The document discusses fractions, including:
- What fractions are and examples of fractions
- The parts of a fraction including the numerator and denominator
- Different types of fractions such as proper, improper, mixed, equivalent and unit fractions
- How to perform operations on fractions including addition, subtraction, multiplication and division
- How to compare and convert between different types of fractions
Teach Students about equivalent fractions
This free teaching resource is from Innovative Teaching Resources. You can access hundreds of their excellent resources here. https://www.teacherspayteachers.com/Store/Innovative-Teaching-Ideas
Proper; Improper & Mixed Number FractionsLorenKnights
How many equal parts of a whole. We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.
Teach Students about equivalent fractions
This free teaching resource is from Innovative Teaching Resources. You can access hundreds of their excellent resources here. https://www.teacherspayteachers.com/Store/Innovative-Teaching-Ideas
Proper; Improper & Mixed Number FractionsLorenKnights
How many equal parts of a whole. We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Biological screening of herbal drugs: Introduction and Need for
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2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2. IndexIndex
1.1. What are FractionsWhat are Fractions
2.2. ExamplesExamples
3.3. Need of FractionsNeed of Fractions
4.4. Parts of FractionsParts of Fractions
5.5. ExampleExample
6.6. Types of Fractions-Types of Fractions-
Proper fractions & Improper FractionsProper fractions & Improper Fractions
Mixed FractionsMixed Fractions
Like Fractions & Unlike FractionsLike Fractions & Unlike Fractions
Equivalent FractionsEquivalent Fractions
7.7. Operations of FractionsOperations of Fractions
AdditionAddition
SubtractionSubtraction
MultiplicationMultiplication
DivisionDivision
8.8. ComparisonComparison
Greater than and SmallerGreater than and Smaller
thanthan
How does the DenominatorHow does the Denominator
controls the Fractioncontrols the Fraction
How does the DenominatorHow does the Denominator
controls the Fractioncontrols the Fraction
3. What are Fractions?What are Fractions?
Fractions are for counting part of something.Fractions are for counting part of something.
Loosely speaking, a fraction is a quantity that cannot beLoosely speaking, a fraction is a quantity that cannot be
represented by a whole number.represented by a whole number.
A fraction (from the Latin fractus, broken) is a number thatA fraction (from the Latin fractus, broken) is a number that
can represent part of a whole. The earliest fractions werecan represent part of a whole. The earliest fractions were
reciprocals of integers: ancient symbols representing one partreciprocals of integers: ancient symbols representing one part
of two, one part of three, one part of four, and so on. A muchof two, one part of three, one part of four, and so on. A much
later development were the common or "vulgar" fractionslater development were the common or "vulgar" fractions
which are still used today (½, ⅝, ¾, etc.)which are still used today (½, ⅝, ¾, etc.)
5. Need Of Fractions?Need Of Fractions?
Consider the following scenario.Consider the following scenario.
Can you finish the whole cake?Can you finish the whole cake?
If not, how many cakes did you eat?If not, how many cakes did you eat?
1 is not the answer, neither is 0.1 is not the answer, neither is 0.
This suggest that we need a newThis suggest that we need a new
kind of number i.e.kind of number i.e. FractionFraction..
6. b
a
Parts Of Fractions?Parts Of Fractions?
I’m the NUMERATOR.I’m the NUMERATOR.
I tell you the number of partsI tell you the number of parts
I’m the DENOMINATOR.I’m the DENOMINATOR.
I tell you the name of partI tell you the name of part
TheThe denominatordenominator tells us howtells us how
many congruent pieces the whole ismany congruent pieces the whole is
divided into, thus this number cannotdivided into, thus this number cannot
be 0. (b)be 0. (b)
TheThe numeratornumerator tells us how manytells us how many
such pieces are being considered. (a)such pieces are being considered. (a)
7. ExampleExample
8
7
How much of a pizza do we have below?How much of a pizza do we have below?
