Week 2.1 fractions dilek ozalp_5.31.2013

$Page 1: Week 2.1 fractions dilek ozalp_5.31.2013$
DILEK OZALPWEEK 2.1: FRACTIONS

Fractions are the rational numbers.

They have two parts: The number on the top is called

numerator and the number on the bottom is called

denominator.

5

13=

𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟

𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟

FRACTIONS

If the denominator is 1 the value of the fraction is equal to

the numerator.

5

1= 5

10

1= 10

−8

1= -8

−11

1= -11

IF THE DENOMINATOR IS 1

There are dif ferent ways to read the fractions.

Lets read the fol lowing fractions:

5/8 : five over eight

: five eighths

: five divided by eight

14/29 : fourteen over twenty-nine;

: fourteen twenty -ninths

: Fourteen divided by twenty -nine

24/56 : twenty-four over fifty-six.

: twenty-four fifty -sixths

: twenty-four divided by fifty-six.

READING THE FRACTIONS

Exceptions:

1

2= one half

1

3= one third

1

4= one quarter

1

5= one fifth

READING THE FRACTIONS

An improper fraction is a fraction that has a numerator larger

than or equal to its denominator. The value of the fraction is 1

or greater than 1.

For example 5/2 , 8/3 , 9/7, 15/4, 33/13 , 4/4 are improper

fractions.

A proper fraction is a fraction that has numerator smaller

than the denominator. The value of the fraction is less than 1.

For example 1/2 , 3/5 , 7/11 , 17/23, 4/9 are proper fractions.

PROPER AND IMPROPER FRACTIONS

A mixed number combines a whole number and a proper fraction. In other words a mixed number is a combination of a whole number and a fraction that has a numerator smaller than the denominator.

For example 12

3, 2

5

7, 4

3

10, 3

7

11are mixed numbers.

12

3= 1 +

2

3

2 5

7= 2 +

5

7

4 3

10= 4 +

3

10

3 7

11= 3 +

7

11

MIXED NUMBERS/FRACTIONS

2 1/2 = 21

2= two and one half

4 ½ = 41

2= four and one half

3 ¼ = 31

4= three and one quarter

3 2/3 = 32

3= three and two third

2 3/5 = 23

5= two and three fif ths

READING MIXED FRACTIONS

Read the following fractions.

2 1/3=

3 2/5=

2 1/4=

1 5/6=

READING MIXED FRACTIONS

To convert a mixed fraction to a improper fraction:

Multiply the whole number by the denominator of the fraction.

Add the numerator to the multiplication.

Write the result as numerator.

Keep the denominator same.

Example;

Convert 23

5to an improper fraction.

2*5 = 10

3+10 = 13

13

5

CONVERTING MIXED FRACTIONS TO

IMPROPER FRACTIONS

a𝑏

𝑐*

+

Convert 53


5*7 = 35

3+35 = 38

38

7

Convert 96


9*11 = 99

6+99 = 105

105

11


IMPROPER FRACTIONS

Convert 59


Convert 711


Convert 814



IMPROPER FRACTIONS

To convert an improper fraction as a mixed number:

Divide the numerator by the denominator.

Write the quotient as the whole number.

Write the remainder as the numerator.

Keep the denominator same.

For example;

13

5

13/5 = 2 with a remainder of 3

23

5

CONVERTING IMPROPER FRACTIONS TO

MIXED FRACTIONS

Convert 𝟏𝟕

𝟗to a mixed number.

17/9 = 1 with a remainder of 8

1𝟖

𝟗

Convert 𝟐𝟑

𝟖to mixed number.

23/8 = 3 with a remainder of 2.

3𝟐

𝟗


MIXED FRACTIONS

Convert 𝟐𝟕

𝟓to a mixed number.

Convert 𝟑𝟓

𝟔to a mixed number.

Convert 𝟒𝟏

𝟕to a mixed number.


