Bombay Cambridge School ,Andheri East

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Bombay Cambridge School ,Andheri (East)
Presents
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FRACTIONS
FRACTIONS
FRACTIONS
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Choose the level of the students
III Standard
IV Standard
V Standard
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What are fractions?
How to read fractions?
More about fractions
III
Parts of a collection
Revision
More about fractions
numerator and denominator
Back
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Equivalent fractions
Types of fractions
Fraction as division
IV
Mixed numbers
Comparison of fractions
Addition of like fractions
Subtraction of like fractions
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Reduced form of fractions
Factors and Multiples
Addition of unlike fractions, mixed numbers
V
Subtraction of unlike fractions, mixed numbers
Multiplication of fractions
Reciprocal of a fraction
Division of fractions
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III Standard
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What are Fractions ?
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Look at the figure given below.
It is a whole figure.
We can divide it into 2 equal parts by drawing
a line.
1 2
1 2
Shade only one part of the figure.
Each part is called half of the whole.
1 2
We write it as
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How to read Fractions ?
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How to read a fraction ?
1 2
1 by 2.
is read as
1 upon 2 or
3 7
is read as
3 upon 7 or
3 by 7.
2 5
is read as
2 by 5.
2 upon 5 or
7 9
is read as
7 upon 9 or
7 by 9.
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More about Fractions
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Each figure is divided into two parts.
Are both the parts equal ?
Yes
Yes
Yes
No
No
No
No
Yes
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Draw a line or lines to divide each of the
following shapes into
two equal parts
four equal parts
three equal parts
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Parts of a collection
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Encircle one half(
Total number of insects shown below is 12.
1 2
)of each collection.
4
6
3
One half of 12 is 6
One fourth of 12 is 3
One third of 12 is 4
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Color one half of the collection.
Colour one fourth of the collection.
Colour one third of the collection.
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What fraction do the colored portions in each of
the following show ?
2 5
2 3
3 4
1 4
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Write the fraction for the shaded part.
5
Numerator
Numerator
5
(shaded parts)
(shaded parts)
8
Denominator
Denominator
10
(total parts)
(total parts)
5 8
5 10
Fraction
Fraction
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Is it a third?
Which circles have one third colored?
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IV Standard
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Equivalent fractions
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Is the shaded part in each pair of figures same?
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Is the shaded part in both the figures same?
What is the fraction for the shaded part?
So, we see that
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Equivalent Fractions

• Fractions with same value but have different
  numerators and denominators.

1
2
1
1

4
2
4
2
1
4
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Equivalent Fractions
3
6

4
8
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Equivalent Fractions
2
4

3
6
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To Find Equivalent Fractions

• Multiply the numerator and the denominator
  by the same number.
• ( except zero)

1
3
3
x

3
3
9
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To Find Equivalent Fractions

• Divide the numerator and the denominator by the
  same number.
• ( except zero)

4
4
1


12
4
3
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Types of fractions
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Proper Fraction
Fractions with numerators smaller than the
denominators are called proper fraction.
1

2
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Improper Fraction
Fractions with numerators greater than or equal
to the denominators are called improper fractions.

5

2
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Mixed Numbers

• A mixed number has a part that is a whole number
  and a part that is a fraction.

1
1

4
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Unit-Fractions
A fraction with numerator 1 is called unit
fraction.
1
1
1
1
1
,
,
,
,
7
12
5
1
4
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Like Fraction
Fractions with the same denominator are called
like fractions.
3
2
5
4
11
,
,
,
,
7
7
7
7
7
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Unlike Fraction
Fractions with the different denominator are
called unlike fractions.
5
11
4
3
2
,
,
,
,
7
12
5
11
4
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Mixed Numbers
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Mixed numbers include a whole number and a
fraction.


(fraction)

(whole number)
(mixed number)

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What is the mixed number?
3

3
4
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What is the mixed number?
3

4
4
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Improper Fraction

• A fraction in which the numerator is greater than
  the denominator.

8

4
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What is the improper fraction?
15

4
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What is the improper fraction?
19

4
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How is the mixed number below related to the
improper fraction?
1
5

2
11

2
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How to change an
improper fraction to a
mixed number?

• Divide the numerator by the
• denominator.
• Put your remainder over the
• denominator.

5

2
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How to change an improper
fraction to a mixed number
)
numerator
2
5
denominator
5

2
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How to change an improper
fraction to a mixed number?
2
r
1
)
numerator
2
5
denominator
4
1
5

2
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How to change an improper fraction to a
mixed number?
denominator
)
numerator
2
5
Put your remainder over the Denominator.
1
5
2

2
2
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Change this improper
fraction to a mixed number.
r
2
0
10

)
5
10
5
If there is no remainder your answer is a
whole number.
10
2

5
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How to change a mixed number to an
improper fraction ?
1
7

• Multiply the whole number times the denominator.
• Add your answer to the numerator.
• Put your new number
• over the denominator.

