Learning Fractions
Lets look at the following figure:
This figure is divided into 4 equal parts each having their own different colors.
- If i were to ask, how many part of this figure have red color. Then the answer would be 1 part.
- Now if i were to ask how many parts out of the total parts have red color, then the answer would be 1 part out of 4 parts.
The answer to the second question i.e. 1 out of 4 parts could be written, in mathematics, as (1/4). This quantity 1/4 is known as a fraction.
In the following figures, 4 different pieces are given, followed by the fraction representing grey color pieces out of the total pieces.
value of fraction = 0/4=0
value of fraction = 1/4
value of fraction = 2/4
value of fraction = 3/4
value of fraction= 4/4=1
Numerator: The part of the fraction that is written first or on top of the "/" is called as Numerator.
Denominator:The part of the fraction that is written second or below the "/" is called as Numerator.
Like fractions: Like fractions have same value of denominator but can have different numerator. Example : 1/4, 3/4, 5/4 are like fractions.
Unlike fraction: Unlike fractions have different values in the denominator . Example : 1/5, 3/10, 5/7 are unlike fractions.
Proper fraction: The fraction in which the numerator is less than the denominator is called proper fraction.Example (4/5), (1/4)
Mixed fraction: The fraction that have an integral part and a fraction part are called as mixed fraction. Example 4(1\4 ), 5(1\2).
Complex fraction: A fraction that have fractions in the numerator and denominators are complex fractions.
example
[(1/2) + (2/5)] /[3/2 + 4/5]
Compound fraction : A fraction of a fraction is called a compound fraction.
Example:
1/2 of 3/4 is a compound fraction.
It can be written as 1/2 x 3/4 is a compound fraction.
Continued fraction: Continued fractions have additional fraction in the numerator or the denominator.
Example:
[1/2 + 2/3]/[1-{2/3 -1/(1+2/3)]
Addition of Fraction:
1.Addition of like fraction : As defined, like fractions have equal denominators
but can have unequal numerators. In addition of like fractions, we will take the common denominator and then just add the numerator to get the result.
Example:
- 1/2 + 5/2 = (1 + 5 )/2 = 6/2
- 4/7 + 8/7 = ( 4 + 8)/7 = 12/7
2. Addition of unlike fractions : Unlike fractions have different denominators, the method of addition as was done with like fraction will not be applicable here.
The method of adding unlike fractions is :
1.Take LCM of the denominators.
2. We will divide the denominators of each fraction with the LCM, the result of each division thus obtained will be multiplied with corresponding numerators to get two like fractions.
3. Follow the rules of addition of like fractions to get the answer.
Example:
- Add 2/4 + 5/8
- Taking LCM : LCM of 4 and 8 is 8.
- Now, divide the LCM by the denominator of first fraction . We will have 2 as the answer. Now, multiply the numerator and denominator of first fraction by 2. Now first fraction would be 2/4 => 4/8. Do the same with the second fraction, to get 5/8 = > 5/8. The addition will look like :
3. We have converted the unlike fractions to like fractions.Now just follow the rule of addition of like fractions to get the result.
(4 + 5) /8 = > 9/8
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Solved Examples
1. A teacher asked in a class to represent 1/8 of the following figure
(CTET 2011 - Paper 1)
Explanation:In all the figures the total area of the given figures have been divided into 8 figures of equal ares except in figure 3 where the rectangle have been divided into figures of unequal areas.
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2. To introduce the concept of fractions, a teacher can begin with
(1) identifying numerators and denominators of different fractions
(2) finding fractions on a number line
(3) writing fractions in the form a/b of where b =! 0
(4) identifying fractional parts of things around them
(CTET 2011 - Paper 1)
Answer: (4) identifying fractional parts of things around them
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3. While teaching comparison of fractions in which the numerators are same
e.g. 3/5 and 3/7 Rohit’s response was ‘‘since the numerators are same and since 7 is larger than 5, therefore 3/7 is bigger than 3/5 .’’
This suggests that
(1) Rohit does not understand the magnitude of fractions
(2) Rohit does not know the concept of numerator and denominator
(3) Rohit does not know the concept of equivalent fractions
(4) Rohit has not practiced well
Answer: (1) Rohit does not understand the magnitude of fractions
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4. When teaching addition of fractions, a teacher came across the following error
(1/2) + (1/3) = (2/5 )
What remedial action can the teacher take in such a situation ?
(1) Ask the child to practise as much as she can
(2) No intervention is needed because she will understand as she grows
(3) Help the child to understand the magnitude of each fraction
(4) Help the child to understand the concept of LCM
(CTET 2011 - Paper 1)
Answer: (4) Help the child to understand the concept of LCM
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5. How many ⅛ are in ½ ? (CTET 2012 - Paper 1)
(1). 4
(2). 2
(3). 16
(4). 8
Answer: (1). 4
Explanation: Divide the fraction (1/2) by the fraction (1/8) to arrive at the answer. (½) ÷ (⅛) = ½ x 8 = 4
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6. While teaching the addition of fractions, it was observed by Mr. Singh that the following type of error is very common:
(2/3) + (2/5) = (4/10)
Mr. Singh Should take the following remedial action:
(1). Give pictorial representation to clear the concept of unlike fractions, followed by drill of same type of problems.
(2).Advise the students to work hard and practise the problems of fraction addition.
(3). Explain the concept of LCM of denominator.
(4). Give more practice of same type of problems.
Answer: (1) Give pictorial representation to clear the concept of unlike fractions, followed by drill of same type of problems.
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7. While planning a lesson on the concept of fraction addition, a teacher is using the activity of strip folding:
The above activity is a
(1). post-content activity
(2). wastage of time
(3). pre-content activity
(4). content activity
Answer (3). pre-content activity
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