tag:blogger.com,1999:blog-53597086547742960472014-10-04T22:16:48.002-07:00how to add fractionsaddition made easy, understanding concepteasy mathhttp://www.blogger.com/profile/14712493045416920408noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5359708654774296047.post-29422017717986858992010-08-24T19:43:00.000-07:002011-12-01T21:19:31.108-08:00How to add fractions<div dir="ltr" style="text-align: left;" trbidi="on">HOW TO ADD FRACTIONS<br /><br />We know 2/3, 5/7, 3/7, 5/8, 4/9, 3/5, 7/3 are all fractions. It is of the form p/q<br /><br />The upper part is called numerator and lower part is called as denominator.<br /><br />In 3/7, 3 → numerator, 7 → denominator<br /><br />Now, what is fraction? Where it comes in my life?<br /><br />Take a paper and divide it into exactly four equal parts. Out of four equal parts made by one single paper, if we select exactly one part then here comes the fraction.<br /><br />i.e. 1/4 Out of four equal parts, you have taken one part.<br /><br />Now how much is 3/4 ? From four equal parts made by one single paper 3 parts is taken.<br /><br />but we must Know , 3/4 itself is one single number(fraction)<br /><br />We know, in 3/4 , 3 is numerator and 4 is denominator, because of our knowledge about number system our mind is conditioned to think 3 as one number and 4 as different number ,but it is wrong. The whole 3/4 itself is single number.<br /><br />In 3/4 entire ( ¾) is one number, it is a single number<br /><br />Now 3/4 is one fraction, 1/4 is one more fraction.<br /><br />Then how to add these fractions?<br /><br />Simple, 1/4 + 3/4 =<br /><br />Here 4 is the common denominator Write 4 as denominator and just add numerator<br /><br />i.e. 1/4 + 3/4 = ( 1 + 3 ) / 4 = 4/4<br /><br />What is 4/4 ? Out of 4 equal parts, made by using 1 single paper, you have selected all 4, nothing but whole paper.<br /><br />i.e. whole one paper you have taken i.e. 4/4 = 1<br /><br />Rule NO 1. While adding fractions whenever denominator is same, just add/subtract numerator and keep common denominator as a denominator.<br /><br />2/3 + 1/3 = 3/3 = 1<br /><br />2/5 + 1/5 = 3/5<br /><br />3/7 + 1/7 + 2/7 = 6/7<br /><br />2/9 + 5/9 + 1/9 = 8/9<br /><br />6/13 - 2/13 = 4/13<br /><br />12/17 - 5/17 = 7/17<br /><br /><a href="http://howmathblog.blogspot.com/">Is there any different rule whenever denominator is different?</a><br /><br />Yes, what it is? Why it is so?<br /><br />Take 2/3 and 5/6<br /><br />2/3 + 5/6 = ?<br /><br />What is 2/3 ? Take one paper divided it into 3 equal parts and keep 2 . i.e. 2/3<br /><br />Remember the word ‘equal’<br /><br />What is 5/6 ?<br /><br />Take one more paper divide it into six equal parts and keep 5 out of it i.e.<br /><br />Then how much papers you keep now?<br /><br />2/3 + 5/6 = ?<br /><br />It is not so easy; think it again, 2 out of 3 and 5 out of 6 is how much?<br /><br />It is difficult to say, how much it is;<br /><br />Use different technique;<br /><br />Dividing a paper in to 3 equal parts and taking 2 parts is 2/3<br /><br />Dividing same paper into 6 equal parts and taking 4 parts is 4/6<br /><br />Both are one and the same or not? 2/3= 4/6 (2/3 and 4/6 are same)<br /><br />Dividing a paper in to 6 equal parts and taking 5 parts is 5/6<br /><br />Rule NO2: is following Rule NO 1. (While adding fractions whenever denominator is same just add/subtract numerator and keep common denominator as a denominator.)<br /><br />2/3 + 5/6 =<br /><br />4/6 + 5/6 = (4 + 5)/6 = 9/6<br /><br />So while adding fractions whenever denominators are different we must make same (common) denominator. Why?<br /><br />To make equal number of divisions in each different events, so that it can be compared/added/subtracted. Instead of asking 2 out of 3 and 5 out of 6 is how much? It is better to ask 4 out of 6 and 5 out of 6 are how much?<br /><br />But all the time it is difficult to apply this theory. So it is better to apply some technique to make equal denominator. Technique is<br /><br />2/3 + 3/5 = ?<br /><br />Denominators of given fractions are 3 and 5.<br /><br />Find the product of denominators. (3 X 5 = 15)<br /><br />2/3 x what /what = something / 15<br /><br />2/3 x what /5 = something/15<br /><br />2/3 x 5/5 = 10/15<br /><br />similarly<br /><br />3/5 x what/what = something/15<br /><br />3/5 x what/3 = something /15<br /><br />3/5 x 3/3 = 9/15<br /><br />therefore<br /><br />2/3 + 3/5 = 10/15 + 9/15 = 19/15<br /><br />Add 3/5 and 4/7<br /><br />Denominator product is (5 x 7=35)<br /><br />3/5 + 7/7 = 21/35 , and 4/7 x 5/5 = 20/35 therefore<br /><br />3/5 + 4/7 = 21/35 + 20/35 = 41/35<br /><a href="http://www.blogger.com/goog_1020680971"><br /></a><br /><a href="http://howmathblog.blogspot.com/">How to add three different fractions with three different denominators? And how to add mixed fractions?</a></div>easy mathhttp://www.blogger.com/profile/14712493045416920408noreply@blogger.com0