Standard Fraction
Standard form of Fraction: When numerator and denominator are co-prime, then the fraction is said to be in standard form.
Two numbers are co-prime if they have no common factor other than 1.Following are some examples of fractions in standard form.
`1/2, 3/4, 4/5, (11)/(12)`
In these fractions there are no common factors other than 1 in the numerator or denominator. Sometimes, standard form of fraciton is also called simple fraction.
Sample Problems
Question 1: Reduce the following fractions in their standard form.
`2/4, 6/9, (16)/(20), (9)/(18)`, `(12)/(30), (18)/(27), (19)/(57)`, `(20)/(50), (27)/(108)`, `(55)/(275), (57)/(108), (102)/(625)`, `(625)/(1275), (212)/(1000), (500)/(1500)`
(a) Solution: To solve it write the prime factorization of numerator and denominator.
`2/4=(2)/(2xx2)=1/2`
Now, cancel the equal numbers, if they are present in numerator and denominator both.
Or, `2/4=1/2`
Hence, `1/2` is the standard form of the fraction `2/4`.
Answer: `6/9=(2xx3)/(3xx3)=2/3`
Answer: `(16)/(20)=(2xx2xx2xx2)/(2xx2xx5)=4/5`
Answer: `(9)/(18)=(3xx3)/(2xx3xx3)=1/2`
Answer: `(12)/(30)=(2xx2xx3)/(2xx3xx5)=2/5`
Answer: `(18)/(27)=(2xx3xx3)/(3xx3xx3)=2/3`
Answer: `(19)/(57)=(19)/(19xx3)=1/3`
Answer: `(20)/(50)=(2xx2xx5)/(2xx5xx5)=2/5`
Answer: `(27)/(108)=(3xx3xx3)/(2xx2xx3xx3xx3)=1/4`
Answer: `(55)/(275)=(5xx11)/(5xx5xx11)=1/5`
Answer: `(57)/(108)=(3xx19)/(2xx2xx3xx3xx3)=(19)/(36)`
Answer: `(102)/(625)=(2xx3xx17)/(5xx5xx5xx5)=(102)/(625)`
Answer: `(625)/(1275)=(5xx5xx5xx5)/(3xx5xx5xx17)=(25)/(51)`
Answer: `(212)/(1000)=(2xx2xx53)/(2xx2xx2xx5xx5xx5)=(53)/(250)`
Answer: `(500)/(1500)=(2xx2xx5xx5xx5)/(2xx2xx3xx5xx5xx5)=1/3`
Question 2: Reduce the following fractions in their standard form:
`7/5, (16)/(15), (25)/(20)`, `(27)/(12), (12)/(27), (120)/(150)`, `(150)/(120), (45)/(50), (50)/(45)`, `(14)/(20), (20)/(14), (76)/(95)`, `(95)/(76), (12)/(100), (100)/(12)`
(a) Solution: In this fraction, numerator is greater than the denominator hence it is an improper fraction. And there is no common factor in the numerator and denominator. Therefore change this fraction into mixed fraction.
Follow these steps to change a fraction into mixed fraction:
- Step 1: Divide the numerator with denominator.
- Step 2: Write the quotient as the whole number.
- Step 3: Write the remainder as numerator.
- Step 4: Write the divisor as denominator.
When we divide 7 (numerator of fraction) by 5 (denominator of fraction), we get Quotient = 1, Remainder = 2.
`text(Mixed Fraction) = text(Quotient)\text(Remainder)/text(Denominator)`
`7/5=1\2/5`
Note: If the numerator is greater than the denominator and they are not co-prime then change the fraction into standard fraction. After that change it into a mixed fraction.
Answer: `(16)/(15)=1\(1)/(15)`
Answer: `(25)/(20)=(5xx5)/(2xx2xx5)=5/4=1\1/4`
Since, in this fraction the numerator and denominator are not co-prime. Therefore, make them co-prime first and then change it into a mixed fraction.
Answer: `(27)/(12)=(3xx3xx3)/(2xx2xx3)=9/4=2\1/4`
Answer: `(12)/(27)=(2xx2xx3)/(3xx3xx3)=4/9`
Answer: `(120)/(150)=(12)/(15)=(2xx2xx3)/(3xx5)=4/5`
Answer: `(150)/(120)=(15)/(12)=(3xx5)/(2xx2xx5)=5/4=1\1/5`
Answer: `(45)/(50)=(3xx3xx5)/(2xx5xx5)=(9)/(10)`
Answer: `(50)/(45)=(2xx5xx5)/(3xx3xx5)=(10)/(9)=1\1/9`
Answer: `(14)/(20)=(2xx7)/(2xx2xx5)=(7)/(10)`
Answer: `(20)/(14)=(2xx2xx5)/(2xx7)=(10)/(7)=1\3/7`
Answer: `(76)/(95)=(2xx2xx19)/(5xx19)=4/5`
Answer: `(95)/(76)=(5xx19)/(2xx2xx19)=5/4=1\1/4`
Answer: `(12)/(100)=(2xx2xx3)/(2xx2xx5xx5)=(3)/(25)`
Answer: `(100)/(12)=(2xx2xx5xx5)/(2xx2xx3)=(25)/(3)=8\1/3`