Introduction to Math Fractions:
Fraction represents a part of a whole. A fraction of material or thing is a piece or section of it. It is a quantity
which cannot be represented as a whole number.A fraction has two parts one is numerator and the other is
denominator.
The rectangular picture above can be divided into 8 equal parts.
4 parts of total rectangle is painted with Brown colour .Hence brown colour constitutes 4/8 of total.
2 parts of total rectangle is painted with Black colour.Hence Black colour constitutes 2/8 of total.
1 part of total rectangle is painted with Blue colour.Hence Blue colour constitutes 1/8 of total.
1 part of total rectangle is painted with Red colour.Hence Red colour constitutes 1/8 of total.
MATH FRACTIONS IN DAILY LIFE:-
i) Grades awarded to students for example (4/5, 5/5).
ii) To represent time such as quarter past the hour.Quarter is nothing but a fraction equivalent to 1/4.
iii) Percentages which are also fraction .50% is equivalent to 50/100 =1/2.
Math fractions description:
TYPES OF MATH FRACTIONS :-
i) Proper fractions:These are the fractions having numerator always less than the denominator
The value of a proper fraction is always less than 1.
Examples:- 1/3 ,5/6 ,7/9
ii) Improper fractions:These are the fractions having numerator greater or equal to denominator
The value of a improper fraction will be always greater than or equal to
Any whole number can be transformed into a improper fraction.
Examples:- 8/3 , 6/6 , 9/2
iii) Mixed fractions :Mixed fraction is whole number and fraction together. An improper
fraction be rewritten as mixed fraction and vice versa.
Examples :- 2`(3)/(7)`, 4`(4)/(11)`
iv) Equivalent fractions :Fraction which reduce to same number on simplification are called
equivalent fractions.
Examples :- the equivalent fraction of 10/25 is 2/5 as 5 is common factor
in numerator and denominator.
MATH FRACTIONS OPERATIONS :
i) Division : Fractions can be divided . Fraction in numerator is multiplied by reciprocal of fraction in
the denominator.
Example : `(3)/(4)` `-:` `(5)/(7)` = `(3)/(4)` `x` `(5)/(7)`
= `(15)/(28)`
ii) Subtraction : Fractions can be subtracted provided the denominators of fractions are same.For
fractions having unequal denominators ,denominators are to be made same for
subtraction.
Example1 : `(2)/(9)` `**` `(1)/(9)` = `(1)/(9)`
Example2 : `(1)/(2)` - `(1)/(4)` = `(1*2)/(2*2)` - `(1)/(4)` = `(2)/(4)` - `(1)/(4)` = `(1)/(4)`
iii) Multiplication: Fractions can be multiplied directly ie numerators with numerators and
denominators with denominators.
Example : `(2)/(9)` `xx` `(1)/(9)` = `(2)/(81)`
iv) Addition :Fractions can be added provided the denominators of fractions are same.For
fractions having unequal denominators ,denominators are to be made same for
addition.
Example1 : `(2)/(9)` + `(1)/(9)` = `(3)/(9)`
Example2 : `(1)/(2)` + `(1)/(4)` = `(1*2)/(2*2)` + `(1)/(4)` = `(2)/(4)` + `(1)/(4)` = `(3)/(4)`
I have recently faced lot of problem while learning Volume of a Rectangular Prism, But thank to online resources of math which helped me to learn myself easily on net.
More Examples for Math Fractions:
Ex1:
Multiply the fractions is `8/5` and `5/9`
Sol:
Here we can observe than there is a common factor in numerator and denominator which is 5.
so cancelling 5 we will be left with `(8)/(9)`
Ex2:
Arrange the following fractions in ascending order `(3)/(4)` `(2)/(3)` `(1)/(6)`
Sol:
To compare fractions their denominators should be equal .so least common multiple of 4,3,6 is
12 .So now we make denominators equal
`(3)/(4)`` = ` `(3xx3)/(4xx3) =9/12`
similarly
`(2)/(3)`` = ` `(8)/(12)`
`(1)/(6)``=``(2)/(12)`
Since denominators are equal and so numerators can be compared
so 1/6 ,2/3,3/4 is the required order.
Ex3:
Add the following mixed fractions
i) `(1)/(3)` + 5 `(1)/(3)`
`sol:`
`(1)/(3)` + 5 `(1)/(3)`
= 1+5 + (1/3)+ (1/3)
` =6 + ``(2)/(3)`
= 6`(2)/(3)`
Fraction represents a part of a whole. A fraction of material or thing is a piece or section of it. It is a quantity
which cannot be represented as a whole number.A fraction has two parts one is numerator and the other is
denominator.
