1. WEEK 2.1: FRACTIONS DILEK OZALP

2. FRACTIONS
 Fractions are the rational numbers.
 They have two par ts: The number on the top is cal led
numerator and the number on the bottom is cal led
denominator.
5
13
=
푛푢푚푒푟푎푡표푟
푑푒푛표푚푖푛푎푡표푟

3. IF THE DENOMINATOR IS 1
 I f 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

4. READING THE FRACTIONS
 There are di f ferent ways to read the f ract ions.
 Lets read the fol lowing f ract ions:
 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.

5. READING THE FRACTIONS
 Exceptions:
 1
2
= one half
 1
3
= one third
 1
4
= one quarter
 1
5
= one fifth

6. PROPER AND IMPROPER 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 smal ler
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.

7. MIXED NUMBERS/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 smal ler than the
denominator.
 For example 1
2
3
, 2
5
7
, 4
3
10
, 3
7
11
are mixed numbers.
 1
2
3
= 1 +
2
3
 2
5
7
= 2 +
5
7
 4
3
10
= 4 +
3
10
 3
7
11
= 3 +
7
11

8. READING MIXED FRACTIONS
 2 1/2 = 2
1
2
= two and one half
 4 ½ = 4
1
2
= four and one half
 3 ¼ = 3
1
4
= three and one quar ter
 3 2/3 = 3
2
3
= three and two third
 2 3/5 = 2
3
5
= two and three fif ths

9.  Read the fol lowing fractions.
 2 1/3=
 3 2/5=
 2 1/4=
 1 5/6=
READING MIXED FRACTIONS

10. CONVERTING MIXED FRACTIONS TO
 To conver t 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 2
3
5
to an improper fraction.
 2*5 = 10
 3+10 = 13
 13
5
IMPROPER FRACTIONS
a
푏
푐
*
+

11. CONVERTING MIXED FRACTIONS TO
 Conver t 5
3
7
to an improper fraction.
 5*7 = 35
 3+35 = 38
 38
7
 Conver t 9
6
11
to an improper fraction.
 9*11 = 99
 6+99 = 105
 105
11
IMPROPER FRACTIONS

12. CONVERTING MIXED FRACTIONS TO
 Conver t 5
9
13
IMPROPER FRACTIONS
to an improper fraction.
 Conver t 7
11
14
to an impro per f ra ct io n.
 Conver t 8
14
15
to an improper fraction.

13. CONVERTING IMPROPER FRACTIONS TO
 To conver t 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
 2
3
5
MIXED FRACTIONS

14. CONVERTING IMPROPER FRACTIONS TO
 Conver t
ퟏퟕ
ퟗ
to a mixed number.
 17/9 = 1 with a remainder of 8
 1
ퟖ
ퟗ
 Conver t
ퟐퟑ
ퟖ
to mixed number.
 23/8 = 3 with a remainder of 2.
 3
ퟐ
ퟗ
MIXED FRACTIONS

15. CONVERTING IMPROPER FRACTIONS TO
 Conver t
ퟐퟕ
ퟓ
MIXED FRACTIONS
to a mixed number.
 Conver t
ퟑퟓ
ퟔ
to a mixed number.
 Conver t
ퟒퟏ
ퟕ
to a mixed number.

16.  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.
푎
푏
+
푐
푏
=
푎 +푐
푏
 For example i f 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

17. ADDING FRACTIONS
 If the denominators are di f ferent we have to make them equal by
mul tipl ication:
 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

18.  Find the results for the fol lowing additions:
 9
11
+
5
7
= ?
 6
7
+
9
13
= ?
 4
9
+
10
11
= ?
ADDING FRACTIONS

19. SUBTRACTING 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.
 Simplify the fraction if needed.
푎
푏
-
푐
푏
=
푎−푐
푏
 If the denominators are same:
 11
7
-
5
7
=
6
7
 12
5
-
2
5
=
10
5
= 2

20. SUBTRACTING FRACTIONS
 If the denominators are di f ferent we have to make them equal by
mul tipl ication:
 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

21. SUBTRACTING FRACTIONS
 Find the results of the fol lowing subtractions.
 9
13
-
7
5
= ?
 8
11
-
6
7
= ?
 6
17
-
3
34
= ?

22. MULTIPLYING FRACTIONS
 To mul tiply the fractions:
 Multiply the numerators
 Multiply the denominators.
 Write the results as a fraction.
 Simplify if needed.
푎
푏
*
푐
푑
=
푎 ∗푐
푏 ∗ 푑
 Examples:
 2
5
*
3
7
=
6
35
 (-
4
3
) *
6
7
= -
24
21
= -
8
7
 5
6
*
12
15
=
60
90
=
2
3

23. MULTIPLYING FRACTIONS
 Find the results for the fol lowing multiplications.
 4
5
*
7
3
*
6
8
= ?
 (-
1
2
) *
4
3
*
6
7
= ?
 2
3
*(-
5
6
)*
9
2
= ?

24. DIVIDING FRACTIONS
 Keep the fi rst fraction same.
 Turn the second fraction upside-down: New fraction is called as
“reciprocal”
 Multiply the first fraction by the reciprocal.
 Simplify the fraction if needed.
푎
푏
÷
푐
푑
=
푎
푏
*
푑
푐
=
푎∗푑
푏∗푐
 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

25.  Find the results for the fol lowing divisions.
 5
7
÷
10
6
= ?
 (-
8
11
) ÷
7
14
= ?
 12
13
÷
36
26
= ?
DIVIDING FRACTIONS

26.  What do you think about the results of the fol lowing
questions?
 0
2
= ?
 0
5
= ?
 0
−10
= ?
ZERO NUMERATOR

27.  I f the numerator is zero the result wi l l be zero.
 0
5
= 0
 0
11
= 0
 0
−12
= 0
ZERO NUMERATOR

28.  What do you think about the results of the fol lowing
questions?
 7
0
= ?
 −9
0
= ?
DIVIDING BY ZERO

29. DIVIDING BY ZERO
 Dividing a number by zero is undefined.
 2
0
= undefined
 4
0
= undefined
 −6
0
= undefined
 0/0 = indeterminate

30. QUESTIONS???