Similar Fractions
If we multiply the numerator and denominator of a fraction with same number simultaneously, the fractions we get are similar, same or equal to the previous fraction. Such fractions are called similar or equal fractions.
Let us take a fraction `1/2`. If we multiply the numerator and denominator of the fraction by any number; we get following fractions:
`1/2=(1xx2)/(2xx2)=2/4`
`1/2=(1xx3)/(2xx3)=3/6`
`1/2=(1xx4)/(2xx4)=4/8`
`1/2=(1xx5)/(2xx5)=(5)/(10)`
`1/2=(1xx6)/(2xx6)=(6)/(12)`
In this case all are similar fractions, i.e. all have same value.
`1/2=2/4=3/6``=4/8=(5)/(10)=(6)/(12)`
The numerical values of similar fractions are equal.
Similarly:
`2/3=(2xx2)/(3xx2)=4/6`
`2/3=(2xx5)/(3xx5)=(10)/(15)`
`2/3=(2xx8)/(3xx8)=(16)/(24)`
`2/3=(2xx9)/(3xx9)=(18)/(27)`
`2/3=4/6=(10)/(15)``=(16)/(24)=(18)/(27)`
Thus we can obtain any number of fractions by multiplying their numerator and denominator by same numbers.
Similarly if we divide the numerator and denominator with same number, we get similar fractions. Following are some examples:
`(40)/(60)=(40÷2)/(60÷2)=(20)/(30)`
`(40)/(60)=(40÷4)/(60÷4)=(10)/(15)`
`(40)/(60)=(40÷10)/(60÷10)=(4)/(6)`
`(40)/(60)=(40÷20)/(60÷20)=(2)/(3)`
`(40)/(60)=(20)/(30)=(10)/(15)=4/6=2/3`
Sample Problems
Question 1: Obtain 2 similar fractions for each of the following by multiplying 2 and 3.
`2/3, 3/2, 5/9`, `2/5, 2/7, 3/7`, `(5)/(11), (5)/(13), (3)/(11)`, `(5)/(21)`
Answer: `2/3=(2xx4)/(3xx4)=(8)/(12)`
`2/3=(2xx5)/(3xx5)=(10)/(15)`
Answer: `3/2=(3xx4)/(2xx4)=(12)/(8)`
`3/2=(3xx5)/(2xx5)=(15)/(10)`
Answer: `5/9=(5xx4)/(9xx4)=(20)/(36)`
`5/9=(5xx5)/(9xx5)=(25)/(45)`
Answer: `2/5=(2xx4)/(5xx4)=(8)/(20)`
`2/5=(2xx5)/(5xx5)=(10)/(25)`
Answer: `2/7=(2xx4)/(7xx4)=(8)/(28)`
`2/7=(2xx5)/(7xx5)=(10)/(35)`
Answer: `3/7=(3xx4)/(7xx4)=(12)/(28)`
`3/7=(3xx5)/(7xx5)=(15)/(35)`
Answer: `5/11=(5xx4)/(11xx4)=(20)/(44)`
`5/11=(5xx5)/(11xx5)=(25)/(55)`
Answer: `5/13=(5xx4)/(13xx4)=(20)/(52)`
`5/13=(5xx5)/(13xx5)=(25)/(65)`
Answer: `3/11=(3xx4)/(11xx4)=(12)/(44)`
`3/11=(3xx5)/(11xx5)=(15)/(55)`
Answer: `5/21=(5xx4)/(21xx4)=(20)/(84)`
`5/21=(5xx5)/(21xx5)=(25)/(105)`
Question 2: Obtain the similar fractions dividing by 2.
`2/4, 6/8, (12)/(10)`, `(20)/(30), (40)/(60), (4)/(10)`, `(16)/(40), (20)/(100), (14)/(44), (8)/(20)`
Answer: `2/4=(2÷2)/(4÷2)=1/2`
Answer: `6/8=(6÷2)/(8÷2)=3/4`
Answer: `(12)/(10)=(12÷2)/(10÷2)=6/5`
Answer: `(20)/(30)=(20÷2)/(30÷2)=(10)/(15)`
Answer: `(40)/(60)=(40÷2)/(60÷2)=(20)/(30)`
Answer: `(4)/(10)=(4÷2)/(10÷2)=(2)/(5)`
Answer: `(16)/(40)=(16÷2)/(40÷2)=(8)/(20)`
Answer: `(20)/(100)=(20÷2)/(100÷2)=(10)/(50)`
Answer: `(14)/(44)=(14÷2)/(44÷2)=(7)/(22)`
Answer: `(8)/(20)=(8÷2)/(20÷2)=(4)/(10)`