fractions.ppt

(1)

(2)

Index

1. What are Fractions

2. Examples

3. Need of Fractions

4. Parts of Fractions

5. Example

6. Types of

Fractions- Proper fractions & Improper Fr actions

 Mixed Fractions

 Like Fractions & Unlike Fracti ons

 Equivalent Fractions

7. Operations of Fractions  Addition

 Subtraction

 Multiplication

 Division

8. Comparison

 Greater than and Smaller than

 How does the Denominator con trols the Fraction

(3)

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 be _{Loosely 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 that _{A fraction (from the Latin fractus, broken) is a number that} can represent part of a whole. The earliest fractions were

can represent part of a whole. The earliest fractions were

reciprocals of integers: ancient symbols representing one part reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions later development were the common or "vulgar" fractions which are still used today (½, ⅝, ¾, etc.)

(4)

1

22

/

10

1

22

/

10

1

/

12

1

/

12

1

/

8

1 1

/

8 8

1

½

1

½

11

/

12

11 11

/

12 12 55

55

/

60

55

/

60

Examples

(5)

Need Of Fractions?



Consider the following scenario.



Can you finish the whole cake?



If not, how many cakes did you eat?



1 is not the answer, neither is 0.



This suggest that we need a new

kind of number i.e.

(6)

b

a

Parts Of Fractions?

I’m the NUMERATOR.

I tell you the number of parts

I’m the DENOMINATOR.

I tell you the name of part



The

denominator

tells us how

many congruent pieces the whole is

divided into, thus this number

cannot be 0. (b)



The

numerator

tells us how many

such pieces are being considered. (a)

(7)

Example

8

7

How much of a pizza do we have below?

The blue circle is our whole.

if we divide the whole into 8 congruent pieces,

- the denominator would be

8

.

We can see that we have 7 of these pieces.

Therefore the numerator is

7

, and we

have

(8)

Proper fractions Proper fractions & & Improper Fractions Improper Fractions Proper fractions Proper fractions & & Improper Fractions

Improper Fractions Equivalent Equivalent Equivalent Equivalent _Fractions_Fractions_Fractions_Fractions

Like Fractions Like Fractions & & Unlike Fractions Unlike Fractions Like Fractions Like Fractions & & Unlike Fractions Unlike Fractions Mixed Fractions Mixed Fractions Mixed Fractions

Mixed Fractions Unit FractionsUnit Fractions_&_&

Whole Fractions Whole Fractions Unit Fractions Unit Fractions & & Whole Fractions Whole Fractions

Types Of Fractions

(9)

In Proper Fractions the

numerator is less than the

denominator.

E.g.. – 1/2 ,3/4 ,2/7 etc.

In Proper Fractions the

numerator is less than the

denominator.

E.g.. – 1/2 ,3/4 ,2/7 etc.

1

4

1

4

In Improper Fractions the

numerator 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 Improper

Fraction

E.g. – 24 = 24/1

In Improper Fractions the

numerator 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 Improper

Fraction

E.g. – 24 = 24/1

7

4

7

4

Proper

&

Improper

Fractions

I’m Smaller

I’m Bigger

(10)

1 ¾

7/8

Mixed Fractions



In Mixed Fractions a whole number

and a proper fraction are together.

E.g.. –2 1/4, 16 2/5 etc.



Mixed Fractions and Improper

Fractions are same.



We can use any to show the same

amount.

=

(11)

Conversion

8 1 9 8 1

9 1

= 1

8 8

7

17

7

3

7

2

7

3

2









Improper

Fraction

to

Mixed

Fraction

divide the numerator by the denominator the

quotient is the leading number, the remainder as

the new numerator.

Mixed

Fraction to Improper Fraction

multiply the whole number with the denominator

and add the numerator to it. The answer is the

numerator and the denominator is same

(12)

Like

&

Unlike

Fractions

In Like Fractions the denominators of

the Fractions are same

In Unlike Fractions the denominators

of the Fractions are different.

(13)

Unit Fractions

&

Whole Fractions

In Unit Fractions the

numerator of the

Fraction is 1.

In Whole Fractions the

denominators of the Fraction is

1.

(14)

Convert Unlike Fractions to Like

Fractions

Convert Unlike Fractions to Like

Fractions



Simplify all the Fractions.



Find LCM of all the Denominators.



Multiply all the fractions with a special form of 1

to get 84 (here). Now these are Like Fractions.

3 5 4

4 3 7

,

4,3,7 4,3,7 2,3,7 2,3,7 1,3,7 1,3,7 1,1,7 1,1,7 1,1,1 1,1,1 2 2 2 3 7

2 2 3 7 = 84

2 2 3 7 = 84  

63 113 48

84 84 84

,

=

(15)

Equivalent Fractions

They are the fractions that may have many _{They are the fractions that may have many}

different appearances, but are same.

In the following picture we have ½ of a cake as the _{In the following picture we have ½ of a cake as the}

cake is divided into two congruent parts and we have

only one of those parts.