The blue circle is our whole.The blue circle is our whole.
if we divide the whole into 8 congruent pieces,if we divide the whole into 8 congruent pieces,
- the denominator would be- the denominator would be 88..
We can see that we have 7 of these pieces.We can see that we have 7 of these pieces.
Therefore the numerator isTherefore the numerator is 77, and we, and we
havehave
of a pizza.of a pizza.
8. Proper fractionsProper fractions
&&
Improper FractionsImproper Fractions
Proper fractionsProper fractions
&&
Improper FractionsImproper Fractions
EquivalentEquivalent
FractionsFractions
EquivalentEquivalent
FractionsFractions
Like FractionsLike Fractions
&&
Unlike FractionsUnlike Fractions
Like FractionsLike Fractions
&&
Unlike FractionsUnlike Fractions
Mixed FractionsMixed FractionsMixed FractionsMixed Fractions
Unit FractionsUnit Fractions
&&
Whole FractionsWhole Fractions
Unit FractionsUnit Fractions
&&
Whole FractionsWhole Fractions
Types Of FractionsTypes Of Fractions
9. In Proper Fractions theIn Proper Fractions the
numerator is less than thenumerator is less than the
denominator.denominator.
E.g.. – 1/2 ,3/4 ,2/7 etc.E.g.. – 1/2 ,3/4 ,2/7 etc.
In Proper Fractions theIn Proper Fractions the
numerator is less than thenumerator is less than the
denominator.denominator.
E.g.. – 1/2 ,3/4 ,2/7 etc.E.g.. – 1/2 ,3/4 ,2/7 etc. 11
44
In Improper Fractions theIn Improper Fractions the
numerator is greater than (ornumerator is greater than (or
equal to)equal to) the denominator.the denominator.
E.g. – 4/2 ,9/5 ,6/6 etc.E.g. – 4/2 ,9/5 ,6/6 etc.
Every whole no is ImproperEvery whole no is Improper
FractionFraction
E.g. – 24 = 24/1E.g. – 24 = 24/1
In Improper Fractions theIn Improper Fractions the
numerator is greater than (ornumerator is greater than (or
equal to)equal to) the denominator.the denominator.
E.g. – 4/2 ,9/5 ,6/6 etc.E.g. – 4/2 ,9/5 ,6/6 etc.
Every whole no is ImproperEvery whole no is Improper
FractionFraction
E.g. – 24 = 24/1E.g. – 24 = 24/1
77
44
ProperProper && ImproperImproper FractionsFractions
I’m SmallerI’m Smaller
I’m BiggerI’m Bigger
10. 1 ¾1 ¾ 7/87/8
Mixed FractionsMixed Fractions
In Mixed Fractions a whole numberIn Mixed Fractions a whole number
and a proper fraction are together.and a proper fraction are together.
E.g.. –2 1/4, 16 2/5 etc.E.g.. –2 1/4, 16 2/5 etc.
Mixed Fractions and ImproperMixed Fractions and Improper
Fractions are same.Fractions are same.
We can use any to show the sameWe can use any to show the same
amount.amount.
==
11. ConversionConversion
8
1
9
8
1
9 1
= 1
8 8
7
17
7
372
7
3
2 =
+×
=
ImproperImproper FractionFraction toto MixedMixed FractionFraction
divide the numerator by the denominator thedivide the numerator by the denominator the
quotient is the leading number, the remainder asquotient is the leading number, the remainder as
the new numerator.the new numerator.
MixedMixed Fraction to Improper FractionFraction to Improper Fraction
multiply the whole number with the denominatormultiply the whole number with the denominator
and add the numerator to it. The answer is theand add the numerator to it. The answer is the
numerator and the denominator is samenumerator and the denominator is same
12. LikeLike && UnlikeUnlike FractionsFractions
In Like Fractions the denominators ofIn Like Fractions the denominators of
the Fractions are samethe Fractions are same
In Unlike Fractions the denominatorsIn Unlike Fractions the denominators
of the Fractions are different.of the Fractions are different.