4

x
2
2
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How to change a mixed number to an improper
fraction
1
4 x 2 1
4

2
2
9
8 1


2
2
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Addition of like fractions
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Addition of like fractions
In the circle given below only one part out of
five is shaded.
Two more parts of the circle are shaded.
The circle has three shaded parts.
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Adding Like Denominators
Only add the numerators
1/4
1/4
3
1
4


4
4
4
1/4
1/4
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Addition of like fractions


1 4
2 4
3 4
1 4
2 4
3 4


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Subtraction of like fractions
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Subtracting Like Denominators
Only subtract the numerators
1/4
1/4
4
1
3
-

4
4
4
1/4
1/4
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Subtract these fractions
1/4
1/4
3
1
2
-

4
4
4
1/4
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V Standard
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Factors and Multiples
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A number that divides a given number completely
(without leaving a remainder) is called its
factor.
e.g.
5 divides 20 exactly.
So, 5 is a factor of 20.
And 20 is a multiple of 5.
Is 20 exactly divisible by 3?
No
No
Is 3 a factor of 20?
No
Is 20 a multiple of 3?
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List the numbers that divide 15 exactly.
So, we can say that factors of 15 are 1, 3, 5
and 15.
List the numbers that divide 12 exactly.
So, we can say that factors of 12 are 1, 2, 3,
4, 6 and 12.
Every number has atleast 2 factors
the number itself.
1 and
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Which of the following are factors of 16?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 16
?
?
?
?
?
?
?
?
?
?
?
1
2
4
16
8
Try the following.
Is 4 a factor of 14 ?
No
Yes
Is 6 a factor of 24 ?
Yes
Is 4 a factor of 32 ?
Is 3 a factor of 17 ?
No
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Which of the following are multiples of 4 ?
8, 10, 12, 14, 16, 18, 20, 22, 24, 26,
28, 30
?
?
?
?
?
?
?
?
?
?
?
?
12
16
20
28
8
24
Try the following.
No
Is 15 a multiple of 6 ?
Yes
Is 28 a multiple of 7 ?
Yes
Is 24 a multiple of 8 ?
Is 21 a multiple of 9 ?
No
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Common factors
The factors of 24 are
1, 2, 3, 4, 6, 8, 12 and 24.
The factors of 30 are
1, 2, 3, 5, 6, 10, 15 and 30.
Common factors of 24 and 30 are
3,
1,
2,
6
Highest common factor (H.C.F.) of 24 and 30 is
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Common multiples
The multiples of 3 are
3, 6, 9, 12, 15, 18, 21, 24
The multiples of 4 are
4, 8, 12, 16, 20, 24, 28 ...
Common multiples of 3 and 4 are
12 ,
24
Least common multiple (L.C.M.) of 3 and 4 is
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Addition of unlike fractions, mixed numbers
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When we add two unlike fractions (with
different denominators), we need to find the
least common multiple ( L.C.M.) of the two
denominators.
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Common Multiple

• A number that is a multiple of two or more
  numbers.

Some multiples of 3 6 6,12, 18, 24, 30, 36, 42.
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Least Common Multiple

• The smallest common multiple of a set of two or
  more numbers.

5 5, 10, 15, 20, 25, 30
6 6, 12, 18, 24, 30, 36
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To Add or Subtract Fractions With Unlike
Denominators

• Find the multiples of each denominator.

1
5, 10, 15, 20, 25, 30
5
1

10, 20, 30, 40, 50
10
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• Compare the lists of multiples. Circle the
  common multiples between the two lists.

1
5 5, 10, 15, 20, 25, 30
1

10 10, 20, 30, 40, 50
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• Use the lowest common multiple as the
  denominator.

1
5 5, 10, 15 ,20 ,25 ,30
1

10 10, 20, 30, 40, 50
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• Rewrite the fractions using the least common
  denominator or least common multiple.

You know that 1/10 is equal to 1/10 so Put a 1
over the Bottom 10.
1
10
5

1

10
10

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• Find the equivalent fractions for 1/5 1/10
  with 10 as the denominator.

.
To find the top number, ask yourself what do you
multiply the 5 by to get 10
1
5
10

1
1

10
10
10

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• Find the equivalent fractions for 1/5 1/10
  with 10 as the denominator.

Thats right 2. Since you are looking for the
equivalent fraction you know the top number must
also be multiplied by 2.
1
x 2
5
10
x 2
1
1

10
10
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• Find the equivalent fractions for 1/5 1/10
  with 10 as the denominator.

To find the top number just multiply 2 x 1 to get
your equivalent fraction.
1
2
x 2
5
10
x 2
1
1
10
10

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• Now just add the numerators.

1
2
x 2
5
10
x 2
Remember when adding fractions you never add the
denominators.
.
1
1
x 1

10
x 1
10
2 2
3
1


10
10
10
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Add these Fractions
2
1
Find the common Multiples for 5 and 3.
Write This number As your new denominator.


5
3
d 15
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Add these Fractions
Ask yourself what you multiply the bottom
number by to get 15.
1
2

3
x 5
5
x 3


15
15
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Add these Fractions
Multiply the top number by the same number
you did in the bottom.
2
x 3
5
15
x 3
1
x 5
3
15
x 5
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Add these Fractions
Multiply across.
2
6
x 3
5
15
x 3
1
5
x 5
3
15
x 5
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Add these Fractions
Now add your new numerators.
2
6
x 3
5
15
x 3
1
5
x 5
3
15
x 5
6
11
5
6


15
15
15
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Addition of mixed numbers
2 5

Change the mixed number to an improper fraction.
Step 1
21 5


(21 2) 5 5
Step 2
Add both the fractions.
21 2 5
23 5


So,
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Subtraction of unlike fractions, mixed numbers
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Subtraction of mixed numbers
Change the mixed number to an improper fraction.
Step 1
23 7


Step 2
(23 - 2) 7 7
Subtract both the fractions.
23 - 2 7
21 7


So,
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