_source=top_banner_ad&utm_medium=edurev_websiteATTENTION!Sale expiring soon, act now & get EduRev Infinity at 40% off!(/Subscription?utm_source=top_banner_ad&utm_medium=edurev_website&utm_campaign=Sale_is_live_Hurry_up_offer_banner_top)

Example: Compare: 1/4 and 2/3.Step 1: First, observe the denominators of the given fractions, i.e., 1/4 and 2/3. Since thedenominators are different make them equal by finding the LCM of 4 and 3. LCM(4,3) =12.Step 2: Now, let us convert the given fraction in such a way that they have the samedenominators. So, multiply the first fraction with 3/3, i.e., 1/4 × 3/3 = 3/12. Step 3: Similarly, multiply the second fraction with 4/4, i.e., 2/3 × 4/4 = 8/12. Thus, thefirst fraction becomes 3/12 and the other becomes 8/12.Step 4: Compare the obtained new fractions, i.e., 3/12 and 8/12. As the denominators arethe same, we will compare the numerators. We can observe that 3 < 8.Step 5: The fraction that has a large numerator is the larger fraction. So, 8/12 > 3/12. So,2/3 > 1/4.Addition and Subtraction of FractionsAddition and Subtraction of Fractions mean putting together or taking away parts of awhole. To add or subtract fractions, they need to have the same bottom number(denominator). If they don't, you must find a common denominator first. This is usuallythe lowest common multiple (LCM) of the denominators.1. Addition and Subtraction of fractions with same denominator:

When we add or subtract like fractions, we add or subtract their numerators and thedenominator remains the same.1)  + The two fractions are like fractions, so we add their numerators and keep thedenominator the same. +  =   = 2)   - Here, the given fractions are like fractions. So, we subtract their numerators and keep thedenominator the same.  -   = = 2. Addition and Subtraction of two fractions with differentdenominators: When we add or subtract unlike fractions we follow the following steps:1)  + The given fractions are unlike fractions, so we first find LCM of their denominators.LCM of 8 and 24 = 2 × 2 × 2 × 3 = 24Now, we convert the fractions into like fractions.(Changing the denominator of fractions to 24)

 =  and +    = 2)  - As the given fractions are unlike fractions, we find the LCM of their denominator.LCM of 15 and 27 = 3 × 3 × 3 × 5 = 135Next, we convert the fractions into like fractions(Fractions with the same denominator) =  and  =  -  =  = 

Reciprocal of a FractionThe reciprocal of a fraction is found by flipping the top and bottom numbers. For instance,the reciprocal of 2/3 is 3/2.Also watch: FractionsA Pinch of HistoryIn ancient India, fractions were known as bhinna in Sanskrit, which means "broken."They were also called bhaga or ansha, referring to "part" or "piece."The Bakshali manuscript is one of the oldest texts featuring fractions, dating back toaround 300 CE, showcasing the historical use of fractions in India.This technique was utilised by renowned mathematicians like Aryabhata (c. 476-550CE), Brahmagupta (598-668 CE), Sridharacharya (c. 750 CE), and Mahaviracharya(c. 817-875 CE).The notation of a line segment between the numerator and denominator in fractionswas introduced by Al-Khwarizmi, a Persian mathematician, in the 9th century.Fractions also appeared in ancient cultures like Egypt and Babylon, primarily usingfractional units where the numerator was 1. More complex fractions were expressedas sums of these units, known as Egyptian fractions.India was the first to introduce general fractions (where the numerator isn'tnecessarily along with rules for arithmetic operations like addition, subtraction,multiplication, and division.The Sulba-sutras from Vedic times indicate that Indians had established rules forworking with fractions long ago.Brahmagupta formally outlined these rules and methods for fractions in astructured manner. His techniques for manipulating fractions are still applied today.For instance, Brahmagupta noted that to add or subtract fractions, you shouldequalise their denominators by multiplying the numerator and denominator of each

fraction by the other denominators, then add or subtract the numerators.Indian ideas and methods regarding fractions were transmitted to Europe throughthe Arabs, greatly impacting the evolution of mathematics in Europe. Let's Practice!Question 1: Five balls together weight 1 kg. If they are roughly the same size, thenwhat is the weight of each ball?Type Your AnswerView AnswerQuestion 2: Shade the parts of the figures according to the given fraction.Type Your AnswerView AnswerQuestion 2: Match each fractional unit with the correct picture.

Type Your AnswerView AnswerQuestion 3:  Write the following fractions as mixed fractions.(a) 8/3(b) 12/7(c) 25/9Type Your AnswerView AnswerQuestion 4: Write these fractions appropriately as additions or subtractions.

Type Your AnswerView AnswerKey PointsFraction as Equal Share: A fraction is created when a whole is split into equal partsand shared fairly.Fractional Units: Each equal part of a whole is known as a fractional unit.Reading Fractions: In a fraction like 5/6, 5 is referred to as the numerator and 6 isthe denominator.Proper and Improper Fractions: Proper fractions have a numerator smaller than thedenominator (e.g., 1/2, 2/3). Improper fractions have a numerator that is equal to orlarger than the denominator (e.g., 5/4, 6/6).Mixed Fractions: Mixed fractions consist of both a whole number and a fraction.Number Line: Fractions can be represented on a number line, with each fractioncorresponding to a specific point.Equivalent Fractions: Fractions that show the same value or amount are known asequivalent fractions.

Lowest Terms: A fraction is in its lowest terms when the numerator anddenominator share no common factors apart from 1.Reciprocal of a Fraction: To find the reciprocal of a fraction, switch its numeratorand denominator.Brahmagupta's Method for Adding Fractions: To add fractions, turn them intoequivalent fractions with the same denominator and then add the numerators.Brahmagupta's Method for Subtracting Fractions: To subtract fractions, convertthem to equivalent fractions with the same denominator and then subtract thenumerators.(https://edurev.in/courses/87735_Mathematics-for-…Mathematics for Class 6(https://edurev.in/courses/87735_Mathematics-for-Class…Go to Course (https://edurev.in/Up NextFractionsVideo | 06:20 min(https://edurev.in/v/530639/Fractions)Important Formulas: FractionsDoc | 3 pagesAre you preparing for Class 6 exam? EduRev has the perfect solution for all your studyneeds. With courses, docs, videos and tests for the complete syllabus, you will get all thatyou need in one place. So if you are seriously preparing for Class 6 exam, EduRev Infinityis your go-to resource for learning anytime, anywhere. Join Infinity today.View Plans

(https://edurev.in/t/373033/Important-Formulas-Fractions)Worksheet: Fractions - 2Doc | 1 page(https://edurev.in/t/399563/Worksheet-Fractions-2)Other OptionsView Pricing Plans (/Subscription?bundleId=43&utm_medium=website&utm_source=upgrade_btn_content_rightside_ad&utm_campaign=subscription_link)Download this Doc© EduRev (/android-download?t=https%3A%2F%2Fplay.google.com%2Fstore%2Fapps%2Fdetails%3Fid%3Dcom.edurev%26referrer%3Dhttp%253A%252F%252Fedurev.in%253Futm_source%253DLandingPage%2526utm_campaign%253DLanding_page_Google_Play_btn_crcl_1%2526utm_medium%253Dedurev_website) (/ios-download?t=https%3A%2F%2Fapps.apple.com%2Ftt%2Fapp%2Fedurev%2Fid1529835494)EducationRevolution

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