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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
7to an improper fraction.
5*7 = 35
3+35 = 38
38
7
Convert 96
11to an improper fraction.
9*11 = 99
6+99 = 105
105
11
CONVERTING MIXED FRACTIONS TO
IMPROPER FRACTIONS
Convert 59
13to an improper fraction.
Convert 711
14to an improper fraction.
Convert 814
15to an improper fraction.
CONVERTING MIXED FRACTIONS TO
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
CONVERTING IMPROPER FRACTIONS TO
MIXED FRACTIONS
Convert 𝟐𝟕
𝟓to a mixed number.
Convert 𝟑𝟓
𝟔to a mixed number.
Convert 𝟒𝟏
𝟕to a mixed number.
CONVERTING IMPROPER FRACTIONS TO
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.
Simplify the fraction if needed.
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
SUBTRACTING FRACTIONS
Find the results of the following subtractions.
9
13-7
5= ?
8
11-6
7= ?
6
17-3
34= ?
SUBTRACTING FRACTIONS
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.
Simplify the fraction if needed.
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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