13. Unit FractionsUnit Fractions &&
Whole FractionsWhole Fractions
In Unit Fractions theIn Unit Fractions the
numerator of thenumerator of the
Fraction is 1.Fraction is 1.
In Whole Fractions theIn Whole Fractions the
denominators of the Fraction isdenominators of the Fraction is
1.1.
14. Convert Unlike Fractions to LikeConvert Unlike Fractions to Like
FractionsFractions
Simplify all the Fractions.Simplify all the Fractions.
Find LCM of all the Denominators.Find LCM of all the Denominators.
Multiply all the fractions with a special form of 1Multiply all the fractions with a special form of 1
to get 84 (here). Now these are Like Fractions.to get 84 (here). Now these are Like Fractions.
3 5 43 5 4
4 3 74 3 7
, ,
4,3,74,3,7
2,3,72,3,7
1,3,71,3,7
1,1,71,1,7
1,1,11,1,1
22
2
3
7
2 2 3 7 = 842 2 3 7 = 84×× ×
63 113 4863 113 48
84 84 8484 84 84
, ,
==
15. Equivalent FractionsEquivalent Fractions
They are the fractions that may have many differentThey are the fractions that may have many different
appearances, but are same.appearances, but are same.
In the following picture we have ½ of a cake as theIn the following picture we have ½ of a cake as the
cake is divided into two congruent parts and we havecake is divided into two congruent parts and we have
only one of those parts.only one of those parts.
But if we cut the cake into smaller congruentBut if we cut the cake into smaller congruent
pieces, we can see thatpieces, we can see that
½ = 2/4 = 4/8 = 3/6½ = 2/4 = 4/8 = 3/6
16. Equivalent FractionsEquivalent Fractions
To know that two or more Fractions areTo know that two or more Fractions are
Equivalent we must simplify (change to its lowestEquivalent we must simplify (change to its lowest
term) them.term) them.
Simplify: A fraction is in its lowest terms (or isSimplify: A fraction is in its lowest terms (or is
reduced) if we cannot find a whole number (otherreduced) if we cannot find a whole number (other
than 1) that can divide into both its numerator andthan 1) that can divide into both its numerator and
denominator.denominator.
E.g.- 5 : 5 & 10 can be divided by 5. 5 1E.g.- 5 : 5 & 10 can be divided by 5. 5 1
10 10 210 10 2
18. Making Equivalent FractionsMaking Equivalent Fractions
To make Equivalent Fractions we multiply theTo make Equivalent Fractions we multiply the
Fraction with a special form of 1 (same numerator &Fraction with a special form of 1 (same numerator &
denominator- 4/4, 10/10 etc.)denominator- 4/4, 10/10 etc.)
E.g. : 4 = 4 5 = 20E.g. : 4 = 4 5 = 20
5 5 5 255 5 5 25
×
×
19. Operations Of FractionsOperations Of Fractions
SubtractionSubtractionSubtractionSubtraction MultiplicationMultiplicationMultiplicationMultiplicationAdditionAdditionAdditionAddition DivisionDivisionDivisionDivision
20. Addition Of FractionsAddition Of Fractions
Things To Know !!!!Things To Know !!!!
SimplifyingSimplifying
Like and Unlike FractionsLike and Unlike Fractions
Like fractions are Compulsory to add.Like fractions are Compulsory to add.
If there are Unlike Fractions then convert them to likeIf there are Unlike Fractions then convert them to like
fractions.fractions.
The Denominator should not be added.The Denominator should not be added.
Always change Improper fraction to a mixedAlways change Improper fraction to a mixed
fraction.fraction.
21. Adding FractionsAdding Fractions
Addition means combining objects in two or moreAddition means combining objects in two or more
setssets
The objects must be of the same type, i.e. weThe objects must be of the same type, i.e. we
combine bundles with bundles and sticks with sticks.combine bundles with bundles and sticks with sticks.
