subject: Fraction Concepts [print this page] Introduction to Fraction Concepts: Introduction to Fraction Concepts:
Fraction is a number which is written in the form 'n/d' . n is Numerator which is placed as the top number. d is Denominator which placed as the bottom number. Here numerator and denominator is separated by a line that is called as Fraction bar. For example, '4/7 ' 4 is numerator and 7 is denominator.
Fractions are used to represent a part of whole. Here 'n/d' can be read as n out of d, n over d, n is divided by d . Fractions are used when we are considering about collection of parts.
For ex: A Collection of 30 balls, 23 are used. The fraction represents as '23/30' .
Fraction Concepts: Kinds of Fractions
We are going to learn how to represent different forms of fractions using fraction concepts. They are following,
Proper fraction:
It is a fraction in which numerator should be less than denominator. This is called as proper fraction. Proper fractions are '7/9' , '9/12' , '15/20' .
Improper fraction:
It is a fraction in which numerator should be equal or greater than denominator. This is called as improper fraction. Improper fractions are '10/7' , '8/6' , '5/5' , '7/6' .
Compound fraction or mixed fraction:
It is a fraction with whole numbers and fractions. When an improper fraction is written as a combination of whole number and a proper fraction it is called as compound fraction. Mixed fractions represents as 5 '7/8' , -10 '5/7' . Here the numerator and denominator will get after converting compound fraction to simple fraction.
Equivalent fraction:
An equivalent fraction of a given fraction can be obtained by multiplying its numerator and denominator by the same number other than zero.
Equivalent fractions of '1/2' are '2/4' , '3/6' , '4/8' , '5/10' . Here each one got by multiplying number 2, 3, 4, 5 to each numerator and denominator.
And also equivalent fractions can be obtained by dividing its numerator and denominator by the same number other than one.
Equivalent fraction of '15/25' is '3/5' because '(15/5)/(25/5)' = '3/5' .
For learning equivalent fractions, the product of numerator of first fraction and the denominator of second fraction is equal to product of denominator of first fraction and numerator of second fraction.
Example Based on Fraction Concepts:
Pro 1: Find the subtraction of two fractions: '7/3' from '9/2' .
Sol:
The given two fractions are '7/3' , '9/2' .
Subtraction of two fractions :
'7/3' - '9/2'
The LCM of 3 and 2 is 6.
Convert fractions into equivalent fractions with the LCM as the denominator of each.
' 7/3' =' 7/3' x '2/2'
= '(7*2)/(3*2)'
= '14/6'
' 9/2' =' 9/2' x '3/3'
= '(9*3)/(2*3)'
= '27/6'
Thus, '7/3' - '9/2' = '14/6' - '27/6'
= '(14-27)/6'
= '-13/6'
This is negative proper fraction.
Pro 2: Divide '21/3' by '7/2' and simplifying it.
Sol:
Thus the given fractions,
'21/3' '7/2 '
we take the inverse operation of multiplication. And the reciprocal of '7/2' is '2/7' .
so therefore,
' 21/3' x '2/7'
'(21*2)/(3*7)'
' 42/21'
Simplifying this by dividing each one by 21.
'(42/21)/(21/21)'
= ' 2/1' = 2.
Pro 3: Simplifying the compound fraction 8 '1/2' .
Sol:
8 '1/2' can be written as 8 + '1/2' .
Write whole number 8 to the fraction '8/1' .
Now 8 + '1/2' can be written as '8/1' + '1/2' .
Therefore,
'8/1' + '1/2' we rewrite the fraction,
'8/1' x '2/2' + '1/2'
'16/2' + '1/2 '
Add these two fractions, here denominator is same so just add the numerators.
'(16+1)/2'
'17/2' .
This is improper fraction.
Pro 4: Calculate the addition of two compound fraction: 9 '2/3' + 7 '1/9'
Sol:
Now we rewrite the compound fraction.
9 '2/3' + 7 '1/9' = 9 + '2/3' + 7 + '1/9'
Now separate the fraction and whole numbers.
= 9 + 7 + '2/3' + '1/9'
= 16 + '2/3' + '1/9'
Here the highest denominator is 9 so we convert this to equivalent fraction of 9.
= '16/1' x '9/9' + '2/3' x '3/3' + '1/9'
= '144/9' + '6/9' + '1/9'
Now add the numerators because here all have same denominator.
= '(144+6+1)/9'
= '151/9' .
This is also an improper fraction.
Ex 5: Give any three equivalent fractions to '5/12'
Sol:
5/12 = (5 2)/ (12 2) = 10 / 24
5/12 = (5 4)/ (12 4) = 20 / 48
5/12 = (5 7)/ (12 7) = 35 / 84
'10/24, 20/48, 35/84' are some equivalent fractions to '5/12' .
Ex 6: Express 120 / 280 in its lowest form.
Sol:
120 / 280 = (2 2 3 10) / (2 2 7 10) = (3 / 7)
'120/280 = 3/7'
(Divide the numerator & denominator by 2, 2 and 10)
Ex 7: Harris reads a book for 5 '3/4' hours every day. She reads the entire book in 7 days. How many hours in all were required by her to read the book?
