Subscribe To This Site
Fraction means part of a whole. There are 10 balls in a box. I take 3 balls out of it. The fraction of balls I take out of the box is 3 out of 10.
This expression 3 out of 10 is written as 3/10. 3/10 is a fraction. In this fraction, the number above is called numerator and the number below is called denominator. Numerator and Denominator : 12/19 : In this fraction, 12 is numerator and 19 is denominator. 11/34 : In this fraction, 11 is numerator and 34 is denominator. 9/101 : In this fraction, 9 is numerator and 102 is denominator. x/y : In this fraction, x is numerator and y is denominator. Types of Fractions : There are three types of fractions. They are… (1) Proper Fraction : In proper fraction, the numerator will be less than the denominator. 1/2, 3/4, 11/23, 28/37, 4/29, 10/67 and 4/51 are few examples for proper fractions. (2) Improper Fractions : In improper fraction, the numerator will be greater than the denominator. 3/2, 21/10, 34/9, 5/2, 6/5, 25/24, 44/9 and 29/2 are few examples for improper fractions. (3) Mixed Fractions : In mixed fraction, a whole number and a proper fraction will be together. 2 2/5, 8 1/6, 77 6/11, 13 4/9 and 33 3/10 are few examples for mixed fraction. Like Fractions : If the denominators of two or more fractions are the same, then those fractions are Like Fractions. 2/9, 3/9, 4/9, 5/9, 11/9 are like fractions. Because, the denominators of all these fractions are the same 9. 11/25, 10/25, 3/25, 15/25 and 20/25 are Like Fractions. Because, the denominators of all these fractions are the same 25. Unlike Fractions : If the denominators of two or more fractions are the different, then those fractions are Unlike Fractions. 2/7, 11/13, 2/67, 3/5, 10/27 and 4/13 are unlike fractions because the denominators of these fractions are different. 2/9, 3/10, 4/15, 6/18, 10/38, 11/90 and 1/9 are unlike fractions because the denominators of these fractions are different. Equivalent Fractions : Equivalent Fractions have the same absolute value even though their numerators and denominators are different from those of each other. (1/5) = (2/10) = (3/15) = (4/20) The absolute value of these fractions is 0.2 The equivalent fraction of a fraction can be obtained by multiplying or dividing both the numerator and the denominator of the fraction by the same number. 1/5 : now multiply both the numerator and the denominator by 2. 1/5 = (1 x 2) / (5 x 2) = 2/10 (1/5) = (2/10) 2/10 : now multiply both the numerator and the denominator by 2. 2/10 = (2 x 2) / (10 x 2) = 4/20 2/10 = 4/20 So, (1/5) = (2/10) = 4/20 Thus, we could get innumerable equivalent fractions for a fraction. Addition of Fraction : Addition of like fractions is to be done differently from the addition of unlike fractions. Addition of Like Fractions : When we add two or more like fractions, both proper fractions and improper fractions, we simply add the numerators and use the same denominator for the answer-fraction. (3/10) + (1/10) = (3+1)/10 = 4/10 (7/18) + (3/18) = (7+3)/18 = 10/18 (10/59) + (21/59) = (10+21)/59 = 31/59 Addition of Unlike Fractions : But, when we add two or more unlike fractions, both proper fractions and improper fractions, first we have to convert both the fractions into their equivalent fractions so that the denominators of the new equivalent fractions are the same number. (1/2) + (2/3) = what? To add these fractions, we should not add the numerators as we do in the case of addition of like fractions. We have to convert these fractions into their respective equivalent form so that the denominator will be come the same number. (1/2) + (2/3) = what? The denominators of these fractions are 2 and 3 respectively. The Least Common Multiple of 2 and 3 is 6. Let us take the first fraction : 1/2 LCM/the denominator of the first fraction = 6/2 = 3 Now multiply both 1 and 3 by 3. (1/2) = (1x3)/(2x3) = 3/6 (1/2) = (3/6) Let us do this same operation on the second fraction. The second fraction is 2/3. LCM/the denominator of the second fraction = 6/3 = 2 Now multiply both 2 and 3 by 2. (2/3) = (2x2)/(3x2) = 4/6 (2/3) = 4/6 (1/2) + (2/3) = (3/6) + (4/6) = (3+4)/6 = 7/6 (1/2) + (2/3) = 7/6
|