In fractions, we can only combine pieces of theIn fractions, we can only combine pieces of the
same size. In other words, the denominators must besame size. In other words, the denominators must be
the same.the same.
22. Adding Fractions WithAdding Fractions With
Same DenominatorsSame Denominators
+ =
Add the numerator
and
leave the denominator as it is.
1 2 3 11 2 3 1
+ = =+ = =
6 6 6 26 6 6 2
23. Adding Fractions withAdding Fractions with
Different DenominatorsDifferent Denominators
If there are different denominators in theIf there are different denominators in the
fractions, then we change them to likefractions, then we change them to like
fractions.fractions.
15
5
3
1
= =
5
2
15
65
2
3
1
+
15
11
15
6
15
5
5
2
3
1
=+=+
24. Adding Mixed FractionsAdding Mixed Fractions
Change the Mixed fractions toChange the Mixed fractions to
Improper Fractions and then toImproper Fractions and then to
Like Fractions.Like Fractions.
At last add the Improper LikeAt last add the Improper Like
Fractions.Fractions.
Don’t forget to change theDon’t forget to change the
answer to Mixed Fraction again.answer to Mixed Fraction again.
25. Subtraction Of FractionsSubtraction Of Fractions
Things To Know !!!!Things To Know !!!!
SimplifyingSimplifying
Like and Unlike FractionsLike and Unlike Fractions
Like fractions are Compulsory to subtract.Like fractions are Compulsory to subtract.
If there are Unlike Fractions then convert them to likeIf there are Unlike Fractions then convert them to like
fractions.fractions.
The Denominator should not be subtracted.The Denominator should not be subtracted.
Always change Improper fraction to a mixedAlways change Improper fraction to a mixed
fraction.fraction.
The numerator can be negative.The numerator can be negative.
26. Subtracting FractionsSubtracting Fractions
Subtraction means taking objects away.
The objects must be of the same type, i.e. we
can only take away apples from a group of
apples.
In fractions, we can only take away pieces of
the same size.
In other words, the denominators must be
the same.
27. Subtracting Fractions WithSubtracting Fractions With
Same DenominatorsSame Denominators
- =
Subtract the numerator
and
leave the denominator as it is.
4 2 2 14 2 2 1
= == =
6 6 6 36 6 6 3
28. Subtracting Fractions withSubtracting Fractions with
Different DenominatorsDifferent Denominators
If there are different denominators in theIf there are different denominators in the
fractions, then we change them to likefractions, then we change them to like
fractions.fractions.
15
10
3
2
= =
5
2
15
65
2
3
2
−
15
4
15
6
15
10
5
2
3
2
=−=−
29. Subtracting Mixed FractionsSubtracting Mixed Fractions
Change the Mixed fractions toChange the Mixed fractions to
Improper Fractions and then toImproper Fractions and then to
Like Fractions.Like Fractions.
At last subtract the ImproperAt last subtract the Improper
Like Fractions.Like Fractions.
Don’t forget to change theDon’t forget to change the
answer to Mixed Fraction again.answer to Mixed Fraction again.
30. Multiplication Of FractionsMultiplication Of Fractions
Things To Know !!!!Things To Know !!!!
SimplifyingSimplifying
The Denominator are always multiplied.The Denominator are always multiplied.
““ Of ” : Of means multiply. E.g. : ½ of 2 = ½Of ” : Of means multiply. E.g. : ½ of 2 = ½ × 2 = 1× 2 = 1
Product of two Proper Fractions is always less than both of them.Product of two Proper Fractions is always less than both of them.
Product of two Improper Fractions is alwaysProduct of two Improper Fractions is always greatergreater than both ofthan both of
them.them.
Product of one Improper Fraction and one ProperProduct of one Improper Fraction and one Proper
Fraction is always less than the Improper FractionFraction is always less than the Improper Fraction
and greater than the Proper Fraction.and greater than the Proper Fraction.
31. Multiplying FractionsMultiplying Fractions
To Multiply Fractions we Multiply both - TheTo Multiply Fractions we Multiply both - The
numerators and the Denominators separately.numerators and the Denominators separately.