MIXED FRACTIONS

To add the fractions; Make sure that the denominators are same

Add the numerators together and write it as numerator of the answer.

Write the denominator.

Simplify the fraction if needed.

𝑎

𝑏+

𝑐

𝑏=

𝑎+𝑐

𝑏

For example if the denominators are same:

2

3+

5

3=

7

3

4

7+

11

7=

15

7

6

11+

16

11=

22

11= 2

ADDING FRACTIONS

If the denominators are different we have to make them equal by multiplication:

4

5+

2

7= ?

= 7∗4

7∗5+

5∗2

5∗7=

28

35+

10

35=

38

35

3

8+

5

9= ?

= 9∗3

9∗8+

8∗5

8∗9=

27

72+

40

72=

67

72

2

3+

5

4

= 4∗2

4∗3+

3∗5

4∗3=

8

12+

15

12=

23

12

ADDING FRACTIONS

Find the results for the following additions:

9

11+

5

7= ?

6

7+

9

13= ?

4

9+

10

11= ?

ADDING FRACTIONS

To subtracting the fractions;

Make sure that the denominators are same

Subtract the numerators and write it as numerator of the answer.

Write the denominator.


𝑎

𝑏-𝑐

𝑏=

𝑎−𝑐

𝑏

If the denominators are same:

11

7-5

7=

6

7

12

5-2

5=

10

5= 2

SUBTRACTING FRACTIONS

If the denominators are different we have to make them equal by multiplication:

1

3-1

6=?

= 2∗1

2∗3-1

6=

2−1

6=

1

6

4

7-

5

21=?

= 3∗4

3∗7-

5

21=

12−5

21=

7

21=

1

3

5

11-4

7=?

= 7∗5

7∗11-11∗4

11∗7=

35−44

77= -

9

77


Find the results of the following subtractions.

9

13-7

5= ?

8

11-6

7= ?

6

17-3

34= ?


To multiply the fractions:

Multiply the numerators

Multiply the denominators.

Write the results as a fraction.

Simplify if needed.

𝑎

𝑏*

𝑐

𝑑=

𝑎∗𝑐

𝑏∗𝑑

Examples:

2

5*

3

7=

6

35

(-4

3) *

6

7= -

24

21= -

8

7

5

6*

12

15=

60

90=

2

3

MULTIPLYING FRACTIONS

Find the results for the following multiplications.

4

5*

7

3*

6

8= ?

(-1

2) *

4

3*

6

7= ?

2

3*(-

5

6)*

9

2= ?

MULTIPLYING FRACTIONS

Keep the first fraction same. Turn the second fraction upside-down: New fraction is called as “reciprocal”

Multiply the first fraction by the reciprocal.


𝑎

𝑏÷

𝑐

𝑑=

𝑎

𝑏*

𝑑

𝑐=

𝑎∗𝑑

𝑏∗𝑐

For example:

1

2÷

3

4= ?

1

2*

4

3=

1∗4

2∗3=

4

6=

2

3

(-5

7) ÷

20

14=?

(-5

7) *

14

20= -

70

140= -

1

2

DIVIDING FRACTIONS

Find the results for the following divisions.

5

7÷

10

6= ?

(-8

11) ÷

7

14= ?

12

13÷

36

26= ?

DIVIDING FRACTIONS

What do you think about the results of the following

questions?

0

2= ?

0

5= ?

0

−10= ?

ZERO NUMERATOR

If the numerator is zero the result will be zero.

0

5= 0

0

11= 0

0

−12= 0

ZERO NUMERATOR

What do you think about the results of the following

questions?

7

0= ?

−9

0= ?

DIVIDING BY ZERO

Dividing a number by zero is undefined.

2

0= undefined

4

0= undefined

−6

0= undefined

0/0 = indeterminate

DIVIDING BY ZERO

QUESTIONS???

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Week 2.1 fractions dilek ozalp_5.31.2013