But if we cut the cake into smaller congruent _{But if we cut the cake into smaller congruent}

pieces, we can see that

½ = 2/4 = 4/8 = 3/6

(16)

Equivalent Fractions



To know that two or more Fractions are

Equivalent we must simplify (change to its lowest

term) them.



Simplify: A fraction is in its lowest terms (or is

reduced) if we cannot find a whole number (other

than 1) that can divide into both its numerator and

denominator.



E.g.- 5 : 5 & 10 can be divided by 5. 5 1

(17)

Example

Are 14 & 30 equal ?

21 45

2 = 2 14 = 30

3 3 21 45

(18)

Making Equivalent Fractions

To make Equivalent Fractions we multiply the _{To make Equivalent Fractions we multiply the}

Fraction with a special form of 1 (same numerator &

denominator- 4/4, 10/10 etc.)

E.g. : 4 = 4 5 = 20

(19)

Operations Of Fractions

Subtraction

Multiplication

Addition

(20)

Addition Of Fractions

Things To Know !!!!



Simplifying



Like and Unlike Fractions



Like fractions are Compulsory to add.



If there are Unlike Fractions then convert them to like

fractions.



The Denominator should not be added.



Always change Improper fraction to a mixed

fraction.

(21)

Adding Fractions

Addition means combining objects in two or more _{Addition means combining objects in two or more}

sets

The objects must be of the same type, i.e. we _{The objects must be of the same type, i.e. we}

combine bundles with bundles and sticks with sticks.

In fractions, we can only combine pieces of the _{In fractions, we can only combine pieces of the}

same size. In other words, the denominators must be

the same.

(22)

Adding Fractions With

Same Denominators

+

=

Add the numerator

and

leave the denominator as it is.

1 2 3 1

(23)

Adding Fractions with

Different Denominators

If there are different denominators in the

fractions, then we change them to like

fractions.

15

5

3

1



5

2

15

6

5

2

3

1



15

11

15

6

15

5

2

3

(24)

Adding Mixed Fractions



Change the Mixed fractions to

Improper Fractions and then to

Like Fractions.



At last add the Improper Like

Fractions.



Don’t forget to change the

answer to Mixed Fraction again.

(25)

Subtraction Of Fractions

Things To Know !!!!



Simplifying



Like and Unlike Fractions



Like fractions are Compulsory to subtract.



If there are Unlike Fractions then convert them to like

fractions.



The Denominator should not be subtracted.



Always change Improper fraction to a mixed

fraction.

(26)

Subtracting 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

(27)

Subtracting Fractions With

Same Denominators

-

=

Subtract the numerator

and

leave the denominator as it is.

4 2 2 1

= =

6 6 6 3

(28)

Subtracting Fractions with

Different Denominators

If there are different denominators in the

fractions, then we change them to like

fractions.

15

10

3

2



5

2

15

6

5

2

3

2



15

4

15

6

15

10

5

2

3

(29)

Subtracting Mixed Fractions



Improper Fractions and then to

Like Fractions.



At last subtract the Improper

Like Fractions.



(30)

Multiplication Of Fractions

Things To Know !!!!

 Simplifying_Simplifying

 The Denominator are always multiplied._{The Denominator are always multiplied.}

 “ _“Of ” : Of means multiply. E.g. : ½ of 2 = ½ Of ” : 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 always _{Product of two Improper Fractions is always}greatergreater than both of than both of them.

them.

 Product of one Improper Fraction and one Proper _{Product of one Improper Fraction and one Proper}

Fraction is always less than the Improper Fraction

and greater than the Proper Fraction.

(31)

Multiplying Fractions

To Multiply Fractions we Multiply both - The _{To Multiply Fractions we Multiply both - The}

numerators and the Denominators separately.

2 3 2

×

3 6 3

×

= =

=

4 2 4 × 2 8 4

(32)

Multiplying Mixed Fractions



Improper Fractions.



Then multiply the Improper

Fraction.



(33)

Addition Of Fractions

Things To Know !!!!



Simplifying



Multiplication



Always change Improper fraction to a mixed fraction.



Reciprocal: The inverse of fraction

E.g. – 2/3 = 3/2 = 1 ½ , 2 ½ = 5/2 = 2/5

(34)

Dividing Fractions



To Divide Fractions we change the Second Fraction

with its Reciprocal.



Then Multiply the Reciprocal with the First

Fraction.

(35)

Dividing Mixed Fractions



Improper Fractions.



Then Multiply the Improper

Fraction.



Don’t forget to change the

(36)

Comparison

• Greater than and Smaller than_{Greater than and Smaller than}

(37)

Greater 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

& =

(38)

How does the Denominator

controls 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, and

if the numerator is kept fixed, the larger the

denominator the smaller the fraction,

(39)

How does the Numerator controls

the 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.

And if the denominator is kept fixed, the larger numerator

makes a bigger fraction.

(40)