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Index

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?

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

1

22

/

/

10

10

1

1

22

/

/

10

10

1

1

/

/

12

12

1

1

/

/

12

12

1

1

/

/

8

8

1 1

/

/

8 8

1

1

½

½

1

1

½

½

11

11

/

/

12

12

11 11

/

/

12 12 55

55

/

/

60

60

55

55

/

/

60

60

Examples

(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 new

This suggest that we need a new

kind of number i.e.

(6)

b

a

Parts Of Fractions?

Parts Of Fractions?

I’m the NUMERATOR.

I’m the NUMERATOR.

I tell you the number of parts

I tell you the number of parts

I’m the DENOMINATOR.

I’m the DENOMINATOR.

I tell you the name of part

I tell you the name of part

The

The

denominator

denominator

tells us how

tells us how

many congruent pieces the whole is

many congruent pieces the whole is

divided into, thus this number

divided into, thus this number

cannot be 0. (b)

cannot be 0. (b)

The

The

numerator

numerator

tells us how many

tells us how many

such pieces are being considered. (a)

(7)

Example

Example

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

8

8

.

.

We can see that we have 7 of these pieces.

We can see that we have 7 of these pieces.

Therefore the numerator is

Therefore the numerator is

7

7

, and we

, and we

have

have

(8)

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

Improper Fractions Equivalent Equivalent Equivalent Equivalent FractionsFractionsFractionsFractions

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

In Proper Fractions the

numerator is less than the

numerator 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 the

In Proper Fractions the

numerator is less than the

numerator is less than the

denominator.

denominator.

E.g.. – 1/2 ,3/4 ,2/7 etc.

E.g.. – 1/2 ,3/4 ,2/7 etc.

1

1

4

4

1

1

4

4

In Improper Fractions the

In Improper Fractions the

numerator is greater than (or

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

Every whole no is Improper

Fraction

Fraction

E.g. – 24 = 24/1

E.g. – 24 = 24/1

In Improper Fractions the

In Improper Fractions the

numerator is greater than (or

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

Every whole no is Improper

Fraction

Fraction

E.g. – 24 = 24/1

E.g. – 24 = 24/1

7

7

4

4

7

7

4

4

Proper

Proper

&

&

Improper

Improper

Fractions

Fractions

I’m Smaller

I’m Smaller

I’m Bigger

(10)

1 ¾

1 ¾

1 ¾

1 ¾

7/8

7/8

7/8

7/8

Mixed Fractions

Mixed Fractions

In Mixed Fractions a whole number

In 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 Improper

Mixed Fractions and Improper

Fractions are same.

Fractions are same.

We can use any to show the same

We can use any to show the same

amount.

amount.

=

(11)

Conversion

Conversion

8 1 9 8 1

9 1

= 1

8 8

7

17

7

3

7

2

7

3

2

Improper

Improper

Fraction

Fraction

to

to

Mixed

Mixed

Fraction

Fraction

divide the numerator by the denominator the

divide the numerator by the denominator the

quotient is the leading number, the remainder as

quotient is the leading number, the remainder as

the new numerator.

the new numerator.

Mixed

Mixed

Fraction to Improper Fraction

Fraction to Improper Fraction

multiply the whole number with the denominator

multiply the whole number with the denominator

and add the numerator to it. The answer is the

and add the numerator to it. The answer is the

numerator and the denominator is same

(12)

Like

Like

&

&

Unlike

Unlike

Fractions

Fractions

In Like Fractions the denominators of

In Like Fractions the denominators of

the Fractions are same

the Fractions are same

In Unlike Fractions the denominators

In Unlike Fractions the denominators

of the Fractions are different.

(13)

Unit Fractions

Unit Fractions

&

&

Whole Fractions

Whole Fractions

In Unit Fractions the

In Unit Fractions the

numerator of the

numerator of the

Fraction is 1.

Fraction is 1.

In Whole Fractions the

In Whole Fractions the

denominators of the Fraction is

denominators of the Fraction is

1.

(14)

Convert Unlike Fractions to Like

Convert Unlike Fractions to Like

Fractions

Fractions

Convert Unlike Fractions to Like

Convert Unlike Fractions to Like

Fractions

Fractions

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 1

Multiply 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 4

3 5 4

4 3 7

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

63 113 48

84 84 84

84 84 84

,

,

=

(15)

Equivalent Fractions

Equivalent Fractions

They are the fractions that may have many They are the fractions that may have many

different appearances, but are same.

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

cake 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 congruent But if we cut the cake into smaller congruent

pieces, we can see that

pieces, we can see that

½ = 2/4 = 4/8 = 3/6

(16)

Equivalent Fractions

Equivalent Fractions

To know that two or more Fractions are

To know that two or more Fractions are

Equivalent we must simplify (change to its lowest

Equivalent we must simplify (change to its lowest

term) them.

term) them.

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

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

reduced) if we cannot find a whole number (other

reduced) if we cannot find a whole number (other

than 1) that can divide into both its numerator and

than 1) that can divide into both its numerator and

denominator.

denominator.

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

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

(17)

Example

Example

Example

Example

Are 14 & 30 equal ?