The rectangular picture above can be divided into 8 equal parts.
4 parts of total rectangle is painted with Brown colour .Hence brown colour constitutes 4/8 of total.
2 parts of total rectangle is painted with Black colour.Hence Black colour constitutes 2/8 of total.
1 part of total rectangle is painted with Blue colour.Hence Blue colour constitutes 1/8 of total.
1 part of total rectangle is painted with Red colour.Hence Red colour constitutes 1/8 of total.
MATH FRACTIONS IN DAILY LIFE:-
i) Grades awarded to students for example (4/5, 5/5).
ii) To represent time such as quarter past the hour.Quarter is nothing but a fraction equivalent to 1/4.
iii) Percentages which are also fraction .50% is equivalent to 50/100 =1/2.
Math fractions description:
TYPES OF MATH FRACTIONS :-
i) Proper fractions:These are the fractions having numerator always less than the denominator
The value of a proper fraction is always less than 1.
Examples:- 1/3 ,5/6 ,7/9
ii) Improper fractions:These are the fractions having numerator greater or equal to denominator
The value of a improper fraction will be always greater than or equal to
Any whole number can be transformed into a improper fraction.
Examples:- 8/3 , 6/6 , 9/2
iii) Mixed fractions :Mixed fraction is whole number and fraction together. An improper
fraction be rewritten as mixed fraction and vice versa.
Examples :- 2`(3)/(7)`, 4`(4)/(11)`
iv) Equivalent fractions :Fraction which reduce to same number on simplification are called
equivalent fractions.
Examples :- the equivalent fraction of 10/25 is 2/5 as 5 is common factor
in numerator and denominator.
MATH FRACTIONS OPERATIONS :
i) Division : Fractions can be divided . Fraction in numerator is multiplied by reciprocal of fraction in
the denominator.
Example : `(3)/(4)` `-:` `(5)/(7)` = `(3)/(4)` `x` `(5)/(7)`
= `(15)/(28)`
ii) Subtraction : Fractions can be subtracted provided the denominators of fractions are same.For
fractions having unequal denominators ,denominators are to be made same for
subtraction.
Example1 : `(2)/(9)` `**` `(1)/(9)` = `(1)/(9)`
Example2 : `(1)/(2)` - `(1)/(4)` = `(1*2)/(2*2)` - `(1)/(4)` = `(2)/(4)` - `(1)/(4)` = `(1)/(4)`
iii) Multiplication: Fractions can be multiplied directly ie numerators with numerators and
denominators with denominators.
Example : `(2)/(9)` `xx` `(1)/(9)` = `(2)/(81)`
iv) Addition :Fractions can be added provided the denominators of fractions are same.For
fractions having unequal denominators ,denominators are to be made same for
addition.
Example1 : `(2)/(9)` + `(1)/(9)` = `(3)/(9)`
Example2 : `(1)/(2)` + `(1)/(4)` = `(1*2)/(2*2)` + `(1)/(4)` = `(2)/(4)` + `(1)/(4)` = `(3)/(4)`
I have recently faced lot of problem while learning Volume of a Rectangular Prism, But thank to online resources of math which helped me to learn myself easily on net.
More Examples for Math Fractions:
Ex1:
Multiply the fractions is `8/5` and `5/9`
Sol:
Here we can observe than there is a common factor in numerator and denominator which is 5.
so cancelling 5 we will be left with `(8)/(9)`
Ex2:
Arrange the following fractions in ascending order `(3)/(4)` `(2)/(3)` `(1)/(6)`
Sol:
To compare fractions their denominators should be equal .so least common multiple of 4,3,6 is
12 .So now we make denominators equal
`(3)/(4)`` = ` `(3xx3)/(4xx3) =9/12`
similarly
`(2)/(3)`` = ` `(8)/(12)`
`(1)/(6)``=``(2)/(12)`
Since denominators are equal and so numerators can be compared
so 1/6 ,2/3,3/4 is the required order.
Ex3:
Add the following mixed fractions
i) `(1)/(3)` + 5 `(1)/(3)`
`sol:`
`(1)/(3)` + 5 `(1)/(3)`
= 1+5 + (1/3)+ (1/3)
` =6 + ``(2)/(3)`
= 6`(2)/(3)`
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