What is a Fraction and Types of fractions. * 1. Unit fractions * 2. Like fractions. * 3. Unlike fraction. * 4. Proper fraction. * 5. Improper fraction. * 6. Mixed fraction. * 7. Equivalent fractions:
* Fraction
A part of a whole is called a fraction.
For example: 1/2, 2/3, 5/8.
In the fraction 1/2, 1 is called the numerator and 2 is called the denominator.
* Fractional number
When one whole is divided into equal parts, each part is represented by a fractional number.
For example: 5/8 is a fraction. It has two fractional numbers. like 5 and 8.
Numerator & Denominator
The numerator defines the number of equal parts taken, while the denominator defines the total number of equal parts in the whole.
Types of fractions.
1. Unit fractions
2. Like fractions.
3. Unlike fraction.
4. Proper fraction.
5 Improper fraction.
6. Mixed fraction.
7. Equivalent fractions:
1. Unit fractions: The fraction having 1 as numerator is called unit fraction.
For example: 1/2, 1/3, 1/4, 1/5 etc.
2. Like Fractions : The fractions with same denominators are called Like Fractions.
For example: 1/5, 3/5, 2/5, 6/5 etc
[ All fractions have the same denominator, so all are like fractions.]
3. Unlike Fractions: The fractions with different denominators are called Unlike Fractions
For example: 1/4, 3/8, 2/5, 6/7 etc
[ All fractions have the different denominator, so all are Unlike fractions.]
4. Proper fraction: The fraction whose numerator is smaller than its denominator is called proper fraction.
For example: 2/7, 3/8, 4/9 etc.
5. Improper fraction: The fraction whose numerator is greater than its denominator is called improper fraction.
For example: 8/7, 9/8, 11/7 etc.
* Proper and Improper fractions:
[ In a proper fraction the numerator is less than the denominator if the numerator of a fraction is greater than its denominator then the fraction is called an improper fraction.]
6. Mixed fraction: The fraction with a whole number with proper fraction is called mixed fraction
2 whole 1/5,
3 whole 2/7 etc.
* Convert into mixed fraction.
To convert an improper fraction into mixed numeral, We divide the numerator by the denominator and write the mixed fraction as 23/7 (23÷7) = 3 wholes and 2/7.
* Convert into improper fraction. To convert a mixed fraction into an improper fraction, we multiply the whole number by the denominator and to the product we add the numerator of the mixed fraction.
(3 wholes and 2/7)
Step 1: Multiply the whole number part by the fraction's denominator.
(3×7=21)
Step 2: Add that to the numerator.
(21+2=23)
Step 3: Then write the result on top of the denominator.(= 23/7)
7. Equivalent fractions: we get fraction equivalent to a given fraction by multiplying its numerator and denominator by the same numeral except zero.
For example: 3/5
( 3×2 /5×2) = 6/10
(3×3 /5×3) = 9/15
(3×5 /5×5) = 15/25
* Comparison of fractions:
Rule number 1: When two fractions have the same denominator, the greater fraction is that which has the greater numerator.
For example: 4/6 is greater than 3/6.
[ 4/6 > 3/6 ]
Rule number 2: When two fractions have the same numerator, the greater is that which has the smaller denominator.
For example: 2/7 is greater than 2/21.
[ 2/7 > 2/21 ]
* Change into unlike to like fraction.
If two or more fractions with different denominators are to be compared, they must be reduced to equivalent fractions whose denominator are equal to the LCM of the denominators of the given fraction.
For example: 1/3 , 2/7 and 4/21.
Step 1: L.C.M. of the denominators.
(3, 7, 21, is 21.)
Step 2: Divid the L.C.M. by denominators.
(21÷ 3= 7), (21÷ 7= 3), (21÷ 21= 1).
Step 3: Multiply the numerator and denominator of each by the quotient.
(1×7/3×7 = 7/21),
(2×3/7×3 = 6/21),
(4×1/21×1= 4/21)
So, 7/21, 6/21 and 4/21.
All fractions have the same denominator, so all are like fractions.
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