2 3 22 3 2 ×× 3 6 33 6 3
×× = == = ==
4 2 4 × 2 8 44 2 4 × 2 8 4
32. Multiplying Mixed FractionsMultiplying Mixed Fractions
Change the Mixed fractions toChange the Mixed fractions to
Improper Fractions.Improper Fractions.
Then multiply the ImproperThen multiply the Improper
Fraction.Fraction.
Don’t forget to change theDon’t forget to change the
answer to Mixed Fraction again.answer to Mixed Fraction again.
33. Addition Of FractionsAddition Of Fractions
Things To Know !!!!Things To Know !!!!
SimplifyingSimplifying
MultiplicationMultiplication
Always change Improper fraction to a mixed fraction.Always change Improper fraction to a mixed fraction.
Reciprocal: The inverse of fractionReciprocal: The inverse of fraction
E.g. – 2/3 = 3/2 = 1 ½ , 2 ½ = 5/2 = 2/5E.g. – 2/3 = 3/2 = 1 ½ , 2 ½ = 5/2 = 2/5
34. Dividing FractionsDividing Fractions
To Divide Fractions we change the Second Fraction
with its Reciprocal.
Then Multiply the Reciprocal with the First
Fraction.
2 4 2 × 5 10 5
÷ = = =
4 5 4 × 4 16 8
35. Dividing Mixed FractionsDividing Mixed Fractions
Change the Mixed fractions toChange the Mixed fractions to
Improper Fractions.Improper Fractions.
Then Multiply the ImproperThen Multiply the Improper
Fraction.Fraction.
Don’t forget to change theDon’t forget to change the
answer to Mixed Fraction again.answer to Mixed Fraction again.
36. ComparisonComparison
ComparisonComparison
• Greater than and Smaller thanGreater than and Smaller than
• How does the Denominator controls the FractionHow does the Denominator controls the Fraction
• How does the Numerator controls the FractionHow does the Numerator controls the Fraction
37. Greater than and Smaller thanGreater than and Smaller than
Change the Fractions to Like Fractions.
The fraction with greater numerator is bigger
than the other one.
If the Numerators are same, then the Fraction
with smallest Denominator is the Biggest.
>
2 3 10 9
& =
3 5 15 15
38. How does the DenominatorHow does the Denominator
controls the Fractioncontrols the Fraction
Denominator represents the total number of pieces.Denominator represents the total number of pieces.
If we share a Pizza with 2 people, we get ½ of pizza.If we share a Pizza with 2 people, we get ½ of pizza.
If we share a Pizza with 4 people, we get ¼ of pizza.If we share a Pizza with 4 people, we get ¼ of pizza.
If we share a Pizza with 8 people, we get 1/8 of pizza.If we share a Pizza with 8 people, we get 1/8 of pizza.
Conclusion:Conclusion:
The larger the denominator the smaller the pieces, andThe larger the denominator the smaller the pieces, and
if the numerator is kept fixed, the larger theif the numerator is kept fixed, the larger the
denominator the smaller the fraction,denominator the smaller the fraction,
39. How does the Numerator controlsHow does the Numerator controls
the Fractionthe Fraction
Numerator represents the number of pieces.Numerator represents the number of pieces.
If we share a Pizza with 16 people, we get 1/16 of pizza.If we share a Pizza with 16 people, we get 1/16 of pizza.
If we share a Pizza with 13 people, we get 3/16 of pizza.If we share a Pizza with 13 people, we get 3/16 of pizza.
If we share a Pizza with 5 people, we get 5/16 of pizza.If we share a Pizza with 5 people, we get 5/16 of pizza.
Conclusion :Conclusion :
When the numerator gets larger we have more pieces.When the numerator gets larger we have more pieces.
And if the denominator is kept fixed, the larger numeratorAnd if the denominator is kept fixed, the larger numerator
makes a bigger fraction.makes a bigger fraction.