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HorseCrazyGirlForever
How do I add fractions?
Are the denominators the same?
www.webmath.com/addfract.html
www.youtube.com/watch?v=lavgnJAkfKM
I don't like to watch videos because I never learn from them... :(
\[\frac{a}{b}+\frac{c}{d}=\frac{a\times d+c\times b}{b\times d}\]
What @Zarkon did , is said to be use of LCM ..
If the denominator is not the same then you will have to find the most common one. then add the top numbers and keep the denominator same. Been awhile sence i done then.
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\[{\heartsuit \over \spadesuit}+{\diamondsuit \over \clubsuit} = {\heartsuit\clubsuit + \diamondsuit \spadesuit \over \spadesuit \clubsuit}\]
LCM ---> Least common multiple just like I want to give you an example of LCM in addition of fractions : \[\large{\frac{3}{4} + \frac{4}{5} = ?}\] Now, to add these fractions , we need to take LCM of the denominators of both of the fractions... i.e. of 4 and 5 Multiples of 4 = 4,8,12,16,20,32,36,40 .... Multiples of 5 = 5,10,15,20,25,30,35,40... Common multiples = 20, 40 , ... Least common multiple = 20 So from this we get LCM of 4 and 5 is 20 Now divide 20 by 4 , you get 5, multiply 5 by the numerator of the first fraction i.e. 5 * 3 = 15 .Similarly for second fraction, divide 20 by 5, you get 4, multiply 4 by 4 = 16 \[\large{\frac{5*3 + 4*4}{20} = \frac{15+16}{20} = \frac{31}{20} }\]
Although, you can straightforwardly add the numerators if the denominators are same.
Why we use LCM is to get to a point where we can straightforwardly add the numerators.
SO what would 4/3 + 7/6 =
Get a common denominator.
Instead of LCM you can also do "common denominators" : \[\large{\frac{4}{3} + \frac{7}{6} = ? }\] Let us take 4/3 first : multiply denominators and numerators by 2 \[\large{\frac{4\times 2}{3\times 2} = \frac{8}{6}}\] So, we can also write 4/3 as : 8/6 Now let us take L: 7/6 See we have to get common denominators in both the fractions. we have one fraction as 8/6 and another one is 7/6 Their denominators are same i.e. 6 so we can just add numerators "now" : \[\large{\frac{8}{6} + \frac{7}{6} = \frac{8+7}{6} = \frac{15}{6}}\]
Note: Don't add denominators, only numerators are to be added.
@HorseCrazyGirlForever I hope you got it now, any confusion you have now?