21 45

2 = 2 14 = 30

3 3 21 45

(18)

Making Equivalent Fractions

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 &

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 = 20

E.g. : 4 = 4 5 = 20

(19)

Operations Of Fractions

Operations Of Fractions

Subtraction

Subtraction

Subtraction

Subtraction

Multiplication

Multiplication

Multiplication

Multiplication

Addition

Addition

Addition

(20)

Addition Of Fractions

Addition Of Fractions

Things To Know !!!!

Things To Know !!!!

Simplifying

Simplifying

Like and Unlike Fractions

Like and Unlike Fractions

Like fractions are Compulsory to add.

Like fractions are Compulsory to add.

If there are Unlike Fractions then convert them to like

If 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 mixed

Always change Improper fraction to a mixed

fraction.

(21)

Adding Fractions

Adding Fractions

Addition means combining objects in two or more Addition means combining objects in two or more

sets

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.

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

same size. In other words, the denominators must be

the same.

(22)

Adding Fractions With

Adding Fractions With

Same Denominators

Same Denominators

+

=

Add the numerator

and

leave the denominator as it is.

1 2 3 1

1 2 3 1

(23)

Adding Fractions with

Adding Fractions with

Different Denominators

Different Denominators

If there are different denominators in the

If there are different denominators in the

fractions, then we change them to like

fractions, then we change them to like

fractions.

fractions.

15

5

3

1

5

2

15

6

5

2

3

1

15

11

15

6

15

5

5

2

3

(24)

Adding Mixed Fractions

Adding Mixed Fractions

Change the Mixed fractions to

Change the Mixed fractions to

Improper Fractions and then to

Improper Fractions and then to

Like Fractions.

Like Fractions.

At last add the Improper Like

At last add the Improper Like

Fractions.

Fractions.

Don’t forget to change the

Don’t forget to change the

answer to Mixed Fraction again.

(25)

Subtraction Of Fractions

Subtraction Of Fractions

Things To Know !!!!

Things To Know !!!!

Simplifying

Simplifying

Like and Unlike Fractions

Like and Unlike Fractions

Like fractions are Compulsory to subtract.

Like fractions are Compulsory to subtract.

If there are Unlike Fractions then convert them to like

If 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 mixed

Always change Improper fraction to a mixed

fraction.

fraction.

(26)

Subtracting Fractions

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

Subtracting Fractions With

Same Denominators

Same Denominators

-

=

Subtract the numerator

and

leave the denominator as it is.

4 2 2 1

4 2 2 1

= =

= =

6 6 6 3

(28)

Subtracting Fractions with

Subtracting Fractions with

Different Denominators

Different Denominators

If there are different denominators in the

If there are different denominators in the

fractions, then we change them to like

fractions, then we change them to like

fractions.

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

Subtracting Mixed Fractions

Change the Mixed fractions to

Change the Mixed fractions to

Improper Fractions and then to

Improper Fractions and then to

Like Fractions.

Like Fractions.

At last subtract the Improper

At last subtract the Improper

Like Fractions.

Like Fractions.

Don’t forget to change the

Don’t forget to change the

answer to Mixed Fraction again.

(30)

Multiplication Of Fractions

Multiplication 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 = 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

Fraction is always less than the Improper Fraction

and greater than the Proper Fraction.

(31)

Multiplying Fractions

Multiplying Fractions

To Multiply Fractions we Multiply both - The To Multiply Fractions we Multiply both - The

numerators and the Denominators separately.

numerators and the Denominators separately.

2 3 2

2 3 2

×

×

3 6 3

3 6 3

×

×

= =

= =

=

=

4 2 4 × 2 8 4

(32)

Multiplying Mixed Fractions

Multiplying Mixed Fractions

Change the Mixed fractions to

Change the Mixed fractions to

Improper Fractions.

Improper Fractions.

Then multiply the Improper

Then multiply the Improper

Fraction.

Fraction.

Don’t forget to change the

Don’t forget to change the

answer to Mixed Fraction again.

(33)

Addition Of Fractions

Addition Of Fractions

Things To Know !!!!

Things To Know !!!!

Simplifying

Simplifying

Multiplication

Multiplication

Always change Improper fraction to a mixed fraction.

Always change Improper fraction to a mixed fraction.

Reciprocal: The inverse of fraction

Reciprocal: The inverse of fraction

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

(34)

Dividing Fractions

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

Dividing Mixed Fractions

Change the Mixed fractions to

Change the Mixed fractions to

Improper Fractions.

Improper Fractions.

Then Multiply the Improper

Then Multiply the Improper

Fraction.

Fraction.

Don’t forget to change the

Don’t forget to change the

answer to Mixed Fraction again.

(36)

Comparison

Comparison

Comparison

Comparison

• Greater than and Smaller thanGreater than and Smaller than

(37)

Greater than and Smaller than

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

How does the Denominator

controls the Fraction

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

The larger the denominator the smaller the pieces, and

if the numerator is kept fixed, the larger the

if the numerator is kept fixed, the larger the

denominator the smaller the fraction,

(39)

How does the Numerator controls

How does the Numerator controls

the Fraction

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.

When the numerator gets larger we have more pieces.

And if the denominator is kept fixed, the larger numerator

And if the denominator is kept fixed, the larger numerator

makes a bigger fraction.

(40)

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